Conceptual design of the Spin Physics Detector
V.M. Abazov, V. Abramov, L.G. Afanasyev, R.R. Akhunzyanov, A.V. Akindinov, N. Akopov, I. G. Alekseev, A.M. Aleshko, V.Yu. Alexakhin, G.D. Alexeev, M. Alexeev, A. Amoroso, I.V. Anikin, V.F. Andreev, V.A. Anosov, A.B. Arbuzov, N.I. Azorskiy, A.A. Baldin, V.V. Balandina, E.G. Baldina, M.Yu. Barabanov, S.G. Barsov, V.A. Baskov, A.N. Beloborodov, I.N. Belov, A.P. Belova, A.V. Belyaev, A.Ya. Berdnikov, Ya.A. Berdnikov, A.V. Berezhnoy, V.V. Bleko, A.V. Bobkov, D.N. Bogoslovsky, I.N. Boguslavsky, E.V. Boltushkin, E.E. Boos, V.E. Burtsev, Lei Chen, A.S. Chepurnov, M. Chiosso, A. Chumakov, O.D. Dalkarov, A. Datta, E.I. Demikhov, I.I. Denisenko, O.Yu. Denisov, V.N. Duginov, V.B. Dunin, K. Dygnarowicz, A.V. Efremov, R. El-Kholy, D.A. Eliseev, T.L. Enik, O.L. Fedin, G.A. Feofilov, Yu.N. Filatov, M. Finger, M. Finger, V.N. Frolov, G. Galinski, A.S. Galoyan, C.E Garsia Trapaga, O.P. Gavrishchuk, S.G. Gerasimov, L. Glonti, S.V. Goloskokov, G.A. Golovanov, A.A. Golubev, Golubykh S.M., Goncharov P.V., Grafov N.O., Gribkov D.Y., A.S. Gribovsky, A.O. Gridin, B.V. Grinyov, K.I. Gritsay, S.A. Gromov, V.A. Gromov, Yu.V. Gurchin, Yu.V. Gusakov, A.V. Guskov, F. Guzman, J. Haidenbauer, M. Havranek, A.V. Ivanov, N.Ya. Ivanov, A.Yu. Isupov, V. Jary, Shi-Hai Jia, D. Jokovic, A. Kaplii, A.V. Karpishkov, E.A. Kasianova, G.D. Kekelidze, S.V. Khabarov, P.R. Kharusov, A.N. Khrenov, V.T. Kim, N.V. Kirichkov, D.Yu. Kirin, et al. (193 additional authors not shown)
JJOINT INSTITUTE FOR NUCLEAR RESEARCH
February 3, 2021
Conceptual design of the Spin Physics Detector
Version 1.0The SPD proto-collaboration * * Contact person: A. Guskov (JINR), [email protected] a r X i v : . [ h e p - e x ] J a n ontents x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151.3 Tests of TMD factorization with gluon probes . . . . . . . . . . . . . . . . . . 171.4 Linearly polarized gluons in unpolarized nucleon . . . . . . . . . . . . . . . . . 181.5 Hadron structure and heavy charmonia production mechanisms . . . . . . . . . 191.6 Non-nucleonic degrees of freedom in deuteron . . . . . . . . . . . . . . . . . . 211.7 Gluon polarization ∆ g with longitudinally polarized beams . . . . . . . . . . . 221.8 Gluon-related TMD and twist-3 effects with transversely polarized beams . . . 251.9 Gluon transversity in deuteron . . . . . . . . . . . . . . . . . . . . . . . . . . . 271.10 Deuteron tensor polarization and shear forces . . . . . . . . . . . . . . . . . . . 291.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 Quarks in proton and deuteron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.1 Single-transverse spin asymmetries in the production of light mesons . . . . . . 312.2 Drell-Yan pair production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3 Generalized parton distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4 Polarized fragmentation functions . . . . . . . . . . . . . . . . . . . . . . . . . 353 Tests of the QCD basics at low energies . . . . . . . . . . . . . . . . . . . . . . . . . . 363.1 Elastic scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Single-spin asymmetries at low energies . . . . . . . . . . . . . . . . . . . . . . 393.3 Exclusive hard processes with deuterons . . . . . . . . . . . . . . . . . . . . . . 393.4 Scaling behavior of exclusive reactions with the lightest nuclei and spin observables 411 3.5 Vector mesons and the open charm near the threshold . . . . . . . . . . . . . . . 423.6 Central nucleon-nucleon collisions . . . . . . . . . . . . . . . . . . . . . . . . . 453.7 Onset of deconfinement in p - p and d - d central collisions . . . . . . . . . . . . . 463.8 Study of the lightest neutral hypernuclei with strangeness − − π production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1063 Single transverse spin asymmetry for very forward neutron production . . . . . . . . . . 108
10 Integration and services 146
11 Beam test facilities 149
12 Running strategy 152
13 Cost estimate 15514 Participating institutions and author list 15615 Conclusion 15916 List of abbreviations 160 reface
According to the astrophysical and cosmological data, the relative contribution of visible baryonic matter,the properties of which are determined by strong and electromagnetic interactions, is about 5% of theUniverse mass. With respect to two other components, dark matter and dark energy, baryonic matterseems to be a well-studied subject. In fact, despite the great advances in quantum chromodynamics madein describing the interaction of quarks and gluons within the framework of the perturbative approach, thequestion of why nucleons are exactly like we see them, remains open. Understanding the structure andthe fundamental properties of the nucleon directly from the dynamics of its quarks and gluons based onthe first principles is one of the main unsolved problems of QCD.The nucleon behaves like a spinning top with a spin of (cid:125) /
2. This spin is responsible for such fundamentalproperties of Nature as the nucleon magnetic moment, different phases of matter at low temperatures,the properties of neutron stars, and the stability of the known Universe. That is why the study of the spinstructure of the nucleon is of particular importance. The naive quark model has successfully predictedmost of the gross properties of hadrons, such as charge, parity, isospin and symmetry properties andtheir relations. Some of the dynamics of particle interactions can be qualitatively understood in termsof this model as well. However, it falls short in explaining the spin properties of hadrons in terms oftheir constituents. Since the famous ”spin crisis” that began in 1987, the problem of the nucleon spinstructure remains one of the most intriguing puzzles in the contemporary high-energy physics. Thecentral problem, for many years attracting both enormous theoretical and experimental efforts, is theproblem of how the spin of the nucleon is built up from spins and orbital momenta of its constituents– the valence and sea quarks and gluons. A full description can be given in terms of the so-calledtransverse-momentum dependent parton distribution functions.Over the last 25 years, both polarized deep inelastic scattering experiments (CERN, DESY, JLab, SLAC)and high-energy polarized proton-proton collisions (RHIC at BNL) have been the major providers ofinformation about spin-dependent structure functions of the nucleon. Nevertheless, our knowledge ofthe internal structure of the nucleon is still limited. This is especially true of the gluon contribution. Newfacilities for spin physics, such as the Electron-Ion Collider at BNL and the fixed-target experiments atCERN LHC are planned to be built in the near future to get the missing information.The Spin Physics Detector, a universal facility for studying the nucleon spin structure and other spin-related phenomena with polarized proton and deuteron beams, is proposed to be placed in one of thetwo interaction points of the NICA collider that is under construction at the Joint Institute for NuclearResearch (Dubna, Russia). At the heart of the project there is huge experience with polarized beams atJINR. The main objective of the proposed experiment is the comprehensive study of the unpolarized andpolarized gluon content of the nucleon. Spin measurements at the Spin Physics Detector at the NICAcollider have bright perspectives to make a unique contribution and challenge our understanding of thespin structure of the nucleon.In this document the Conceptual Design of the Spin Physics Detector is presented.6 hapter 1
Executive summary
The Spin Physics Detector (proto-)collaboration proposes to install a universal detector in the secondinteraction point of the NICA collider under construction (JINR, Dubna) to study the spin structure ofthe proton and deuteron and the other spin-related phenomena with polarized proton and deuteron beamsat a collision energy up to 27 GeV and a luminosity up to 10 cm − s − . In the polarized proton-proton collisions, the SPD experiment [1] at NICA will cover the kinematic gap between the low-energymeasurements at ANKE-COSY and SATURNE and the high-energy measurements at the RelativisticHeavy Ion Collider, as well as the planned fixed-target experiments at the LHC (see Fig. 1.1). Thepossibility for NICA to operate with polarized deuteron beams at such energies is unique.
10 100 s - s - L , c m PHENIX & STAR (RHIC, BNL) p ↑ − p ↑ ANKE (COSY, Julich) p ↑ − p ↑ SPD (NICA, JINR) p ↑ − p ↑ SPASCHARM (U-70, Protvino) p ↑ − p ↑ AFTER & LHCspin (LHC, CERN) p − p ↑ E704 (Fermilab) p ↑ − p ↑ SATURNE II Saclay p ↑ − p ↑ , GeV Figure 1.1: NICA SPD and the other past, present, and future experiments with polarized protons.The SPD is planned to operate as a universal facility for comprehensive study of the unpolarized andpolarized gluon content of the nucleon at large Bjorken- x , using different complementary probes suchas: charmonia, open charm, and prompt photon production processes. The experiment aims at providingaccess to the gluon helicity, gluon Sivers, and Boer-Mulders functions in the nucleon, as well as thegluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single7and double spin asymmetries (see Tab. 1.1). The results expected to be obtained by the SPD will playan important role in the general understanding of the nucleon gluon content and will serve as a comple-mentary input to the ongoing and planned studies at RHIC, and future measurements at the EIC (BNL)and fixed-target facilities at the LHC (CERN). Simultaneous measurement of the same quantities usingdifferent processes at the same experimental setup is of key importance for minimization of possiblesystematic effects. Other polarized and unpolarized physics is possible, especially at the first stage ofNICA operation with reduced luminosity and collision energy of the proton and ion beams.Table 1.1: Gluon TMD PDFs at twist-2. The columns represent gluon polarization, while the rowsrepresent hadron polarization. The PDFs planned to be addressed at SPD are highlighted in red.Unpolarized Circular LinearUnpolarized g(x) h ⊥ g ( x , k T ) density Boer-Mulders functionLongitudinal ∆ g ( x ) Kotzinian-Muldershelicity functionTransverse ∆ gN ( x , k T ) Worm-gear ∆ T g ( x ) Sivers function function transversity (deuteron only),pretzelosityFigure 1.2: General layout of the SPD setup.The physics goals dictate the layout of the detector. The SPD experimental setup is being designed asa universal 4 π detector with advanced tracking and particle identification capabilities based on moderntechnologies. The silicon vertex detector (VD) will provide resolution for the vertex position on thelevel of below 100 µ m needed for reconstruction of secondary vertices of D -meson decays. The strawonceptual design of the Spin Physics Detector 9tube-based tracking system (ST) placed within a solenoidal magnetic field of up to 1 T at the detectoraxis should provide the transverse momentum resolution σ p T / p T ≈
2% for a particle momentum of 1GeV/ c . The time-of-flight system (PID) with a time resolution of about 60 ps will provide 3 σ π / K and K / p separation of up to about 1.2 GeV/ c and 2.2 GeV/ c , respectively. Possible use of the aerogel-basedCherenkov detector could extend this range. Detection of photons will be provided by the sampling elec-tromagnetic calorimeter (ECal) with the energy resolution ∼ / √ E . To minimize multiple scatteringand photon conversion effects for photons, the detector material will be kept to a minimum throughoutthe internal part of the detector. The muon (range) system (RS) is planned for muon identification. Itcan also act as a rough hadron calorimeter. The pair of beam-beam counters (BBC) and zero-degreecalorimeters will be responsible for the local polarimetry and luminosity control. To minimize possiblesystematic effects, SPD will be equipped with a triggerless DAQ system. A high collision rate (up to4 MHz) and a few hundred thousand detector channels pose a significant challenge to the DAQ, onlinemonitoring, offline computing system, and data processing software.The proposed physics program covers at least 5 years of the SPD running.The estimated cost of the Spin Physics Detector at current prices is about 96 M$. This value doesnot cover the R&D expenses and the construction of the SPD Test zone. Any expenses related to thedevelopment and construction of the infrastructure for polarized beams at NICA are also out of thisestimation. hapter 2 Physics case
Gluons, together with quarks, are the fundamental constituents of the nucleon. They play a key rolein generation of its mass and carry about half of its momentum in hard (semi)inclusive processes. Thespin of the nucleon is also built up from the intrinsic spin of the valence and sea quarks (spin-1/2),gluons (spin-1), and their orbital angular momenta. Notwithstanding the progress achieved during thelast decades in the understanding of the quark contribution to the nucleon spin, the gluon sector is muchless developed. One of the difficulties is the lack of the direct probes to access gluon content in high-energy processes. While the quark contribution to the nucleon spin was determined quite precisely insemi-inclusive deep-inelastic scattering (SIDIS) experiments like EMC, HERMES, and COMPASS, thegluon contribution is still not well-constrained even so it is expected to be significant.In recent years, the three-dimensional partonic structure of the nucleon became a subject of a carefulstudy. Precise mapping of three-dimensional structure of the nucleon is crucial for our understandingof Quantum Chromodynamics (QCD). One of the ways to go beyond the usual collinear approximationis to describe nucleon content in the momentum space employing the so-called Transverse-Momentum-Dependent Parton Distribution Functions (TMD PDFs) [2–7].The most powerful tools to study TMD PDFs are the measurements of the nucleon spin (in)dependentazimuthal asymmetries in SIDIS [2, 5, 6, 8] and Drell–Yan processes [9, 10]. Complementary infor-mation on TMD fragmentation process, necessary for the interpretation of SIDIS data, is obtained from e + e − measurements [11]. Being an actively developing field, TMD physics triggers a lot of experimen-tal and theoretical interest all over the world, stimulating new measurements and developments in TMDextraction techniques oriented on existing and future data from lepton-nucleon, electron-positron andhadron-hadron facilities at BNL, CERN, DESY, FNAL, JLab, and KEK. For recent reviews on experi-mental and theoretical advances on TMDs see Refs. [12–16]. While a lot of experimental measurementswere performed (and are planned) and theoretical understanding was achieved for Leading Order (LO)(twist-2) TMD PDFs such as Sivers, transversity and Boer-Mulders functions of quarks, only few datarelevant for the study of gluon TMD PDFs are available [17–22].The simplest model of the deuteron is a weakly-bound state of a proton and a neutron mainly in theS-wave with a small admixture of the D-wave state. This approach is not much helpful in the descrip-tion of the deuteron structure at large Q . Possible non-nucleonic degrees of freedom in deuteroncould play an important role in the understanding of the nuclear modification of PDFs (the EMC ef- We use Q (or µ ) as a generic notation for the hard scale of a reaction: the invariant mass square of lepton pairs inDrell-Yan processes, Q , transverse momentum square p T of produced hadron or its mass square M . The polarized gluon content of proton and deuteron at intermediate and high values of the Bjorken x will be investigated using three complementary probes: inclusive production of charmonia, open charm,and prompt photons. Study of these processes is complementary to such proven approaches to accessthe partonic structure of the nucleon in hadronic collisions as the inclusive production of hadrons withhigh transverse momentum and the Drell-Yan process. Unfortunately, the latter one is unlikely to beaccessible at SPD due to the small cross-section and unfavourable background conditions. For effectiveregistration of each aforementioned gluon probes, the SPD setup is planned to be equipped with a range(muon) system, an electromagnetic calorimeter, a time-of-flight system, straw tracker, and a silicon ver-tex detector. Nearly a 4 π coverage of the setup and a low material budget in the inner part of the setupshould provide a large acceptance for the detection of the desired final states. In Fig. 2.1(a) the kinematicphase-space in x and Q to be accessed by the SPD is compared to the corresponding ranges of previ-ous, present and future experiments. Parameters of the experimental facilities planning to contribute togluon physics with polarized beams are listed in Tab. 2.1. Figure 2.1(b) illustrates the behavior of thecross-sections for the inclusive production of J / ψ , ψ ( S ) , D -mesons and high- p T prompt photons in p - p collisions as a function of √ s .We do not discuss separately such gluon probe as inclusive production of neutral and charged pions andother light mesons, for which the qg → qg hard process dominates in a certain kinematic region. Theyhave been successfully used to access the polarized gluon content of the proton at the RHIC experimentsand can of course be used at SPD for this purpose. Registration of these processes does not imposeadditional specific requirements on the experimental setup and can be performed in parallel with theaforementioned main probes. From the experimental point of view, for considered energies, hadronic production of charmonia seemsto be particularly suited to access gluon content in hadrons. Production of prompt J / ψ -mesons looksmost attractive, since large data set of J / ψ → µ + µ − (the branching fraction BF is 0.06 [31]) events isaccumulated in beam-dump experiments with proton and pion beams at √ s close to 20 GeV. However J / ψ -meson is not the cleanest probe of the proton structure, since a significant fraction (about 20%[32]) of J / ψ -mesons observed in hadronic collisions is produced indirectly through decays of χ cJ and ψ ( S ) (the so-called feed-down contribution), and modeling of this contribution introduces additionaluncertainties in theoretical calculations. Hence, to provide additional constraints to production models,it is important to study the production of χ cJ and ψ ( S ) separately, through their decays χ cJ → γ J / ψ ( BF = . .
343 and 0 .
19 for J = , , ψ ( S ) → J / ψπ + π − ( BF = .
347 [31]). Thelatter state is of special interest, because it is essentially free from feed-down contamination from highercharmonium states, due to the proximity of D D -threshold. However, the separation of the χ c , , signals2 x -3 -2 -1 ] [ G e V Q EMCSMCSMClowxE143E154E155COMPASS-DCOMPASS-PHERMES97HERMES COMPASS-OC ± STAR-WSTAR-jetsPHENIX-jetsEICNICA SPD AFTER (a) J/ ψ ψ (2S)Open charmPrompt photons (b)Figure 2.1: (a) The kinematic coverage, in the ( x , Q ) plane, of the hadronic cross-section data forthe processes commonly included in global QCD analyses of polarized quark (black) and gluon (red)PDFs [27]. The kinematic domain expected to be covered by NICA SPD by charmonia, open charmand prompt-photon production is shown in blue. (b) Cross-section for the processes of open charm, J / ψ , ψ ( S ) and prompt photons ( p T > p ↑ - p ↑ p ↑ - p ↑ e ↑ - p ↑ , d ↑ , He ↑ p - p ↑ , d ↑ p - p ↑ & polarization d ↑ - d ↑ p ↑ - d , p - d ↑ Center-of-mass ≤
27 ( p - p ) 63, 200, 20-140 ( ep ) 115 115energy √ s NN , GeV ≤ d - d ) 500 ≤
19 ( p - d )Max. luminosity, ∼ p - p ) 2 1000 up to 4.710 cm − s − ∼ d - d ) ∼
10 ( p - p )Physics run > > > > gg cc g y J/ (a) gg cc - D + Ddd (b) gq q q g (c)Figure 2.2: Diagrams illustrating three probes to access the gluon content of proton and deuteron in po-larized collisions at NICA SPD: production of (a) charmonium, (b) open charm, and (c) prompt photons.Besides, from the theoretical point of view the task of accessing gluon distributions using heavy quarko-nia is rather challenging. The heavy quark-antiquark pair couples directly to gluons from initial-statehadrons (Fig. 2.2(a)) and its production can be calculated perturbatively, because the hard scale of theprocess is limited from below by the heavy quark mass, providing direct access to polarized and un-polarized gluon distributions. However, the process of transition of the heavy quark-antiquark pair into aphysical bound-state is not well understood at present and can become a source of significant theoreticaluncertainties. We review the modern status of the theory of quarkonium production in more detail inSec. 1.5 to explain the latter point.Therefore, quarkonium production can be used to study the structure of hadrons only with a great cautionand only if results consistent with other probes will eventually emerge. The studies of hadronic structureand heavy quarkonium production mechanism should become complementary. But for now the mostreasonable phenomenological strategy for measurements at SPD concerning quarkonia is to study yieldsand polarization of different quarkonium states in a wide kinematic range, at various energies, and inpolarized as well as unpolarized hadronic collisions, to constrain the theoretical models. When thetheory of production of heavy quarkonia is firmly established – it will become an invaluable tool to studythe details of hadronic structure. It is well-known that heavy flavor production offers direct probes of the gluon distributions in hadrons.The basic mechanism responsible for charm pair production in pp collisions is the gluon fusion (GF, seeFig. 2.2(b)). In the framework of pQCD, the GF contributes to the hadron cross-section as L gg ⊗ ˆ σ c ¯ c ,where the gluon luminosity L gg is a convolution of the gluon densities in different protons, L gg = g ⊗ g .At leading order in pQCD, O ( α s ) , the partonic cross-section ˆ σ c ¯ c describes the process gg → c ¯ c .The GF contribution to the charmonia production in pp collisions has the form L gg ⊗ ˆ σ ( c ¯ c )+ X ⊗ W c ¯ c .At the Born level, the partonic cross-section ˆ σ ( c ¯ c )+ X is of the order of α s because its basic subprocessis gg → ( c ¯ c ) + g . Moreover, the quantity W c ¯ c , describing the probability for the charm pair to form acharmonium, imposes strong restrictions on the phase space of the final state. For these two reasons,the α s -suppression and phase space limitation, the cross-sections for charmonia production are almosttwo orders of magnitude smaller than the corresponding ones for open charm, see Figs. 2.1 (b).To analyze the kinematics of a DD pair, each D -meson has to be reconstructed. The decay modes D + → π + K − π + (BF=0.094) and D → K − π + (BF=0.04) can be used for that. To suppress a combinatorialbackground SPD plans to use the search for a secondary vertex of a D -meson decay that is about 100 µ mfar from the interaction point (the c τ values are 312 and 123 µ m for the charged and neutral D -mesons, To form a charmonium, the momenta of the produced quark and antiquark should be sufficiently close to each other. D ∗ -mesons could be used as additional tags for open-charm events. Single-reconstructed D -mesons also carry reduced but still essential information aboutgluon distribution that is especially important in the low-energy region lacking statistics. Photons emerging from the hard parton scattering subprocess, the so-called prompt photons, serve as asensitive tool to access the gluon structure of hadrons and hadron-hadron collisions. Inclusive direct pho-ton production proceeds without fragmentation, i.e. the photon carries the information directly from thehard scattering process. Hence this process measures a combination of initial k T effects and hard scat-tering twist–3 processes. There are two main hard processes for the production of direct photons: gluonCompton scattering, gq ( ¯ q ) → γ q ( ¯ q ) (Fig. 2.2(c)), which dominates, and quark-antiquark annihilation, q ¯ q → γ g . Contribution of the latter process to the total cross-section is small.Theoretical predictions for inclusive prompt photon production are shown in Fig. 2.3(a) as transversemomentum spectrum at the energy √ s =
27 GeV. Calculations are performed in LO and NLO approxi-mations of the Collinear Parton Model (CPM), as well as in the Parton Reggeization Approach (PRA),which is a QCD and QED gauge-invariant version of k T -factorization. They include direct and fragmen-tation contributions, the latter one is about 15-30 %. The K-factor between LO and NLO calculations inthe CPM slightly depends on p T γ and equals about 1.8 [33]. LO prediction of PRA coincides with theresult of NLO CPM calculation at moderate transverse momenta ( p T < p T PRApredicts somewhat harder p T -spectrum.In experiments prompt photons are detected alongside with a much larger number of photons from decaysof secondary π and η mesons (minimum-bias photons). The main challenge is to subtract these decaycontributions to obtain the photons directly emitted from hard collisions. This kind of background isespecially important at small transverse momenta of produced photons ( p T ) and gives the lower limitof the accessible p T range. Therefore the prompt-photon contribution with p T ≤ − p T spectra ( x T = p T / √ s ) measured in a wide kinematic range of √ s in different fixed-target and collider experimentsand the theoretical NLO calculations performed within the JETPHOX package [36]. While high-energycollider results exhibit rather good agreement with expectations, situation at high- x T is not pretty good.The results of the E706 ( √ s = . . √ s =
63 GeV) [38] experiments breakout the trend and demonstrate some ”slope”. It could be an indication of possible systematic effects thathave not been yet fully understood.A pair of prompt photons can be produced in hadronic interactions in q ¯ q annihilation, quark-gluon scat-tering, and gluon-gluon fusion hard processes (at the leading, next-to-leading, and next-to-next-leadingorders, respectively). The double prompt photon production in nucleon interactions at low energies is notyet well-studied experimentally. The production cross-section for proton-carbon interaction at √ s = . c has been measured by the CERN NA3 experiment [39]. Based on this result we can expect thecross-section of the double photon production with p T > c for each photon on the level of about0.5 nb.Estimations of the expected event rates are evaluated for p - p collisions at √ s =
27 and 13 . − , respectively that corresponds effectively to one year ofdata taking (10 s). The results are listed in Tab. 2.2.onceptual design of the Spin Physics Detector 15
2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 d σ / dp T d y , pb / G e V p T , GeV PRACPM LOCPM NLO10
2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 -3.0 WA70 ppUA6 ppE706 pp / 530E706 pp / 800UA6 pp_R110 ppR806 ppAFS ppPHENIX preliminary ppD0 pp_CDF pp → γ X √ s=1.8 TeV_ D a t a / Theo r y T INCNLO or JETPHOXM= μ =MF=pt/2CTEQ6M Λ =326 MeVfrag BFG II (b)Figure 2.3: (a) Prediction for prompt photon transverse momentum spectrum at √ s = 27 GeV obtainedin LO (red line) and NLO (blue line) approximations of CPM and LO of PRA (black line). Uncertaintybands for PRA predictions are due to factorization/renormalization scale variation only. (b) Data-to-theory ratio for the fixed-target and collider experiments [35].Table 2.2: Expected cross-section and counts for each of the gluon probes per one year of SPD running(10 s). Detector acceptance and reconstruction efficiency are not taken into account. σ 27 GeV , σ , N 27 GeV , N Probe nb ( × BF) nb ( × BF) 10 Prompt- γ ( p T > J / ψ 200 60 → µ + µ − 12 3.6 12 0.36 ψ ( S ) 25 5 → J / ψπ + π − → µ + µ − π + π − → µ + µ − χ c + χ c → γ J / ψ → γ µ + µ − η c → p ¯ p DD pairs 14000 1300Single D -mesons D + → K − π + ( D − → K + π − ) 520 48 520 4.8 D → K − π + ( D → K + π − ) 360 33 360 3.3 x The gluon PDF is one of the less known parton distributions in the proton because the available dataconstrain weakly the quantity g ( x , Q ) , particularly for x greater than 0.5 [42, 43]. In the high- x region,the gluon density is usually parameterized as g ( x , Q ) ∼ ( − x ) L , and values of L extracted from global6 -5 -4 -3 F r ac ti on a l un ce r t a i n ti e s xg(x, ) at = 2 GeV Combined HERA setSeparate HERA sets μ μ (a) -5 -4 -3 -2 -1 G ( x ) G d (x) (GRV98, µ F =1GeV)G p (x) (GRV98, µ F =1GeV) G d ( x ) / G p ( x ) x Ratio deuteron/proton (b)Figure 2.4: (a) Uncertainty of unpolarized gluon PDF based on HERA data ( µ = L vary from 3 to 11 at Q = . [44].To improve the situation with large x , one needs precise data on the heavy flavor production at ener-gies not so far from the production threshold. Concerning the open charm production in pp collisions,the corresponding cross-sections are poorly known for √ s < 27 GeV [45, 46]. Presently, the onlyavailable measurements for this region were performed by the E769 experiment, which corresponds tothree hundred events collected in pA collisions [47]. Unfortunately, the E769 results have large uncer-tainties, which is enough to estimate only the order of magnitude for the pp → c ¯ cX cross-section at √ s ≈ 20 GeV. For this reason, future studies of the open charm production at SPD in pp and dd colli-sions for √ s ≤ 27 GeV are of special interest. In particular, they will allow to reduce significantly thepresent uncertainties in the gluon density (and α s ) at a GeV scale, especially for high x .Detailed information on the gluon distribution at large x is very important for various phenomenologicalapplications. For instance, it is of current interest to estimate the b ¯ b pair production cross-section atNICA energies. Such predictions, however, are not presently reliable due to their strong dependence onthe exponent L which is poorly known. Another example is the DGLAP evolution of the PDFs. Usingprecise data on g ( x , Q ) (and α s ) at Q ∼ m c ( m c is the mass of the c-quark) as boundary conditions in theDGLAP equations, one could reduce essentially the uncertainties in evolution of PDFs for higher valuesof Q .From the theoretical point of view, the threshold behavior of cross-sections is closely related to the so-called infrared renormalon problem. It is well known that radiative corrections to the production cross-sections contain the mass (or threshold) logarithms whose contribution is expected to be sizable near thethreshold. These logarithms are usually taken into account within the soft gluon resummation (SGR)formalism [48–52]. Formally resummed cross-sections are, however, ill-defined due to the Landau polecontribution, and few prescriptions have been proposed to avoid the renormalon ambiguities [53–56].Unfortunately, numerical predictions for heavy quark production cross-sections may significally dependon the choice of resummation prescription. Undoubtedly, anticipated data from SPD on the charm pro-duction not so far from the production threshold will provide an excellent test for these prescriptions.Another interesting problem that could be addressed at NICA SPD is to probe the intrinsic charm (IC) On the contrary, few data exist for the J / ψ production cross-section down to threshold, see Fig. 2.1(b). onceptual design of the Spin Physics Detector 17content of the proton [57, 58]. The IC contribution to open charm production is expected to be sizablenear the threshold because its PDF, c ( x , Q ) , is predicted to be harder than the gluonic one. The IC couldbe also accessed via double J / ψ production. As a result, the IC density in the proton can be dominantat sufficiently large x independently of its overall normalization [59]. To visualize the IC component,one needs to collect enough events like DD pair produced in pp → DD with a large overall x F closeto 1. Those events are predicted to be very rare within the gluon fusion mechanism and would directlyindicate the five-quark component in the proton, | uudc ¯ c (cid:105) .Investigation of the open charm production in p - p , p - d and d - d collisions might be one of the key pointsin the NICA SPD program. The motivation is twofold. On the one hand, production of D -mesons in p - p collisions is practically unmeasured at NICA energies. On the other hand, these presently unavailabledata on open charm production rates are strongly necessary for determination of the gluon density g ( x , µ ) at large x where this PDF is practically unknown.Moreover, anticipated results on the open charm production are very important for many other currentissues in particle physics: from infrared renormalon ambiguities in cross-sections to intrinsic charmcontent of the proton. The description of hard inclusive processes in hadron collisions is based on factorization theorems. Theformulation of factorization theorems in terms of the TMD PDFs of quarks and gluons is the most im-portant step towards studying the 3D structure of hadrons and the nature of their spins. The conventionalTMD-approach [60] can be applied for study of the processes with colorless final states with transversemomenta much smaller than the relevant scale of hadron interactions, q T (cid:28) Q . In recent years a substan-tial success was achieved in the quark sector of TMD PDFs related with their correct theoretical definitionand the connection with experimentally observed cross-sections within the framework of factorizationtheorems [7]. In the case of unpolarized hadron collisions, in the leading twist approximation the produc-tion cross-section is a function of two independent TMD PDFs, i.e. distribution functions of unpolarizedquarks f q and distribution functions of transversely polarized quarks h ⊥ q (referred to as Boer-Muldersfunction) in unpolarized nucleons. For description of cross-sections in collisions of polarized hadrons,the number of TMD PDFs increases.However, the situation with gluon TMD PDFs is significantly different. Until recently, gluon TMD PDFswere used only within the framework of phenomenological models of the type of the Generalized PartonModel (GPM), in which the factorization formula of the Collinear Parton Model is applied if small (non-perturbative-origin) transverse momenta of gluons from colliding hadrons are available.The proof of the factorization theorem for processes with gluon TMD PDFs, as well as the formulationof evolution equations for them, have been presented relatively recently in [61], where they were appliedto describe the Higgs boson production with small transverse momenta. However, hard processes inwhich detailed information on gluon TMD PDFs can be obtained primarily, include the processes ofproduction of heavy mesons ( D , B ) and heavy quarkonia ( J / ψ , ϒ , η c , η b , . . . ). In these processes, thereare two non-perturbative mechanisms to be factorized: the emission of soft gluons in the initial state andthe formation of a colorless hadron in the final state. Even in the case of heavy meson production withsmall transverse momenta when their spectrum is determined only by a non-perturbative q T − distributionof initial gluons, for factorization of hard and soft interactions it is not enough to use the TMD PDFsformalism, the introduction of new non-perturbative process-dependent hadron observables, the so-calledTMDShFs (TMD shape functions) [62, 63] is needed. Moreover, the differential cross-section for the8process of production of the state Q in a collision of unpolarized hadrons is written as d σ dyd q T ∼ f g ⊗ f g ⊗ S Q − w UU ⊗ h ⊥ g ⊗ h ⊥ g ⊗ S Q , (2.1)where S Q is the polarization-independent TMDShFs of this process and w UU is the universal contributionweight function of linearly polarized TMD PDFs.The factorization theorem contains three or more non-perturbative hadronic quantities at low transversemomenta: gluon TMD PDFs and TMDShFs. Thus, the phenomenological extraction of gluon TMDsfrom quarkonium production processes is still possible, i.e., a robust factorization theorem can potentiallybe obtained in any particular case of heavy meson production. However one also needs to model andextract the involved TMDShFs. The search for the polarized quarks and gluons in unpolarized hadrons is of special interest in the studiesof the spin-orbit couplings of partons and understanding of the proton spin decomposition. The corre-sponding intrinsic transverse momentum (cid:126) k T dependent distributions of the transversely polarized quarks, h ⊥ q ( x ,(cid:126) k T ) , and linearly polarized gluons, h ⊥ g ( x ,(cid:126) k T ) , in an unpolarized nucleon have been introduced inRefs. [4] and [64]. Contrary to its quark version h ⊥ q the TMD density h ⊥ g is T - and chiral-even, andthus can directly be probed in certain experiments.Azimuthal correlations in heavy quark pair production in unpolarized ep and pp collisions as probesof the density h ⊥ g have been considered in Refs. [65, 66]. For the case of DIS, the complete angularstructure of the pair production cross-section has been obtained in terms of seven azimuthal modulations.However, only two of those modulations are really independent; they can be chosen as the cos ϕ andcos 2 ϕ distributions, where ϕ is the heavy quark (or anti-quark) azimuthal angle [67, 68]. To probe the TMD distributions, the momenta of both heavy quark and anti-quark, (cid:126) p Q and (cid:126) p ¯ Q , in theprocess pp → Q ¯ QX should be measured (reconstructed). For further analysis, the sum and difference ofthe transverse heavy quark momenta are introduced, (cid:126) K ⊥ = (cid:0) (cid:126) p Q ⊥ − (cid:126) p ¯ Q ⊥ (cid:1) , (cid:126) q T = (cid:126) p Q ⊥ + (cid:126) p ¯ Q ⊥ , (2.2)in the plane orthogonal to the collision axis. The azimuthal angles of (cid:126) K ⊥ and (cid:126) q T are denoted as φ ⊥ and φ T , respectively.The angular structure of the pp → Q ¯ QX cross-section has the following form:d σ pp ∝ A ( q T ) + B ( q T ) q T cos 2 ( φ ⊥ − φ T ) + C ( q T ) q T cos 4 ( φ ⊥ − φ T ) . (2.3)Assuming factorization for the TMD distributions, the terms A , B and C can schematically be written asthe following convolutions [66]: A ∝ f q ⊗ f ¯ q ⊗ A q + f g ⊗ f g ⊗ A g + h ⊥ g ⊗ h ⊥ g ⊗ A ⊥ g , B ∝ h ⊥ q ⊗ h ⊥ ¯ q ⊗ B q + f g ⊗ h ⊥ g ⊗ B g , (2.4) C ∝ h ⊥ g ⊗ h ⊥ g ⊗ C g . Here f g ( x ) ≡ g ( x ) . The function h ⊥ g can also be determined from measurements of the Callan-Gross ratio in DIS [69]. onceptual design of the Spin Physics Detector 19The order α s predictions for the coefficients A i , B i and C i ( i = q , g ) in Eqs.(2.4) are presented in Ref.[66].Using these results, one can, in principle, extract the densities h ⊥ q ( x ,(cid:126) k T ) and h ⊥ g ( x ,(cid:126) k T ) from azimuthaldistributions of the DD pairs produced in pp collisions.Another processes proposed to probe the linearly polarized gluons in unpolarized proton are: pseu-doscalar C -even quarkonia (such as η c and χ c ) [70], di–gamma ( pp → γγ X ) [71] and J / ψ – pair ( pp → J / ψ J / ψ X ) [72] production. These reactions are however strongly suppressed in comparison with pp → DDX . In this section we give a short review of modern status of the theory of heavy quarkonium productionwith an emphasis on possible applications of heavy quarkonium measurements for studies of the gluoncontent of hadrons.Production of heavy quarkonia proceeds in two stages: first, a heavy quark-antiquark pair is producedat short distances, predominantly via gluon-gluon fusion but also with a non-negligible contributionof q ¯ q and qg -initiated subprocesses. The second stage is hadronization of quark-antiquark pair into aphysical quarkonium state, which happens at large distances (low scales) and is accompanied by a com-plicated rearrangement of color via exchanges of soft gluons between the heavy quark-antiquark pair andother colored partons produced in the collision. Existing approaches, aimed to describe hadronizationstage, such as Non-Relativistic QCD factorization (NRQCD-factorization) [73] and (Improved-) Color-Evaporation Model (CEM) [74–77] are currently facing serious phenomenological challenges (see e.g.recent reviews [78, 79]). NRQCD-factorization is challenged by the long-standing “polarization puz-zle” [80, 81] and violation of Heavy-Quark Spin Symmetry relations between Long-Distance MatrixElements (LDMEs) of η c and J / ψ [82], while CEM usually rather poorly reproduces the detailed shapesof inclusive p T -spectra of charmonia and bottomonia and, unlike NRQCD-factorization [83, 84], sig-nificantly under-predicts bulk of cross-section for pair hadroproduction of J / ψ even at NLO in α s [85].Presently, the study of the heavy-quarkonium production mechanism is an active field of research, withnew approaches, such as subleading-power fragmentation [86] and Soft-Gluon Factorization [87–89],being proposed recently.Due to the above-mentioned problems and the multitude of competing theoretical approaches and themodels available on the market, our lack of quantitative understanding of the mechanism of hadronizationcan become a source of significant theoretical uncertainties if quarkonium production is to be used asa tool to study the proton structure. The Fig. 2.5 provides an insight on this situation at NICA SPD.In this figure, predictions of three models for the p T -spectrum (Fig. 2.5(a)) and p T -dependence of thepolarization parameter λ θ (Fig. 2.5(b)) are compared. The first one relies on the NLO calculation inCollinear Parton Model (with LO being O ( α s ) , see Fig. 2.2(a)) to describe short-distance part of thecross-section and uses the NRQCD-factorization formalism for the long-distance part, with LDMEs ofthe latter tuned to charmonium production data in hadronic collisions, DIS and e + e − -annihilation [80,81, 90, 91]. In the second prediction, the short-distance part of the cross-section is calculated in the LO( O ( α s ) for color-octet and P -wave contributions and O ( α s ) for color-singlet S -wave ones) of PRA [92],while LDMEs in this calculation had been fitted to the charmonium hadroproduction data from RHIC,Tevatron and LHC [93, 94]. The third prediction is performed in the LO ( O ( α s ) ) of PRA with the sameunintegrated PDFs as for the second one, but interfaced with an improved Color-Evaporation Model(ICEM) of Ref. [95] for description of hadronization. Non-perturbative parameters of the ICEM had beentaken from the Ref. [95] where they had been fitted to charmonium hadroproduction data at Tevatron andLHC energies. Predictions of all three models for inclusive J / ψ p T -spectrum at NICA SPD appear tobe consistent within their uncertainty bands. However, the structure of these predictions is significantlydifferent, with NRQCD-based predictions being dominated by gluon-gluon fusion subprocess, while0 -6 -5 -4 -3 -2 -1 B ( J / ψ → μ + μ - ) d σ / dp T , nb / G e V p T , GeV pp, √ S=24 GeV, -3.0 24 GeV. At higher p T the shape ofthe spectrum becomes highly model-dependent and at lower p T < M J / ψ the TMD-factorization effects(including possible violation of factorization, see [62, 63]) come into the game and the contribution of q ¯ q -annihilation subprocess becomes uncertain. Nevertheless, predictions and measurements of rapidityor x F -differential cross-sections even in this limited p T -range could help to further constrain the gluonPDF, e.g. to rule-out the extreme values of L in the x → ∼ ( − x ) L .Predictions of NLO CPM and LO of PRA for polarization parameter λ θ (see the Fig. 2.5(b)) are sig-nificantly different, with PRA predicting mostly un-polarized production ( λ θ (cid:39) 0) while CPM predictstransverse polarization ( λ θ = + 1) at high p T . Disagreement of the predictions for polarization param-eters mostly reflects the difference of LDMEs obtained in two fits and their large uncertainty bands aredue to significant uncertainties of LDMEs. Measurements of heavy quarkonium polarization at NICAenergies will provide additional constraints on models, however due to well-known problems with de-scription of polarization at high energies [80, 81] constraints coming from polarization measurementsshould be interpreted with great care and one should try to disentangle conclusions for gluon PDF fromthe results related to heavy quarkonium polarization.We would like to emphasise here also, that studies of η c -production at NICA SPD will be instrumentalfor better understanding of its production mechanism. If the color singlet mechanism dominated NRQCDprediction turns out to be correct, then η c production becomes a unique instrument to study the gluoncontent of the proton without introducing additional free-parameters, such as the color octet LDMEs, tothe analysis. The naive model describes the deuteron as a weakly-bound state of a proton and a neutron mainly inS-state with a small admixture of the D-state. However, such a simplified picture failed to describe theHERMES experimental results on the b structure function of the deuteron [96]. Modern models treatthe deuteron as a six-quark state with the wave function | q (cid:105) = c | NN (cid:105) + c | ∆∆ (cid:105) + c | CC (cid:105) , (2.5)that contains such terms as the nucleon | NN (cid:105) , ∆ -resonance | ∆∆ (cid:105) and the so-called hidden color compo-nent | CC (cid:105) in which two color-octet baryons combine to form a color singlet [97]. Such configurationscan be generated, for example, if two nucleons exchange a single gluon. The relative contribution of thehidden-color term varies from about 0.1% to 80% in different models [98]. The components other than | NN (cid:105) should manifest themselves in the high- Q limit. Possible contributions of the Fock states with avalent gluon like | uuudddg (cid:105) could also be discussed [41, 99].The unpolarized gluon PDF of the deuteron in the light-front quantization was calculated in the Ref. [41]under the approximation where the input nuclear wave function is obtained by solving the nonrelativisticSchr¨odinger equation with the phenomenological Argonne v18 nuclear potential as an input. Gluon PDFscalculated per nucleon are very similar for the proton one in the range of small and intermediate x valueswhile for x > . x that could be tested in the J / ψ production at EIC. Today the gluon content of deuteron and light nuclei2becomes the matter of interest for the lattice QCD studies [101]. Apart from the general understanding ofthe gluon EMC effect, the measurement of the gluon PDF at high- x for deuteron could provide a usefulinput for high-energy astrophysical calculation [41].SPD can perform an explicit comparison of the differential inclusive production cross-sections d σ / dx F for all three gluon probes: charmonia, open charm, and prompt photons using p - p and d - d collisionsat √ s NN = . ∆ g with longitudinally polarized beams The gluon helicity distribution function ∆ g ( x ) is a fundamental quantity characterizing the inner structureof the nucleon. It describes the difference of probabilities to find in the longitudinally polarized nucleona gluon with the same and opposite spin orientations. The integral ∆ G = (cid:82) ∆ g ( x ) dx can be interpreted asthe gluon spin contribution to the nucleon spin. After the EMC experiment discovered that only a smallpart of proton spin is carried by the quarks [102], the gluon spin was assumed to be another significantcontributor. So ∆ G is a key ingredient of the nucleon helicity sum rule12 = ∆Σ + ∆ G + L q + L g , (2.6)where ∆Σ ≈ . 25 [16] is the net contribution from the quark spin and L q , L g represent the contributionsof the orbital angular momenta of quarks and gluons, respectively.The first attempt to measure the gluon polarization in the nucleon was made by the FNAL E581/704 Col-laboration using a 200 GeV polarized proton beam and a polarized proton target [103]. They measuredthe longitudinal double-spin asymmetries A LL for inclusive multi- γ and π π production to be consistentwith zero within their sensitivities. In the following years a set of SIDIS measurements was performedby the HERMES [104], SMC [105] and COMPASS [106–110] experiments. The production of hadronpairs with high transverse momenta and the production of the open charm where the photon-gluon fusionmechanism dominates were studied. It was figured out that with a large uncertainty the value of ∆ G isclose to zero. Nevertheless, for gluons carrying a large fraction x of the nucleon momentum, an evidenceof a positive polarization has been observed, see Fig. 2.6(a). New input for ∆ G estimation was obtainedfrom the measurement of the A LL asymmetries in the inclusive production of high- p T neutral [111–114] and charged pions [115], η -mesons [111], jets [116], di-jets [117, 118], heavy flavors [119], and,recently, J / ψ -mesons [120] in polarized p - p collisions at RHIC. The new data in general are in agree-ment with SIDIS measurements, which demonstrates the universality of the helicity-dependent partondensities and QCD factorization.At the moment the most recent sets of polarized PDFs extracted in the NLO approximation are LSS15 [121],DSSV14 [122, 123], NNPDF-pol1.1 [27], and JAM17 [124]. To obtain them, different approaches, pa-rameterizations, and sets of experimental data were used, see Ref. [125] for more details. Fit results for ∆ g ( x ) from DSSV14 and NNPDF–pol1.1 are presented in Fig. 2.6(b) [123]. The RHIC p - p data put astrong constraint on the size of ∆ g ( x ) in the range 0 . < x < . ∆ g squared is probed (see details below). The small x region remainsstill largely unconstrained and could be covered in future by measurements at EIC [26]. The region ofhigh x is covered at the moment only by SIDIS measurements which still lack a proper NLO descrip-tion [126]. The uncertainty of the contribution to ∆ g from the kinematic range 0 . < x < . 05 vs. thecorresponding contribution from the range x > . 05 for the DSSV global fits is shown in Fig. 2.7(a) [122].In case of the longitudinally polarized p - p collisions the asymmetry A LL is defined as A LL = σ ++ − σ + − σ ++ + σ + − , (2.7)onceptual design of the Spin Physics Detector 23 g x g / g ∆ , 2002 06 >1 (GeV/c) , Q T COMPASS, all p , 2002 03 <1 (GeV/c) , Q T COMPASS, high pCOMPASS, Open Charm, 2002 07 >1 (GeV/c) , Q T SMC, high p , all Q T HERMES, high p (a) -0.4-0.3-0.2-0.1 0 0.1 0.2 0.3 0.4 0.001 0.003 0.01 0.03 0.1 0.3 0.5 1x and 1- σ contoursand 68% C.L. contours NNPDFpol1.1MC-replicasMC-averageDSSV14 x ∆ g(x,Q =10 GeV ) (b)Figure 2.6: (a) SIDIS data on ∆ g ( x ) / g ( x ) extracted in LO [110]. (b) Global fit results for the gluonhelicity distribution ∆ g ( x ) [123]. ∫ dx ∆ g ( x ) . . ∫ dx ∆ g(x) Q = 10 GeV NEW FITDSSV*DSSV 90% C.L. region90% C.L. region -0.500.51 -0.2 -0.1 -0 0.1 0.2 0.3 (a) (b)Figure 2.7: (a) Estimates of contributions of low- x and high- x kinematic ranges into ∆ G for the DSSVseries of the global fit. The 90% C.L. areas are shown [122]. (b) Partonic longitudinal double-spinasymmetries A LL for different hard processes as a function of center-of-mass scattering angle [127].where σ ++ and σ + − denote the cross-sections with the same and opposite proton helicity combinations,respectively. For the prompt photons produced via the gluon Compton scattering A γ LL ≈ ∆ g ( x ) g ( x ) ⊗ A p ( x ) ⊗ ˆ a gq ( ¯ q ) → γ q ( ¯ q ) LL + ( ↔ ) . (2.8)Here A p ( x ) is the asymmetry well-measured in a wide range of x and ˆ a gq ( ¯ q ) → γ q ( ¯ q ) LL is the asymmetry ofthe corresponding hard process. The Fig. 2.7(b) shows the behavior of ˆ a LL for different hard processes4 -0.04-0.0200.020.040.060.080.10.120.14 1 1.5 2 2.5 3 3.5 4 4.5 5 p T (GeV/c)A LL (a) -0.050.02500.0250.050.0750.10.1250.150.1750.2-1.5 -1 -0.5 0 0.5 1 1.5 A LL p T = 2 GeV/c (b)Figure 2.8: Longitudinal double spin asymmetry A LL for inclusive J / ψ production calculated for p - p collisions at √ s = 39 GeV in the LO approximation as a function of a) transverse momentum p T and b)pseudorapidity η [128]. -0.0500.050.10.150.20.25 4 6 8 10 A LL p T (GeV/c) (a) A LL (b)Figure 2.9: Longitudinal double spin asymmetry A LL for inclusive prompt-photon production calculatedfor p - p collisions at √ s = 39 GeV in the LO approximation as a function of a) transverse momentum p T and b) rapidity η ( p T = c ) [128].as a function of the center-of-mass scattering angle. For charmonia and open charm production via thegluon-gluon fusion process the expression for the corresponding asymmetry reads A c ¯ cLL ≈ ∆ g ( x ) g ( x ) ⊗ ∆ g ( x ) g ( x ) ⊗ ˆ a gg → c ¯ cXLL . (2.9)This asymmetry on the one hand is more sensitive to the gluon polarization than the corresponding onefor the prompt photons due to the quadratic dependence on ∆ g . On the other hand the sign of the ∆ g onceptual design of the Spin Physics Detector 25value can not be determined from it. So the measurements with prompt photons and heavy-quark statesare complementary. The contribution of q ¯ q annihilation processes to the above-mentioned asymmetriesis negligible despite ˆ a LL = − A LL measurements in the inclusive J / ψ production comes from our limited knowledge of charmonia production mechanisms includingthe feed-down contribution. Each of them has different partonic asymmetries ˆ a LL [129]. For the ∆ g estimation in Ref. [120] the value of ˆ a J / ψ LL has been forced to − 1. The SPD setup will have the possibilityto reconstruct χ cJ states via their radiative decays and resolve J / ψ and ψ ( S ) signals in a wide kinematicrange and disentangle contributions of different production mechanisms. The quality of the ∆ g estimationcould be significantly improved by measuring A LL separately for each charmonium state.Predictions for the longitudinal double-spin asymmetries A LL in p - p collisions can be found in Refs. [130]( J / ψ ) and [131] (prompt photons). They mostly cover the kinematic range of the RHIC experiments.Some estimates for A LL in charmonia [128] and prompt-photon [128, 132, 133] production at √ s = 39 GeV (see Figs. 2.8 and 2.9, respectively) have been done in preparation of the unrealized HERA- (cid:126) N project.The authors of the Ref. [134] proposed to extract information about the gluon helicity ∆ g via the studyof the production of high- p T prompt photons accompanied by Σ + hyperons. To do that, the singlelongitudinal spin asymmetry A γ Σ L and the polarization of the produced Σ + hyperons should be measured.However, further elaboration of this method is needed. One of the promising ways to investigate the spin structure of the nucleon is the study of transverse single-spin asymmetries (SSAs) in the inclusive production of different final states in high-energy interactions.The SSA A N is defined as A N = σ ↑ − σ ↓ σ ↑ + σ ↓ , (2.10)where σ ↑ and σ ↓ denote the inclusive production cross-sections with opposite transverse polarization ofone of the colliding particles. At the moment, more than forty years after the transverse spin phenom-ena were discovered, a wealth of experimental data indicating non-zero A N in the lepton-nucleon andnucleon-nucleon interactions was collected. However, our understanding of the SSA phenomenon is notyet conclusive.Theoretically two dual approaches are used to explain the transverse single-spin asymmetries: the collineartwist-3 formalism and the transverse momentum dependent (TMD) factorization approach. In the firstone at large transverse momenta p T (cid:29) Λ QCD of a produced particle, the collinear factorization involvingtwist-3 contributions for three-parton (Efremov-Teryaev-Qiu-Sterman) correlations [135–138] is used.Here Λ QCD ≈ 200 MeV is the QCD scale. An alternative approach assumes the TMD factorization, validfor p T (cid:28) Q , where the SSAs come from the initial-state quark and gluon Sivers functions or the final-state Collins fragmentation functions. The Sivers function f ⊥ , q ( g ) T ( x , k T ) is a TMD PDF that describesthe left-right asymmetry in the distribution of the partons w.r.t. to the plane defined by the nucleon spinand momentum vectors. Originating from the correlation between the spin of the nucleon and the orbitalmotion of partons, it is an important detail of the three-dimensional picture of the nucleon. This func-tion is responsible for the so-called Sivers effect (for both quarks and gluons) that was first suggestedin [139] as an explanation for the large single transverse spin asymmetries A N in the inclusive productionof the nucleon. More on the theoretical and experimental status of the transverse spin structure of thenucleon can be found in Refs. [14, 140]. The first attempt to access the gluon Sivers function (GSF)studying azimuthal asymmetries in high- p T hadron pair production in SIDIS of transversely polarised6deuterons and protons, was performed by COMPASS [21]. Using neural network techniques the contri-bution originating from Photon–Gluon Fusion (PGF) subprocess has been separated from the leading-order virtual-photon absorption and QCD Compton scattering subprocesses. The measured combinedproton-deuteron PGF-asymmetry was found to be negative and more than two standard deviations belowzero, which supports the possible existence of a non-zero Sivers function. In the meantime, COMPASSdid not see any signal for the PGF Collins asymmetry, which can analogously be related to the gluontransversity distribution. COMPASS studied GSF also through Sivers asymmetry in the J / ψ -productionchannel [22], again obtaining an indication of a negative asymmetry.Recently, in Ref. [141] a first estimate of the GSF was obtained using the midrapidity data on the A N SSA, measured in π production at RHIC [17]. The extraction was performed within the GPM frame-work using GRV98-LO set for the unpolarized PDF and available parameterizations for the quark Siversfunctions (SIDIS1 from Ref. [142] and SIDIS2 from Ref. [143]). The two parameterizations were ob-tained using different options for fragmentation functions, namely Kretzer [144] and DSS07 [145] sets,which give significantly different results for gluons. The latter point has a strong impact on the extractedGSF especially in low- x region. First k T -moments of the GSF ∆ q ( g ) N ( x , k T ) for the SIDIS1 and SIDIS2sets are shown in Fig. 2.10 (a) and (b), respectively.The gluon Sivers function is expected to satisfy the positivity bound defined as two time the unpolarizedTMD gluon distribution. However, some theoretical expectations are that the gluon Sivers function atrelatively high x is about 1/3 of the quark one [140].Several inclusive processes were proposed to access the gluon-induced spin effects in transversely po-larized p - p collisions. Single spin asymmetries for production of charmonia [146] (RHIC, AFTER),open charm [147–150] (RHIC) [150] (AFTER), and prompt photons [137, 151] (E704), [152] (RHIC)were estimated using both approaches for the experimental conditions of the past, present, and futureexperiments.The SSA A J / ψ N in the J / ψ production was measured by PHENIX in the p - p and p - A collisions at √ s NN = 200 GeV/ c [18, 19]. The obtained values for A J / ψ N are consistent with zero for negative and positive x F . Theoretical predictions [146] based on the Color Evaporation Model with TMD approach and thegluon Sivers function from Ref. [153] for different center-of-mass energies are shown in Fig. 2.11(a) asfunctions of rapidity y . Since the J / ψ production mechanism is not well understood, the measurementof the A J / ψ N may bring a valuable input to that matter as well. Predictions for A J / ψ N in proton-protoncollisions at NICA energy √ s = 27 GeV, obtained in GPM + NRQCD approach, as function of x F and p T are shown in the Figure (2.12). For comparison, results are presented for SIDIS1 [142] and D’Alesioet al. [154, 155] parameterizations of proton Sivers function.A measurement with open-heavy hadrons (both D - and B -mesons) was performed at RHIC (PHENIX, √ s = 200 GeV) [20] using high- p T muons from their semileptonic decays. The obtained results areaffected by relatively large statistical uncertainties and do not exhibit any significant non-zero asymmetry.Nevertheless, the results do not contradict the predictions of the twist-3 approach from Ref. [148]. TheSivers effect contribution to the A DN asymmetry calculated within the Generalized Parton Model for √ s = 27 GeV is presented in Fig. 2.11(b).The measurement of the A γ N SSA with prompt photons provides a unique opportunity to study the SiversPDF and twist-3 correlation functions , since the corresponding hard process does not involve fragmen-tation in the final state and thus is exempt from the Collins effect. The first attempt to measure A γ N at √ s = . − . < x F < . 15 and 2.5 GeV/ c < p T < c . The results were consistent with zero withinlarge statistical and systematic uncertainties [156]. Figure 2.13(a) shows the expected A γ N asymmetry asonceptual design of the Spin Physics Detector 27 N f ( ) g ( x ) xKRE-SIDIS1 / =10% / = 2% (a) N f ( ) g ( x ) xDSS-SIDIS2 / =10% / = 2% (b)Figure 2.10: The first k T -moment of the gluon Sivers function for SIDIS1 [142] and SIDIS2 [143]extractions of the quark Sivers functions [141]. s (cid:61) 115 GeVs (cid:61) 200 GeVs (cid:61) 500 GeV (cid:45) (cid:45) y A N SIDIS10 (cid:60) q T (cid:60) (a) A N ( x F ) x F SIDIS1SIDIS2GSF 0 0.02 0.04 0.06 0.08 0.1-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 p p -> DX, sqrt S=27 GeV, 1
115 GeV (AFTER), 200 GeV and 500 GeV (RHIC) asa function of rapidity y [146]. (b) Sivers effect contribution to the A DN asymmetry calculated within theGeneralized Parton Model.a function of x F for √ s = 27 GeV based on the SIDIS1 extraction of the gluon Sivers function. Quarkand gluon contributions from the gluon Compton scattering, dominating at positive and negative valuesof x F , respectively, are shown separately. The q ¯ q annihilation contribution is also presented. Dashedlines illustrate the twist-3 predictions for √ s = 30 GeV and p T = c for negative [151] and pos-itive [137] values of x F . The p T dependence of the A γ N asymmetry at x F = − . √ s in Fig. 2.13(b). The transversity function ∆ T q ( x ) is defined for partons as the difference of probabilities to find in atransversely polarized nucleon a parton with the same and opposite spin orientations. In spite of thedefinition is similar to the helicity function ∆ q ( x ) , the transversity describes a completely different aspectof the nucleon spin structure. This function is known quite well after a series of SIDIS and Drell-Yanexperiments. As soon as the transversity is related with the spin flip, for the spin-1/2 nucleon only aquark contribution ( ∆ s = 1) is possible while ∆ s = A N J / ψ x F ψ D'AlesioSIDIS1 p ↑ p → J/ ψ (1S)+X √ S = GeV (a) A N J / ψ p T ψ , GeV D'AlesioSIDIS1 p ↑ p → J/ ψ (1S)+X -3.0 ≤ y ≤ √ S = GeV (b)Figure 2.12: Predictions for A J / ψ N as function of x F (b) and p T (b) in p - p collisions at the energy √ s = x F q(pol) qbar->yg (QSF annihil)[q(pol) qbar->yg] + [q(pol) g -> qy] (QSF all)g(pol) q -> yq (GSF)Sum 0 0.02 0.04 0.06 0.08 0.1-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 T <6 GeV, sqrt S=27 GeV, SIDIS1 , µ = p T A N γ (a) A N γ , GeV/c (b)Figure 2.13: (a) x F -dependence of the asymmetry A γ N calculated basing on the SIDIS1 Sivers functionfor √ s = 27 GeV and 4 < p T < c . Gluon and quark contributions are shown separately bycolor solid lines. Dashed lines illustrate the twist-3 predictions for √ s = 30 GeV and p T = c fornegative [151] and positive [137] values of x F . (b) p T -dependence of the A γ N asymmetry for differentvalues of √ s at x F = − . A T T defined for interaction of transversely polarized hadrons by the similar manner as A LL is a way to access the transversity. But due to the absence of a gluonic contribution in the leading orderin the case of the nucleon interactions A T T (cid:28) A LL . As an example, the asymmetry A γ T T for the prompt-photon production at 200 and 500 GeV coming from the q ¯ q annihilation process calculated in LO [158]and NLO [159] is shown in Fig. 2.14.The situation changes [160] for the spin-1 deuteron where a gluon component not embedded into thenucleons is possible. So in the collision of transversely polarized deuterons a nonzero contribution ofthe gluon transversity ∆ T g ( x ) to A T T asymmetries is possible already in the twist-2. At the momentonceptual design of the Spin Physics Detector 29there is no experimental data on the gluon transversity in the deuteron. So, a measurement of the doubletransverse spin asymmetries A T T in the gluon-induced processes at polarized d - d collisions at NICASPD could be a way to access the ∆ T g ( x ) .The gluon-induced (NLO) Drell-Yan process qg → q γ ∗ → q µ + µ − was proposed in Ref. [157] as a wayto access it in the collisions of linearly polarized deuterons and unpolarized protons at the SpinQuestexperiment at Fermilab ( √ s NN = 15 GeV). Under assumption that ∆ T g ( x ) = ∆ d ( x ) , the asymmetry A E xy = d σ ( E x ) − d σ ( E y ) d σ ( E x ) + d σ ( E y ) (2.11)could reach the level of a few percent as it is shown in Fig. 2.14 (b). At NICA SPD, the J / ψ , open charmand prompt-photon production in p - d and d - d collisions with a linearly polarized deuteron can be usedto access the gluon transversity. The asymmetry A E xy in these processes is expected to be of the sameorder of magnitude. p T [GeV] | | < S = 200 GeVS = 500 GeV A TT A NLOLO-0.0100.010.02 0 10 20 30 (a) A E xy M µµ (GeV ) φ = y = q T = GeV q T = GeV q T = . GeV (b)Figure 2.14: (a) A γ T T asymmetry for the prompt-photon production at 200 and 500 GeV coming fromthe q ¯ q annihilation process calculated in LO [158] and NLO [159]. (b) Spin asymmetries | A E xy | for theproton-deuteron Drell-Yan process as a function of the dimuon mass squared for the dimuon rapidity y = . q T [157]. The availability of tensor polarized deuteron beam opens a possibility to study shear forces generatedby quarks and gluons [161]. The natural way to get the traceless part of the energy-momentum tensorrelated to shear is provided just by tensor polarization, as the relevant tensor S µν is a traceless one byconstruction. The contribution of the ”tensor polarized” parton distribution C T [162, 163] (introduced asan ”aligned” one [164]) is constrained by the zero sum rule [164] for its second moment (complementingthe Close-Kumano sum rule [163])which may be decomposed into quark and gluon components [165]: ∑ i = q , ¯ q (cid:90) C Ti ( x ) xdx = δ T ( Q ) , (2.12) (cid:90) C TG ( x ) xdx = − δ T ( Q ) . (2.13)0As a result, the matrix elements of energy momentum tensors of quarks and gluons look like ∑ i (cid:104) P , S | T µν i | P , S (cid:105) Q = P µ P ν ( − δ ( Q )) + M S µν δ T ( Q ) (2.14) (cid:104) P , S | T µν g | P , S (cid:105) µ = P µ P ν δ ( Q ) − M S µν δ T ( Q ) , (2.15)where the second terms describe the average (integrated over transverse distance) shear force. Here M isthe nucleon mass.The zero sum rules (2.12) were later interpreted [166] as yet another manifestation of Equivalence Prin-ciple (EP), as it was done earlier [167] for Ji sum rules. In turn, the smallness of δ T , compatible withthe existing HERMES data, was suggested [166] to be the new manifestation of Extended EquivalencePrinciple (ExEP) [168–170] valid separately for quarks and gluons in non-perturbative QCD due to theconfinement and chiral symmetry violation. It was originally suggested for anomalous gravitomagneticmoments [168, 170]. In particular, it provides the rotation of spin in the terrestrial experiment with theangular velocity of Earth rotation. Let us stress, that it may seem trivial if spin is considered just as avector. However, it becames highly non-trivial if the measurement of spin by the device rotating togetherwith Earth is taken into account. This is a particular example of the practical importance of the quantumtheory of measurement. Another example may be represented by the Unruh radiation in heavy-ion colli-sions [171], which implies that the particles production may be also considered as a quantum-mechanicalmeasurement in the non-inertial hadronic medium.Recently, ExEP was also discovered for the pressure [172].To check ExEP for shear force one may use future studies of DIS at JLab and of Drell-Yan process withtensor polarized deuterons [173] .Note that tensor polarized parton distribution may be also measured in any hard process with the relevantcombination of deuteron polarizations, in particular, for large p T pions production, providing much betterstatistics. The correspondent quantity can be the P-even Single Spin asymmetry A T = d σ (+) + d σ ( − ) − d σ ( ) d σ (+) + d σ ( − ) + d σ ( ) ∼ ∑ i = q , ¯ q , g (cid:82) d ˆ σ i C Ti ( x ) ∑ i = q , ¯ q , g (cid:82) d ˆ σ i q i ( x ) , (2.16)where the differential cross-section with definite polarization of deuteron appears.Note that due to the tensor polarization tensor being traceless the sum rule for the three mutually orthog-onal orientations of coordinate frame is valid [164]: ∑ i S izz = . (2.17)As a result, the leading twist kinematically dominant ”longitudinal” tensor polarization can be obtainedby accelerating transverse polarized deuterons which will be accessible at NICA. The proposed measurements at SPD will be carried out performing high-luminosity p - p , p - d and d - d collisions at the center-of-mass energy up to 27 GeV using longitudinally or transversely polarized protonand vector- or tensor-polarized deuteron beams. The SPD experiment will have a unique possibility toprobe gluon content employing simultaneously three gluon-induced processes: the inclusive productionof charmonia ( J / ψ and higher states), open charm production, and production of the prompt photons.The kinematic region to be covered by SPD is unique and has never been accessed purposefully in Complementary probes are provided by vector mesons [169]. onceptual design of the Spin Physics Detector 31polarized hadronic collisions. The data are expected to provide inputs for gluon physics, mostly in theregion around x ∼ . ∆ g ( x ) A LL asymmetries p L - p L , √ s = 27 GeVGluon Sivers PDF ∆ gN ( x , k T ) , A N asymmetries, p T - p , √ s = 27 GeVGluon Boer-Mulders PDF h ⊥ g ( x , k T ) Azimuthal asymmetries p - p , √ s = 27 GeVTMD-factorization test Diff. cross-sections, p T - p , energy scan A N asymmetriesUnpolarized gluon d - d , p - p , p - d density g ( x ) in deuteron Differential √ s NN = p - p ,density g ( x ) in proton √ s ≤ 20 GeVGluon transversity ∆ g T ( x ) Double vector/tensor d tensor - d tensor , √ s NN = C TG ( x ) Single vector/tensor d tensor - d , p - d tensor asymmetriesThe study of the gluon content in the proton and deuteron at NICA SPD will serve as an importantcontribution to our general understanding of the spin structure of hadrons and QCD fundamentals. Theexpected inputs from the SPD will be highly complementary to the ongoing and planned measurementsat RHIC, future facilities such as EIC at BNL and fixed-target LHC projects at CERN. The single-transverse spin asymmetries (STSA) in the inclusive production of light mesons are the sim-plest spin observables in hadronic scattering and also related with the Sivers, Collins, and Boer-Mulderstransverse momentum dependent functions discussed in the previous section. But unlike the case of char-monia, open charm and prompt photon production, quarks are the main contributors to the correspondingasymmetries. The first result for A N was reported by the E704 collaboration for the production of thecharged and neutral pions in p ↑ - p and ¯ p ↑ - p collisions at √ s = . p - p collisions have been combined with SSA data in SIDIS,Drell-Yan pair production, and e + e − annihilation.Figure 2.15: The extracted from the global analysis JAM20 (JAM collaboration) [184] functions h ( x ) and f ⊥ ( ) T ( x ) at Q = together with the corresponding results of other groups. . . . . δu − . − . . δd GLOBALSIDIS + SIASIDIS JAM20Goldstein et al (2014)Radici, Bacchetta (2018)Gupta et al (2018)Alexandrou et al (2019)Pitschmann et al (2015) . . . . g T JAM20 { GLOBALSIDIS + SIA SIDISD Alesio et al (2020)Benel et al (2019)Radici , Bacchetta (2018)Kang et al (2015)Radici et al (2015)Goldstein et al (2014)Anselmino et al (2013)Alexandrou et al (2019)Gupta et al (2018)Hasan et al (2018)Pitschmann et al (2015) Figure 2.16: The results of the global analysis JAM20 (JAM collaboration) [184] along with others fromphenomenology (black), lattice QCD (purple), and Dyson-Schwinger (cyan) for the tensor charges δ u , δ d and g T = δ u − δ d at Q = .The first momenta h ( x ) and f ⊥ ( ) T ( x ) of the TMD pretzelosity h ( x , k T ) and Sivers f ⊥ ( ) T ( x , k T ) functionsobtained from the global analysis JAM20 together with 1 σ uncertainties at Q = are presentedin Fig. 2.15. The so-called tensor charges δ q = (cid:90) ( h q ( x ) − h ¯ q ( x )) dx (2.18)for u and d quarks and g T = δ u − δ d are shown in Fig. 2.16. New data on the STSA in the light mesonsproduction in the SPD energy range (and especially high- p T data) are very much in demand for suchkind of global analyses [185].onceptual design of the Spin Physics Detector 33 Production of Drell-Yan (DY) pairs in polarized hadronic collisions pp → γ ∗ → µ + µ − is a promisingway to touch the TMP PDFs of valence quarks and sea antiquarks by measuring the azimuthal asymme-tries. A tiny DY cross-section and a huge combinatorial background coming from decays of secondarypions and kaons into muons make this task rather difficult. A typical detector configuration for suchkind of studies at √ s ∼ 20 GeV is a fixed-target beam-dump setup where due to the Lorentz boost mostof secondary pions and kaons are stopped in a thick absorber before decaing. At the moment only theCOMPASS experiment at CERN has presented the results for the three azimuthal asymmetries measuredin pion-induced polarized DY [186, 187]. The observed glimpse of the sign change in the Sivers asym-metries is found to be consistent with the fundamental prediction of QCD that the Sivers TMD PDFextracted from the DY has a sign opposite to the one extracted from the SIDIS data. Unique results forthe Sivers functions of ¯ u and ¯ d are expected from the SpinQuest experiment at Fermilab [188, 189].Figure 2.17: Estimated Sivers asymmetries for the NICA conditions s = GeV , Q = GeV (left) and s = GeV , Q = GeV (right). Fits for the Sivers functions are taken from [190].Figure 2.18: Estimated Boer-Mulders asymmetries for the NICA conditions.Unfortunately, the Spin Physics Detector cannot use the advantage of fixed-target beam-dump setupsand the expected background conditions for the Drell-Yan measurements are rather untoward. However,further improvement of the experimental techniques and analysis procedures could give a chance to4access polarized DY at SPD. The estimated Sivers and Boer-Mulders asymmetries for the SPD conditionsare presented in Fig. 2.17 and 2.18, respectively. The concept of Generalized Parton Distributions (GPDs) is a complementary to the TMD PDFs approachto describe the three-dimensional structure of hadrons. Study of the deeply virtual meson production(DVMP) is one of the proven ways to access GPDs. This process has been investigated at HERMES[191], COMPASS [192, 193], CLAS [194] using electron and muon beams. An exclusive electromag-netic process pp → ppM shown in Fig. 2.19(a), where the first proton radiates a photon with lowvirtuality that interacts with the other proton and produces a meson, could be used to access the Gen-eralized Parton Distributions at SPD. At the SPD energies, the meson photoproduction amplitude canbe presented in a factorized form as a convolution of the hard scattering part which can be calculatedperturbatively and the GPDs [195, 196]. In the case of vector mesons production, the odderon exchange(that could be described as an exchange by at least 3 gluons) is also possible and the interference ofthese two channels is a matter of special interest. Ultraperipheral p - A collisions at SPD, which enhancethe photoproduction contribution by several orders of magnitude could also be considered. In addition,ultraperipheral processes could be used to test the most general non-perturbative concept of the Gener-alized Transverse Momentum dependent Distributions (GTMD). This possibility was explored for highenergies in Ref. [197] but the approach could be extended down to the SPD energies. D - pp = 2 D + pp' = 2 D - kk = 2 D + kk' = D - q' = q p ' p MesonGPDq (a) GPDGPD + m - m (b) GPDGPD + m - m (c)Figure 2.19: (a) Vector meson production at NICA via photoproduction mechanism or odderon exchange.(b, c) Drell-Yan process with gluon and quark GPDs.The exclusive production of the J / ψ meson can be studied at SPD at energies W = (cid:113) ( q + p ) ∼ ÷ 15 GeV. Here q and p are the 4-momenta of a virtual photon (odderon) and a proton, respectively. Thelarge meson mass makes it possible to perform perturbative calculations at sufficiently low Q , wherethe photon exchange should dominate. The corresponding cross-section is estimated to be of about σ J / ψ ∼ 10 nb. The main contribution to the cross-section is coming from the gluon GPDs.The exclusive Drell-Yan (exDY) process was proposed for the study of GPDs in p - p collisions in Ref.[198]. The kinematics of this process is defined by convolution of two GPDs. Both quark and gluonGPDs contribute to the exDY cross-section via the diagrams shown schematically in Fig. 2.19(b, c).Investigation of the cross-section determined by two-GPDs effects is in progress now [199]. It is shownthat the gluon and sea quark GPDs lead to the cross-section which does not decrease with the growth ofenergy. The exDY cross-section d σ / dQ at the NICA kinematics √ s = 24 GeV and Q = is estimated as 5 pb/(GeV/c) which is much smaller with respect to the inclusive Drell-Yan cross-section. Nevertheless, the exclusivity requirement applied in the analysis of the future SPD dimuon datacould increase the signal-to-background ratio. It should be mentioned that J / ψ could also be producedexclusively in a similar way.onceptual design of the Spin Physics Detector 35 The information on the polarization of produced partons can be transmitted to the asymmetries of finalstate hadrons. This process is controlled by the polarized fragmentation functions.JINR played the pioneering role in that activity started with the notion of jet handedness [200, 201] whichwas explored in Z decays [202]. To measure this quantity one should explore the P-odd mixed productzof hadron (usually pions) momenta in the jets and compare the number of these products with differentsigns indicating the right and left triples: A = N L − N R N L + N R . (2.19)In the case of transverse quark polarization the triple may contain its direction as well as that of jetmomentum, so that only the pion momentum is varying. This is the case of Collins function [203]revealed in the specific angular modulations. The Collins functions are systematically studied in e + e − annihilation, SIDIS and hadronic processes.Another opportunity to form the P-odd combination of momenta is the dihadron and interference frag-mentation functions [204]. The dihadron fragmentation function was effectively used for transversitymeasurement [205].The polarized fragmentation functions for both helicity and transversity quark distributions can be usedalso in the case of Λ -hyperon production [206].The polarized quark and gluon fragmentation functions may be explored in the production to tensorpolarized vector mesons [207].The gluon fragmentation to the transverse polarized quarkonium [208] may be also considered as polar-ized fragmentation function. It is known to produce the dominant transverse polarization of colour-octetstates.The exploration of polarized fragmentation function in hadronic processes should involve the measure-ment of rapidity dependence of the hard process, which should be essential in separation of variouspartonic subprocesses. Λ - polarization The Λ -hyperon is an ideal testing ground for spin studies since it has a rather simple spin structure inthe naive quark parton model. Furthermore, its self-analyzing decay makes polarization measurementsexperimentally feasible. Measurements of the Λ polarization in hadronic collisions can provide a clearanswer to the question of whether polarized u and d quarks can transfer polarization to the final state Λ . Polarization of the Λ was the subject to close study in the polarized leptoproduction (COMPASS[209, 210], HERMES [211], E665 [212]), and p - p collisions (E704 [213, 214], STAR [215], PHENIX[216]).There is a well known experimental fact that the hyperons produced in the unpolarized p - p collisionsare polarized transversely to the production plane [217]. That is the result of higher-twist effects. Polar-ization measurement of the Λ -hyperons produced inclusively in p - p collisions with one of the protonslongitudinally polarized, p ↑ p → Λ ↑ X , (2.20)could provide information about the spin-dependent fragmentation function D q , g → Λ ( z ) that describesfragmentation of quarks and gluons into the Λ .6The E704 measurement [214] of the parameter D NN , characterizing the fraction of incident (polarized)proton polarization transferre to the inclusively produced Λ , was performed at √ s = . p T . The obtained result can not betreated easily within the existing models. Quantum chromodynamics has a remarkable success in describing the high-energy and large-momentumtransfer processes, where partons in hadrons behave, to some extent, as free particles and, therefore, theperturbative QCD approach can be used. Cross-section of a process in QCD is factorized into twoparts: the process-dependent perturbatively-calculable short-distance partonic cross-section (the hardpart) and universal long-distance functions, PDFs and FFs (the soft part). Nevertheless, a largest frac-tion of hadronic interactions involves low-momentum transfer processes in which the effective strongcoupling constant is large and the description within a perturbative approach is not adequate. A num-ber of (semi-)phenomenological approaches have been developed through the years to describe stronginteraction in the non-perturbative domain starting from the very basic principles. They successfullydescribe such crucial phenomena, as the nuclear properties and interactions, hadronic spectra, deconfine-ment, various polarized and unpolarized effects in hadronic interaction, etc. The transition between theperturbative and non-perturbative QCD is also a subject of special attention. In spite of a large set ofexperimental data and huge experience in few-GeV region with fixed-target experiments worldwide, thisenergy range still attracts both experimentalists and theoreticians. In addition, the low-energy physics atSPD is some kind of a bridge to the physics program of MPD, another experiment at NICA [218–220].In this Section, we discuss certain problems that could be addressed at the initial stage of SPD operationwith a reduced collision energy and luminosity, realizing, however, that this list is not exhaustive. p - N elastic scattering The p - p and p - n elastic scattering at high energy √ s = ÷ − t = ÷ 10 GeV is powered by the short-range properties of N - N interactions corresponding to asmall separation between nucleons r NN ∼ (cid:125) / √− t ≤ . i ) First, the differential cross-section d σ pp / dt ( s , θ cm ) at a fixed angle θ cm ∼ ◦ on the whole follows the pQCD constituent counting rules d σ pp / dt ( s , θ cm ) ∼ s − [221–224].However, a clear deviation from this prediction in the form of oscillations with an increasing energy isobserved in the region s = ÷ 40 GeV [221–224]. The irregularity in the energy dependence is atthe level of ∼ 50% in the region, where the magnitude of the p - p elastic cross-section falls down by8 orders of magnitude. ( ii ) Second, anomalous polarization asymmetries were observed in hard p - N scattering at p lab = . 75 GeV/c [225–227]. The elastic p - p -cross-section with spins of protons paralleland normal to the scattering plane is almost four times larger than the cross-section with antiparallelspins. The challenge is that in order to generate such a large polarization effect, one needs to have alarge contribution from the double spin-flip helicity amplitude φ or a negligible contribution from thehelicity conserving φ amplitude. However, in pQCD, in contrast, φ is the most suppressed and φ isthe largest [228]. Predicted within the pQCD (quark-interchange model), the double spin asymmetry A NN = / iii ) The third QCD aspect of hard NN scattering is related to theColor Transparency phenomen (CT), that is, a reduction of the absorption in the nuclear medium of hardproduced hadrons, both mesons and baryons [231], [232]. The initial and final hadrons participating inhard process in point-like configurations dictated by mechanism of high momentum transfer, have smallcolor dipole momenta and, therefore, small interaction cross-section with the nuclear medium. Theseonceptual design of the Spin Physics Detector 37expectations resulted in huge theoretical and experimental activities in the 90’s. While the CT effectis observed for the hard production of the q ¯ q systems, the similar effect for qqq is elusive. The data[233, 234] on the reaction p + A → pp + X on the C and Al show an ”oscillatory” effect again, i.e. thetransparency increases with an increasing momentum up to p lb = c , and then decreases below theGlauber calculation predictions at 14 GeV/c. An attempt to connect all the three above-mentioned aspectstogether into one approach was undertaken in Ref. [235] and, recently, in [228]. However, the recentmeasurement of the cross-section of the reaction e C → epX at Q = ÷ 14 (GeV/ c ) [236] showsno CT effect and this fact raises new questions to the analysis made in [228]. Nevertheless, accordingto [235], the observed large variations in spin correlations of p - p elastic scattering are consistent withformation in the s-channel of the ”octoquark” resonances uuds ¯ suud and uudc ¯ cuud near the strangenessand charm production thresholds, respectively. The variations with an increasing energy are explained asa result of interference of the pQCD background amplitude with non-perturbative resonant amplitudes.Furthermore, the model [235] provides a description of the oscillations in the unpolarized differential p - p elastic cross-section. One should mention, however, that another explanation of the oscillation effectin the d σ pp / dt ( s , θ cm ) was suggested in Ref. [237].A different spin-isospin structure of the transition matrix elements for the near threshold J / ψ productionin p - n and p - p collisions [238] means that spin observables in p - n elastic scattering can give independentinformation on the considered dynamics. Data on these observables are almost absent in the consideredenergy region. A task to get such data from the p ↑ d ↑ → pnp reaction is accessible for NICA SPD. p - d elastic scattering within the Glauber model and pN spin amplitudes Nucleon-nucleon elastic scattering contains fundamental information on the dynamics of the NN interac-tion and constitutes a basic process in the physics of atomic nuclei and hadrons. Full information aboutthe spin amplitudes of p - p and p - n elastic scattering can be obtained, in principle, from a complete po-larization experiment, which, however, requires to measure dozens of independent observables at a givencollision energy and constitutes a too complicated experimental task. A systematic reconstruction ofthese amplitudes from the scattering data is provided by the SAID data base [239] and covers laboratoryenergies up to 3 GeV ( p lab ≈ . pp and 1 . p lab ≈ . p - n scattering. Athigher energies there are only non-complete data on p - p scattering, whereas the information about the p - n system is very scarce. In the literature there are several models and corresponding parametrizationsfor p - N amplitudes. Some of them are obtained in the eikonal approach for the lab momentum of 6GeV/c [240] and for the LHC energies [241]. Within the Regge phenomenology, a parametrization isobtained for 3-50 GeV/c (corresponding to 2 . < √ s < 10 GeV)[242] and for the values of s above6 GeV ( p lab ≥ . c ) in Ref. [243]. A possible way to check the existing parametrizations isto study the spin effects in proton-deuteron ( p - d ) and deuteron-deuteron ( d - d ) elastic and quasi-elasticscattering. At high energies and small four-momentum transfer t , p - d scattering can be described bythe Glauber diffraction theory of multistep scattering, which involves on-shell p - N elastic scattering am-plitudes as input data. Applications of this theory with spin-dependent effects included [244] indicatea good agreement with the p - d scattering data at energies of about 1 GeV, if the SAID data on p - N scattering amplitudes are used as input for the calculations [245–247].The spin-dependent Glauber theory [244, 245] has been recently applied [248] to calculate the spinobservables of p - d elastic scattering at 3 ÷ 50 GeV/c, utilizing the pp elastic scattering amplitudes f pp established and parametrized in Ref. [242] within the Regge formalism. The Regge approach allows oneto construct p − n , f pn , (and ¯ p − n , f ¯ pn ) amplitudes together with p − p amplitudes at small − t and large s .This feature allows one to perform a test of a broad set of p - N amplitudes and applicability of the Reggemodel itself to p - N elastic scattering. However, in view of the scarce experimental information about thespin-dependent p - n amplitudes and taking into account that the spin-independent parts of the p - p and p - n amplitudes at high energies are approximately the same, it was assumed in [248], as a first approximation,8that f pn = f pp . The unpolarized differential cross-section, vector ( A py , A dy ) and tensor ( A xx , A yy ) analyzingpowers and some spin correlation parameters ( C x , x , C y , y , C xx , y , C yy , y ) of pd elastic scattering werecalculated at p l = . 85 GeV/ c and 45 GeV/ c at 0 < − t < , using p - N amplitudes from [242]. Asshown in Ref. [248] the available data on p - d elastic differential cross-section in the forward hemisphereare well described by this model. Most sensitive to the spin-dependent pN amplitudes are the vectoranalyzing powers A y and the spin correlation parameters C x , x and C y , y . Thus, even the measurement of theratio A dy / A py at low t gives valuable information on the transverse spin-spin term in NN-amplitudes [250].In contrast, the tensor analyzing powers A xx and A xx are very weakly sensitive to those amplitudes andweakly change with increasing energy. The polarization observables calculated in [248] can be measuredat NICA SPD and will provide a test of the used p - N amplitudes. The corresponding differential cross-section is rather large in the considered region p lab = ÷ 50 GeV/ c and | t | = ÷ being d σ / dt > . . The expected counting rate N at p lab = 50 GeV/ c ( q cmpp = c ) for the luminosity L = × cm − s − and for the solid angle ∆Ω = . 03 is N ≥ s − .The p - N helicity amplitudes φ and φ + φ , which can be tested in the above described procedure arenecessary in the search for time-reversal invariance effects in double-polarized pd scattering [251, 252].The data of the spin-correlation parameters on p - p elastic scattering being analyzed in the framework ofthe eikonal model [241] will allow one to obtain the space structure of the spin-dependent hadron forces[253]. d - d scattering. The spin observables of d - d - elastic scattering in forward hemisphere also can be used to test spin-dependent amplitudes of p - N elastic scattering since the Glauber model can be applied to the descriptionof these observables. Unpolarised differential cross-section of the d - d elastic scattering in forward hemi-sphere measured at energies √ s = ÷ 63 GeV [254] was well described by the modified Glauber theoryincluding Gribov inelastic corrections. At lower energies corresponding to the SPD NICA region, onemay expect that inelastic corrections are not important, that can be checked by direct calculation ofunpolarised cross-section and subsequent comparison with the data. In this calculations the above con-sidered spin dependent amplitudes of the pd elastic scattering [248] can be used as input for the Glaubercalculations of the dd scattering.At large scattering angles θ cm ∼ ◦ the pd → pd and dd → dd processes are sensitive to the short-range(six-quark) structure of the deuteron. Therefore, measurement of the differential cross-sections or spinobservables of these processes at large θ cm will be important to search for non-nucleonic degrees offreedom of the deuteron. p - p scattering and periphery of the nucleon The first evidence of the pion cloud effect in the diffractive scattering | t | ∼ . ≈ m π has beenfound in the ISR measurements [255]. A theoretical study of the effect was provided by Anselm andGribov [256] and recently in Refs. [257] and [258]). The oscillation effect observed at ISR was studiedlater on in Protvino and one more oscillation in the differential cross-section was found there at | t | ∼ . located at a higher t , it might be related to somewhat heavier mesons around the proton.The oscillation effect of the pp scattering amplitude at a small momentum transfer was found also inthe analysis of the recent high-precision experimental data of the TOTEM collaboration at √ s = p - p -scattering to explorethis phenomenon. For this purpose, measurements in the kinematic region of | t | ∼ . ÷ . will We use here notations of Ref. [249] onceptual design of the Spin Physics Detector 39be performed. They will simultaniousely detect in coincidence elastically scattered protons at angles θ ∼ ÷ ◦ with an accuracy of t determination higher than ∼ . 02 GeV . A systematic study of such single-spin phenomena as the transverse single-spin polarization of hadrons( A N ) and the polarization of hyperons ( P N ) in p - p , d - d , C - C , and Ca - Ca collisions is proposed. Asystematic study means a detailed study of the dependence of the observed A N and P N for dozens ofreactions on variables, such as collision energy ( √ s ), Feynman variable ( x F ), transverse momentum( p T ), the atomic weights of the colliding particles ( A and A ), the multiplicity of charged particles ( N ch )in the event, and the centrality of collisions. The study of a large number of reactions will reveal thedependence of A N and P N on the quantum numbers (spin, isospin, flavor, etc.) of the hadrons participatingin the reaction. A systematic study also implies a global analysis of all available single-spin data withina certain model in order to identify general behavior and the mechanism of the origin of polarizationphenomena.One of such models is the chromomagnetic quark polarization (CPQ) model [262]. The CPQ modelassumes the presence of an inhomogeneous circular transverse chromomagnetic field B a in the interac-tion region of colliding hadrons. The interaction of the chromomagnetic moments of test quarks, whichlater form the observed hadron, with the field B a leads, as a result of the Stern-Gerlach effect, to theappearance of spin effects (with non-zero A N and P N ). The spin precession of test quarks leads to thephenomenon of oscillations A N ( x F ) and P N ( x F ) depending on the Feynman variable x F , and the frequencyof these oscillations depends on the number of spectator quarks, color charges of quarks and antiquarks,and the direction of their motion in the c.m. of reactions. The frequency of these oscillations is a linearfunction of the number of quarks and antiquarks - spectators interacting in pairs with each of the testquarks, taking into account the color state of the pair. The highest oscillation frequencies are expected inthe case of antibaryon production in baryon collisions and in ion collisions.The CPQ model also predicts for a number of reactions such a phenomenon as the resonance dependenceof A N and P N on energy ( √ s ), which occurs if the sign of the color charge of the test quark and spectatorsis opposite. The most interesting reaction in this respect is the production of anti-lambda in variousinitial states of the beams of the NICA collider, for which the resonance energy is close to 7 GeV in thecenter-of-mass system.The threshold dependence of A N on the hadron production angle in the center-of-mass system is alsopredicted. An example of the manifestation of the threshold dependence A N is the reaction p ↑ p ( A ) → π − X , for which the threshold angle is 74 o , since the test quark is the d -quark, which is heavier than the u -quark.An important advantage of hyperons is the ability to measure A N and P N through the angular distributionof their deck products, which allows the comparison of these observables with the model predictions.The rate of pion production in p - p collisions varies from 3 × s − at 23 GeV to 2 × s − at 7 GeV.In C + C and Ca + Ca collisions, it will be three orders of magnitude lower. The rate of production ofhyperons is two orders of magnitude lower than that of pions. Antihyperons are produced 5 to 10 timesless frequently than hyperons. Questions involved in the studies of the short-range nuclear structure and the understanding of the micro-scopic nucleon structure and dynamics of large-momentum transfer processes are delicately intertwined:the understanding of hard dynamics of two-body processes is also necessary for precision studies of theshort-range nuclear structure. Exclusive large t reactions like a d p → ppn process can address many of0these questions. The advantages of such a reaction are a good knowledge of the non-relativistic deuteronwave function and the ability to choose both kinematics sensitive to the dynamics of elastic N - N scatter-ing and the kinematics sensitive to the short-range deuteron structure.The collider kinematics presents anumber of advantages, as all particles in the considered reactions have large momenta and hence can beeasily detected. N - N interaction The simplest kinematics is production of two approximately back-to-back nucleons with large transversemomenta and a spectator nucleon with a longitudinal momentum p ∼ p d / ≥ 200 MeV/c [263, 264].In the impulse approximation this process corresponds to elastic scattering of the projectile proton offthe quasi-free nucleon of the target. In this kinematics soft rescatterings of the initial and final nucleons,which accompany the hard pp ( pn ) reaction, are large. The eikonal approximation, which accounts forrelativistic kinematics as dictated by the Feynman diagrams, reveals the important role played by theinitial and final state interactions in the angular and momentum dependences of the differential cross-section in the well-defined kinematics. The condition for the applicability of the generalized eikonalapproximation [265] is that the c.m. scattering angle and invariant mass of the two-nucleon system arelarge enough, so that − t , − u ≥ .It was suggested in [231, 232] that nucleons in the elementary reaction interact in small-size configu-rations with a small cross-section – the color transparency phenomenon. This effect is suppressed bythe space-time evolution of nucleon wave packets [266, 267]. However the effect of evolution is smallfor the deuteron, where typical distances between nucleons in the rescattering amplitude are ≤ p - p and p - n elastic scattering may be rather different [268].Hence it would be instructive to compare the channels where pp and pn are produced with a large p T .Experiments with polarized beams would greatly add to this program: due to a better separation ofkinematic domains where impulse approximation, double and triple scattering dominate, the studies of p ↑ d ↑ → pNN processes will allow one to investigate the spin structure of p - p and p - n elastic scatteringat large t (the latter is practically not known). Also, it would be possible to find out whether the strongdifference between the cross-sections of elastic scattering of protons with parallel and antiparallel spins[225] involves collisions of protons in configurations with sizes depending on the spin orientation.Moreover, it would be possible to study the effects of coherence in the channels, where the exchange bygluons in the t-channel is not possible, for example, pd → ∆ NN . In particular, it would be possible totest the effect of chiral transparency suggested in [269] – suppression of the pion field in the nucleonsexperiencing large − t scattering. It is established now that the dominant source of the short range correlations (SRC) in nuclei are proton-neutron correlations with the same quantum numbers as the deuteron and with a high-momentum tailsimilar to that in the deuteron (see review in [270, 271]). Hence the deuteron serves as a kind of thehydrogen atom of the SRC physics. Only after it has been tested experimentally that the approximationscurrently used for the description of the p - d reaction work well, it will be possible to perform high-precision studies of the SRC in heavier nuclei.It was demonstrated in Ref.[263, 264] that under specific kinematical conditions (in particular, low trans-onceptual design of the Spin Physics Detector 41verse momenta of slow nucleons in the deuteron rest frame) the effect of the initial and final state inter-actions can be accounted for by rescaling the cross-section calculated within the plane wave impulseapproximation. In this kinematics it would be possible to check the universality of the wave function –in particular, its independence on the momentum transfer in the elementary reaction. Such factorizationis expected to break down at sufficiently large − t and − u , where scattering involves interaction of nu-cleons in the small-size configurations (the color transparency mode) since the small-size configurationsare suppressed in bound nucleons with suppression growing with the nucleon off-shellness [267].Studies of the non-nucleonic configurations in the deuteron as well as relativistic effects in the scatteringoff a polarized deuteron are a separate matter of interest. In particular, it would be possible to search fornon-nucleonic degrees of freedom, like 6-quark, two ∆ isobars via a production reaction pd → ∆ ++ p ∆ − with ∆ ++ and proton back to back and ∆ − being slow in the deuteron rest frame. The structure of the lightest nuclei at short distances r NN < . q > (cid:125) / r NN ∼ c constitutes a fundamental problem in nuclear physics. One of the most important questionsis related to the search for the onset of a transition region from the meson-baryon to the quark-gluonpicture on nuclei. A definite signature for transition to the valence quark region is given the constituentcounting rules (CCR) [272, 273]. According the dimensional scaling, the differential cross-section ofa binary reaction at a sufficiently high incident energy can be parametrized as d σ / dt ∼ s − ( n − ) f ( t / s ) ,where n is the sum of constituent quarks in all participants, s and t are the Mandelstam variables. Manyhard processes with free hadrons are consistent with the CCR at energies of several GeV. The CCRproperties of the reactions with the lightest nuclei were observed in photodisintegration of the deuteron γ d → pn at E γ = ÷ He nucleus γ He → ppn , γ He → d p . Earlier data on the reaction dd → t p , dd → He n [274] and pd → pd , as was shown in Ref.[275], also follow the CCR behavior s − and s − , respectively, at surprisingly low energies of 0.5 GeV. Recently, the CCR behavior of thereaction pd → pd was observed in [276, 277] at higher energies. On the other hand, the reaction withpion production pp → d π + does not follow the CCR rule demonstrating the differential cross-section ∼ s − instead of s − . One possible way to explain this is a partial restoration of chiral symmetry at highenough excitation energy [278]. However, a systematic study of these properties of the reactions withthe lightest nuclei are absent. Therefore, it is important to know whether the reaction pn → d ρ followsthe CCR behavior and at what minimal energy there is a CCR onset. Assuming the model of the vectormeson dominance and taking into account the observed CCR behavior of the γ d → pn reaction, one mayexpect the ∼ s − dependence of the cross-section of the reaction pn → d ρ . Furthermore, a possiblerelation between the CCR behavior of the unpolarized cross-section and the spin observables of the samereaction are practically not known. The NICA SPD facility provides a good opportunity for this study,using polarized beams in p - p , d - d , and p - d collisions.The tensor A yy and vector A y analyzing power in d - p - elastic scattering obtained at 60 ◦ , 70 ◦ , 80 ◦ and 90 ◦ in the center-of-mass system versus transverse momentum p T [279, 280] demonstrates negative and posi-tive asymptotics, respectively. Note that the negative sign of A yy is observed also in the deuteron inclusivebreakup at a large p T [281],[282]. It would be interesting to extend the range of the measurements to alarger p T , where the manifestation of non-nucleonic degrees of freedom is expected. New precise mea-surements with small statistical and systematic uncertainties at energies higher than √ s ≥ d p elastic scattering. We also propose to measure different vector and tensor analyzing powers in d - p elastic scattering at the SPD energies.The measurements of d - p elastic scattering can be performed either with polarized deuterons and unpo-larized protons, or with unpolarized deuterons and polarized deuterons. The d - p elastic scattering events2can be selected, using cuts on the azimuthal and polar scattering angles correlations. The vector A y andtensor A yy and A xx analyzing powers will be measured simultaneously in the case of vertically polarizeddeuteron beams. The precision on the tensor ∆ A yy ∼ ∆ A xx ∼ ∆ A y ∼ ∼ ◦ ± ◦ at √ s ∼ p T ∼ c )for 30 days of the beam time at the luminosity L ≈ cm − s − . We expect ∼ 70% of the beam polariza-tion from the ideal values of polarization for different spin modes. The counting rate has been estimatedusing the d - p elastic scattering cross-section parameterization from Ref.[277]. The spin correlations canbe obtained in quasi-free d - p elastic scattering using d - d collisions. The study of charm production (hidden and open) and backward vector meson production at SPD willtake full advantage of the possibility of using polarized p , d beams (as well as heavier ions) in a kinemat-ical region where the data on cross-sections are scarce and polarization effects are mostly unmeasured.In general, threshold meson production in N - N collisions gives a deeper insight in the reaction mecha-nisms, as it is shown by the experimental programs at different proton accelerators, such as SATURNEand COSY. The production mechanisms for charmonium and D ( D ∗ ) mesons in nucleon-nucleon collisions is poorlyunderstood. Charm quarks do not preexist in the nucleon as valence quarks: how they are formed andhow they hadronize is an open question. To interpret the production and the propagation of charm inheavy-ion collisions as a probe of quark-gluon plasma (QGP), it is necessary to have a solid theoreticalbackground based on the understanding of elementary processes.Experimental data and theoretical studies of J / ψ production in different processes and of its decays exist:for a review, see [283], and for the most recent data collection – [284]. In the threshold region, the finalparticles are produced in the S -state and the spin structure of the matrix element is largely simplified.The effective proton size, which is responsible for charm creation, has to be small, r c (cid:39) / m c (cid:39) . m c is the c -quark mass, selecting small impact parameters [285]. The S -wave picture can,therefore, be applied for q ≤ m c , where q is the norm of the J / ψ − three-momentum in the reaction centerof mass (CMS). The momenta of the produced particles are small, but the mechanisms for the productionof charmed quarks must involve large scales. In Ref. [238], the near-threshold J / ψ − production innucleon-nucleon collisions was analyzed in the framework of the general model independent formalism,which can be applied to any reaction N N → N N V , where V = ω , φ , or J / ψ . Such reactions show largeisotopic effects: a large difference for pp - and pn -collisions, which is due to the different spin structureof the corresponding matrix elements at the threshold: σ ( np → npJ / ψ ) / σ ( pp → ppJ / ψ ) = . In Ref. [238] an estimation for the J / ψ production was suggested from the comparison of the cross-sections for the φ and J / ψ production in pp collisions. For the same value of the energy excess, Q = √ s − m − m V , taking into account the different phase space volumes, coupling constants for the decay V → πρ , monopole-like phenomenological form factor for the vertex π ∗ ρ ∗ V , with virtual π and ρ , onefinds the following simple parameterization for the cross-section, holding in the near-threshold regiononly: σ [ nb ] = . ( Q [ GeV ]) . (2.21)In Ref. [286], a parameterization of the exponential form σ [ nb ] = ae − bM J / ψ / √ ( s ) (2.22)was suggested. The values a = 1000 [nb], and b =16.7 GeV reproduce the experimental data above thethreshold rather well.onceptual design of the Spin Physics Detector 43In Fig. 2.20(a), the data for pp → J / ψ pp (red circles) and pA → J / ψ X (blue squares) are plottedfrom the recollections in Refs. [283] (filled symbols) and [284] (open symbols). Different symbolsdifferentiate J / ψ production in pp or (extrapolated from) pA collisions. The data, mostly collected atCERN, are reconstructed from the measurement using models and/or assumptions, and the compiled totalcross-section for J / ψ production may differ up to a factor of two. For example, the original reference forthe measurement from Protvino at √ s = . σ ( pp → ( J / ψ → µ + µ − ) X ) = . ± . σ = ± σ = ± . L = cm − s − , one expects 3 counts/hour for such a process witha cross-section of the order of 1 nb. This number is not corrected for the detector efficiency and re-construction with identification, for example, in a missing mass. The reconstruction of J / ψ through itsdecay into a lepton pair, that is, the preferred mode, requires two additional orders of magnitude, as thebranching ratio is ( (cid:39) . ± . ) − .In Ref. [238], it was shown that only one polarization observable, the J / ψ -polarization, is identicalfor p - p and p - n collisions: the J / ψ meson is transversely polarized, even in collisions of unpolarizednucleons.Open charm production, N N → N ¯ D Λ C ( Σ C ) , gives information on scattering lengths, effective radius,hadronic form factors, and coupling constants and is also related to the dynamics of charm creationin N - N , N - A , A - A ∗ collisions. The spin and isospin structure of the matrix element for the reactions N N → Λ C ( Σ C ) ¯ D N was derived for open charm in Ref. [292]. A detailed estimation of cross-sectionsand the expressions of the polarization observables can be found there. The existing information andestimations indicate that the near-threshold cross-section can be of the order of microbarns. The thresholdcross-section normalized at the lowest existing value is plotted in Fig. 2.20(b), where the insert highlightsthe threshold region. [GeV]s10 ) [ nb ] Y ( J / s - - SPD range [5] Y pp J/ fi pp +X [5] Y J/ fi pA [6] Y pp J/ fi pp +X [6] Y J/ fi pA This work Craigie 1978 (a) [GeV]s10 b ] m ) [ c ( c s - SPD range c c fi pp(pA) (b) [GeV]s 20 40 60 X ) [ m b ] r fi ( pp s - X r fi pp r pp fi pp s-2.1 r R(pp) s SPD range (c)Figure 2.20: (a) Experimental data on J ψ production in p - p (red circles) and p - A (blue squares) reactions,from the recollections in Refs. [283] (filled symbols) and [284] (open symbols). The solid line is thecalculation from Ref. [238]. (b) Total charm production in p - p and p - A collisions. The data are fromRef. [288]. The line is a threshold parametrization (see text). (c) Cross-section for ρ -meson productionin p - p collisions: inclusive (different symbols and colors from different experiments) and exclusive datafrom pp → pp ρ (black squares). The calculation from Ref. [289] shown as a black line. The red dashedline is the renormalization factor. The black dash-dotted line is the total pp cross-section. The first redpoint is the inclusive measurement from Ref. [290]. The blue line is the parametrization from Ref. [291].The green filled region represents the SPD range.4The charm production near threshold cross-section follows the behavior: σ [ µ b ] = . ( Q [ GeV ]) . (2.23)It is plotted in Fig. 2.20(b) over a collection of data from Ref. [288] reanalyzed from several experimentson charm production in p - p and p - A collisions at different facilities. We stress that these are difficultmeasurements, with low counting rates and huge backgrounds, but even setting upper limits will beimportant, as no data at all are present in the threshold region.The understanding of charm production (open or hidden) should unify different steps: parton-level hardprocess with production of cc pairs, after hadronization of cc into J / ψ or into charmed hadrons (mesonsand baryons), including the final state interaction of the produced charmed hadrons with other particles.The relatively large transferred momenta involved in most processes of J / ψ production in hadron-hadroncollisions allow one to treat the first step in the framework of perturbative QCD. But the applicability ofQCD is not so straightforward for the description of the c -quark hadronization. In this respect, precisedata collected in the SPD energy range will bring important information, especially if covering a widerange above the threshold. Larger counting rates are expected for light meson productions, since cross-sections are of the order ofmb. The ρ meson production in elementary collisions and on nuclei has been discussed, for example,in Ref. [293] and references therein. The ρ inclusive cross-section has been measured at differentaccelerators since the 70’s, mostly at CERN [294], and more recently by the HADES collaboration[290]. In Ref. [291], the following parametrization was suggested σ ( pp → ρ X ) = ( . ± . ) ln s − ( . ± . ) . (2.24)In Ref. [289], a specific kinematics, the backward light meson production in p - p or p - A collisions,was discussed in similarity to the ”quasi-real electron method”, where a hard photon is produced on thecollision of electrons on any target [295]. Two important characteristics have been proved for the electroncase: (i) the collinear emission probability has a logarithmic enhancement; (ii) the cross-section can befactorized in a term related to the probability of the meson emission with a given energy at a given anglefrom the beam particle, and a term related to the interaction of the beam remnant after emission on thetarget.In hadron case, the cross-section can be written as: d σ pT → h + X ( s , x ) = σ nT → X ( ¯ xs ) dW h + ( x ) , d σ pT → h X ( s , x ) = σ pT → X ( ¯ xs ) dW h ( x ) , (2.25)where h is a hadron, x ( ¯ x = − x ) is the energy fraction carried by the meson (the beam remnant). dW ρ ( x ) can be inferred using the QED result corrected by a renormalization factor in order to account for theemission of n real soft neutral pions escaping the detection.The prediction of the model for backward ρ -meson production in p p collisions is shown in Fig. 2.20(c)as a thick solid black line. The red dashed line is the renormalization factor, integrated over x . The total p - p cross-section is the black dash-dotted line. The blue line is the parameterization of the inclusive ρ cross-section from Ref. [291]). The available data are also shown as different symbols and colors forinclusive measurements and as black squares for exclusive ρ production. Backward production can be ofthe order of several mb, and, therefore accessible at SPD even with the initial lower luminosity. Collect-ing precise, systematic data should help to refine the models and is of great interest for the collision onheavy targets as well. Backward kinematics could constitute an original contribution to the field, offeringan alternative possibility to produce neutron beams.onceptual design of the Spin Physics Detector 45 The main experimental basis for clarification of the non-perturbative QCD (NPQCD) baryon structureis the baryon spectroscopy and the short-range nucleon-nucleon interaction. The more the nucleonsare overlapped during the collision, the higher sensitivity of the latter is to the NPQCD structure. Themaximum sensitivity can be reached in conditions of overlapping of the quark core of nucleons andsufficiently long time of this overlapping. Unfortunately, these conditions are practically not met in theavailable nucleon-nucleon experimental data: at relatively low energies the effective momentum transfersare not sufficiently high, and at high energies the contents of colliding nucleons diverge too quickly. Thiscircumstance explains why the region of the NN collisions at distances smaller than the radius of thenucleon core still remains unexplored. Access to this area is possible through the central collisions (CC)of the nucleons at adequate energies. The collisions are usually named central if the correspondingimpact parameter R is small, R < r core ≈ . √ s min = U rep ( ) + m N ,where U rep ( ) is the repulsive potential of the NN interaction at a zero distance, U rep ( ) ≈ √ s min ≈ . Λ χ SB ≈ . / π ( r core ) size.Decay of the (6q)* system leads to reconstruction of hadronic states in the form pp → ( q ) ∗ → N N Mesons , (2.26)where Mesons denotes the system of light mesons, predominantly pions.Peripheral N - N collisions proceed mainly via production of excited baryons N* in the intermediate state pp → { ( NN ∗ ) or ( N ∗ N ∗ ) } → N N Mesons (2.27)and have, in general, the final state similar to that in the central collisions (2.26). Therefore, in order todistinguish the central collision process (2.26) from the peripheral (2.27), one needs special centralitycriteria. According to [298, 299], there are two such criteria: A) using of the reaction NN → d ( ◦ ) Mesons , (2.28)where d ( ◦ ) is a deuteron emitted at the angle close to 90 ◦ ; B) smallness of the interaction region size r int < r core , where r int = / ( − Q ) / with Q = P − D / 2. Here P is the four-momentum of one of theinitial nucleons and D is the four-momentum of the final joined nucleon pair.Evaluation of feasibility of the experiments with the above centrality criteria shows [299] that at theexpected luminosity [30] the event rate at SPD could be significant.The following goals can be aimed at, in particular, in the experiments with central collisions:– study of known and search for new dibaryon resonances in the region of √ s ≈ . ÷ . or reaction NN → { pp } S ( ◦ ) Mesons , where { pp } S is a proton pair in the S state K + / π + ratio (a) and the inverse slope parameter T of transversemass spectra (b) at mid-rapidity. The NA61/SHINE results for inelastic p - p interactions are showntogether with the world data [303].– search for the predicted dominance of the σ -meson production [300];– search for the expected effects caused by the chiral symmetry partial restoration (drop of mass andwidth of mesons) [301, 302];– study of the energy dependence of the reaction (2.28) cross-section, which is sensitive to thestrength of the confinement forces and the value of the chiral symmetry breaking momentum;– first measurement of the analyzing power of the reaction (2.28) for transverse and longitudinalbeam polarization.It is worth to mention that experiments of this kind have never been carried out systematically. Thereexists a possibility of observing new unexpected effects that can induce new approaches in solving thefundamental problems of the non-perturbative QCD. p - p and d - d central collisions A study of the phase diagram of strongly interacting matter by varying interaction energy at centralcollisions of heavy ions is a primary goal of the NICA MPD experiment [218]. A structure in the energydependence of several observables in the range of √ s NN ≈ ÷ 12 GeV was predicted for the transition toa deconfined phase. However, recently NA61/SHINE found intriguing similarities in p - p interactions,where no deconfinement transition is expected [303]. It can be interesting to study this effect in p - p and d - d interactions in the first phase of SPD. These measurements can serve as an important crosscheck forthe results of NA61/SHINE and, potentially, results of MPD.The energy dependence of the K + / π + ratio and inverse-slope parameters of transverse-mass spectra (theso-called effective temperature T ) of kaons at mid-rapidity are shown in Fig. 2.21. The results for heavyion collisions are plotted for comparison. The K + / π + ratio in heavy ion collisions shows the so calledhorn structure. Following a fast rise the ratio has maximum at around 8 GeV and then settles to a plateauonceptual design of the Spin Physics Detector 47value at higher energies. Meanwhile, the collision energy dependence of the T parameter shows theso-called step structure at about the same value of √ s NN .The K + yield is proportional to the overall strangeness production and pions can be associated with thetotal entropy produced in the reaction. Thus, the K + / π + production ratio can be a good measure ofstrangeness-to-entropy ratio, which is different in the confined phase (hadrons) and the QGP (quarks,anti-quarks, and gluons). The K + is a proper observable for this measurement, because the anti-hyperonyield is small and the main carriers of anti-strange quarks are K + and K with (cid:104) K + (cid:105) ≈ (cid:104) K (cid:105) due toapproximate isospin symmetry. Thus, the K + (or K ) yield counts about half of all s ¯ s pairs produced inthe collisions and contained in the reaction products. In contrast, the fraction of strange quarks carriedby K − (or ¯ K ) and hyperons is comparable, which makes the structure in the K − / π − distribution lesspronounced.A hydrodynamic expansion model of the strongly interacting matter is used for description of A - A col-lisions. This model is replaced in p - p collisions by excitation of resonances or strong fields betweencolour charges of quarks and diquarks (strings) [304] which makes them qualitatively different. How-ever, the similarity of the transition energy in the central heavy ion collisions and the break energy in p - p interactions observed by NA61/SHINE provokes the question of whether there is a common physicsorigin of the two effects. This makes the precision measurement of the kaon-to-pion ratio in p - p and d - d interactions an interesting topic for the first phase of SPD, when the beam polarization is not availableyet. − and − A = Λ hypernuclei would be crucial for ourunderstanding of the role played by hyperons in nuclear matter [305–307]. While it is still controversialfor model calculations of such a four-body problem in the mode of weak binding [305, 308, 309],[310], [310, 311], we suggest that certain general properties arising from the weakly binding systemsinvolving the 2-body and 3-body bound-state energies provide guidance for a possible stability of ΛΛ n[312, 313]. Meanwhile, we propose a sensitive reaction process for the search for ΛΛ n in deuteron-deuteron scatterings, i.e. dd → K + K + ΛΛ n , (2.29)which is accessible at NICA. After all, it would rely on the experimental study to decide the dedicateddynamics for such an exotic system.The quantum numbers of the ground state ΛΛ n will favor J P = + , where the neutron pair and Λ pairhave spin 0, and namely, their spins are anti-parallel, respectively. At the same time, the total isospin is I = 1. Thus, the total wavefunction of the ground state is anti-symmetric under the interchange of thetwo nucleons or the two Λ .The most ideal reaction for producing ΛΛ n should be dd → K + K + + T , which is an extremely cleanprocess, since the background processes involving the K + K − productions become irrelevant. Here T isa doubly-strange tetra-baryon system. It makes the measurement of the missing mass spectrum recoilingagainst the K + K + pairs sensitive to the existence of any pole structure in the nn ΛΛ system.In Ref. [312], we have shown that the energy region above E cm (cid:39) . ΛΛ nwith the total cross-section of about 2.5 nb. Here, based on the same analysis, we make a rough estimateof its production rate at the kinematics of SPD.We estimate that the total cross-section at E cm = . L = cm − s − ,will drop by about one order of magnitude compared with the peak value of about 2 nb. Thus, the events8expected in one-year runtime (10 s) are N = σ total × L × t = . × cm − s − × s (cid:39) , (2.30)which is sufficient for establishing the state. Even though the detection efficiency will reduce the events,there will be tens to hundreds of events to count.Apart from the process of dd → K + K + ( n , n , Λ , Λ ) , it is also interesting to look at the proton-proton colli-sions, pp → K + K + ΛΛ , where the missing mass spectrum of K + K + also provides a clean and direct wayto search for the di-baryon ΛΛ , or to study the ΛΛ interactions. For the proton-deuteron collisions, thedouble K + channel is pd → K + K + n ΛΛ . The recoiled part of the double K + is n ΛΛ , which literally canproduce the exotic H di-baryon. A direct measurement of such a system would provide rich informationabout both ΛΛ and n Λ interactions [314, 315], [316, 317], [318, 319]. Nevertheless, notice that the finalstates have access to the nK + invariant mass spectrum. The exclusive measurement of this process canalso tell whether the light pentaquark state Θ + ( ) exists or not. Multiquark correlations in the collisions of particles and nuclei play an important role in the understand-ing of QCD. Multiquark correlation phenomena may be divided into three classes. The first one canbe related to parton distribution functions (PDFs) of the colliding hadrons and nuclei. In the leadingtwist approximation, in the nuclear PDFs there is a contribution at large x > 1, which is related with ob-jects known as fluctons [320], or few-nucleon short-range correlations [267]. Beyond the leading twist,two- or three-quark correlations in parton distributions of hadron and nuclei are related with higher twistcontributions. The second one is related to parton subprocesses. Namely, when multiparton scatteringoccurs, that is, e.g., when two partons from each colliding object scatter off each other simultaneously.The third class can be related to production of exotic multiquark resonance states, e.g., pentaquark andtetraquark states. Below one can find a brief possible outline for the studies at SPD, which can shed lighton all the three classes of multiquark phenomena mentioned above. Nuclear fluctons consist of nucleons compressed in distances comparable with nucleon size, so that theflucton with five or six nucleons could be considered as a cold dense baryon matter since the effectivenuclear density [321] would be as high as that in the core of neutron stars [270]. Fluctons are directlyconnected with cumulative hadron production in the nuclear fragmentation region [322, 323]. The fluc-ton approach [324], which is based on hard QCD-factorization and EMC-ratio constraints, predicts anextra nuclear quark sea, which has a rather hard momentum distribution: the extra nuclear sea x -slope isequal to the x -slope of the valence quarks. It leads to ”superscaling” for cumulative hadron productionat x > x -slope of all cumulative hadron distributions includingthe ”sea” ones [324, 325] are the same. The superscaling phenomenon was experimentally confirmed bythe ITEP group [326, 327]. In high- p T cumulative processes at the central region, other contributionsshould be added to the contribution of the nuclear PDFs at x > 1, such as the contributions from the PDFsof the other colliding object and possible intranuclear rescattering effects [328, 329]. Therefore, beyondthe nuclear fragmentation region, one should observe deviations from superscaling for cumulative pro-duction. Another aspect of multiquark correlations is two-quark correlations (diquark states) in baryons[330]. This is an important source of high- p T baryon production [331–333]. Being a higher-twist thediquark contribution can describe the strong scaling violation for baryon production in hard processes atSPD energies [332–334].onceptual design of the Spin Physics Detector 49 Measuring a few-particle correlation at SPD, one can study multiparton scattering processes [334], whichare related to 2D- and 3D- PDFs. It is also significant for production of multiquarks systems [334, 335]. Multiparton scattering [335] provides a unique opportunity to study production of various multiquarkstates, such as, e.g., in Refs. [336–338] at the SPD energies. For multiquark systems with possiblediquark structure [339, 340] it can be an issue of particular interest [334, 335].Near the thresholds of heavy quarks production, where relative velocities of final particles vanish, forma-tion of new type of resonances, such as J / ψ - N , is expected [341–344]. This question became especiallyinteresting after pentaquark observations at LHCb [345, 346] in the decay Λ b → J / ψ pK − .The enhancement effect was observed at the thresholds of the reactions e + e − → p ¯ p and e + e − → Λ ¯ Λ [347] and also in the decay J / ψ → p ¯ p γ [348]. Furthermore, the double spin correlation A NN measured inlarge angle ( ∼ ◦ ) p - p elastic scattering [227] demonstrates an enhancement near the strange ( √ s = . √ s = uuds ¯ suud and uudc ¯ cuud in the s -channel. SPD has a possibility of searching for such states.To summarize this section, SPD, together with the study of the inclusive particle production and few-particle correlations at different kinematic regions in p - p collisions, as well as in the cumulative processeswith light nuclei, has a unique opportunity to test various aspects of multiquark correlations: from thecold dense baryon matter to the exotic multiquark resonance production. Dark matter (DM) is a long-standing mystery in cosmology. It makes up more than 26% of the Universe[349], yet we still do not know its identity. Evidence of DM is mostly gravitational, e.g. the rotationcurves of spiral galaxies and the mass discrepancy in galaxy clusters [350]. The most favored candidatefor DM is the Weakly Interacting Massive Particles [351]. Different search approaches are employedto search for DM, each with its own underlying paradigm. The main approaches are collider searches,direct detection, and indirect detection. The latter includes astrophysical searches that seek to detectpotential anomalous signatures that are hypothetically produced via pair annihilation and decay of DMparticles, in the cosmic ray (CR) spectrum [351]. Naturally, these experiments track different signalcomponents. However, the chance of detection is thought to be higher for rare antimatter components,such as antiprotons. Recently, the AMS-02 experiment [352] has measured a cosmic antiproton flux withunprecedented precision over a wide energy range (from 1 to 450 GeV) [353]. However, we still cannotconfirm or rule out an antiproton signature in these measurements due to several sources of uncertainties[354].Secondary antiprotons are produced in collisions of primary CRs with the interstellar medium (ISM).To be able to detect any anomalous signal, we first need to subtract the flux of antiprotons produced bythese CR-ISM collisions. Even though there are several sources of uncertainty standing in the way ofpinpointing what this ordinary flux is—such as propagation parameters, solar modulation, and primaryspectra slopes—the most significant uncertainty, which ranges from 20% to 50% according to the energy,comes from antiproton-production cross-sections [354]. Almost 70% of the secondary antiproton yieldis produced in p - p collisions. However, the existing datasets for this production channel are incrediblyscarce, and mostly date back to before 1980. Moreover, all old datasets did not account for the hyperondecay or isospin effect [355]. As for other production channels, data are almost non-existent. Thus, if wewere to catch up with the accuracy of AMS-02 measurements, we would have to perform a new preci-0sion measurements of antiproton-production cross-sections in p - p collisions, as well as other productionchannels ( e.g. p - d , p - He , p - He , and He - He ). It is also hoped to study the contribution of differentproduction mechanisms, such as hyperon (namely, ¯ Λ and ¯ Σ − ) and neutron decays. The kinematic rangethat needs to be covered to achieve that has already been outlined [356].Preliminary MC studies [357, 358] show that at the SPD energy range, the production rate is > s − ,which would minimize the statistical uncertainty. In addition, the 4 π angular acceptance will allow SPDto access a wider kinematic range, in terms of transverse momenta, in comparison with fixed-target ex-periments operating at the same energy level. With a precise TOF (time-of-flight) system ( σ TOF ∼ K − / ¯ p separation can be achieved with a high purity of up to ∼ . c . SPD can also contribute tothe measurement of hyperon-decay contribution via reconstruction of secondary vertices [358]. To sum-marize, the SPD detector can make a sizable contribution to the search for physics beyond the standardmodel in terms of the astrophysical search for DM. hapter 3 Polarized beams The basic specification to the available polarization states and combinations is the following:– protons (possibly helium-3 ions at the second stage): vector polarization, longitudinal and trans-verse direction in respect to the particle velocity;– deuterons: vector and tensor polarization, vertical direction of polarization, longitudinal polariza-tion up to about a 4 GeV/ c momentum, and longitudinal polarization at discrete momentum ofabout 13 GeV/ c ;– possibility of colliding any available polarized particles: p - p with a luminosity up to 10 cm − s − and d - d , p - d , p - He , d - He with a luminosity of 10 cm − s − at the collision energy equivalentto p - p collisions;– possibility of asymmetric collisions should be considered as an option for the future developmentof the facility;– for essential reduction of a systematic error, a spin-flipping system is implemented, which allowsone to rotate the polarization direction with a step of 90 ◦ simultaneously in all bunches within aminimal time period.Feasibility of the technical implementation of the above-mentioned conditions is presented in Refs. [359–362]. The beam structure of polarized proton and deuteron beams at the first stage will correspond to the oneoptimized for the NICA heavy-ion mode. Some of the important for SPD operation parameters in thecase of a bunched beam are the following: number of bunches – 22, bunch length σ = 60 cm, colliderorbit length – 503 m, bunch velocity v ≈ c = × m/s, revolution time τ = . × − s, bunchrevolution frequency f ≈ . ∆ τ = . × − s, crossing angle at theSPD interaction point – 0 ◦ . The dependence of the p - p -collision luminosity on the energy and numberof protons is presented in Fig. 3.1 [30]. 512Figure 3.1: Normalized dependence of the luminosity L pp (the red curve and the left scale) and the beamintensity N p (the blue curve and the right scale) on the proton kinetic energy in the p - p -collision [30].As it is clear from the calculations, the luminosity level of 1 × cm − s − is reached at a bunchintensity of 10 polarized protons, whereas to obtain the level of 1 × cm − s − a multi-bunch stor-age mode should be used [363]. The average luminosity in this case is reduced due to the cycle timeefficiency. Basic factors for that are presented in the Table 3.1.The effectiveness (Figure of Merit, FOM) of a collider experiment with two polarized beams dependsnot only on the collision luminosity L , but also on the polarization degrees P and P of the collidingbeams [364]: FOM = LP P . (3.1)The statistical uncertainty of a measurement is proportional to 1 / √ FOM , so the FOM describes sensi-tivity of the experiment or resolution. The value of the FOM depends on a specific scheme applied forsuppression of depolarizing effects in each element of the accelerator complex such as the ion source,Table 3.1: Main parameters of the NICA operation cycle.Parameter Injected beam energy2 GeV 7.5 GeVNuclotron dipole field ramp up/down, T/s 0.6/1Dipole magnetic field, T 0.42 1.22Number of accelerated particles per pulse 7 × Number of cycles to store 2 × particles 2 × 285 (per both rings)Storage time, s 923.5 2291Other time factors, s ∼ ∼ ∼ ∼ ∼ ∼ cm − s − Polarized protons and deuterons from the SPI are first accelerated in the linac LU-20M and afterwardsare injected and accelerated in the Nuclotron to the specified energy and extracted to the collider via thelong transfer line. The main tasks at this stage are the following: i) preservation of the beam polarizationduring acceleration in the Nuclotron (and in the collider as well) and ii) polarization control in the collidermode. Moreover, it is necessary to adjust the polarization direction in the transfer line and the other pointsof the collider orbit. From the spin dynamics point of view, the NICA collider can operate in two modes, namely: in a DistinctSpin mode (DS-mode) and in the Spin Transparency mode (ST-mode) In the DS-mode periodic motionof the spin along the particle orbit is the only possible way, i.e. – stationary magnetic structure selects theonly one stable direction of the polarization vector in any point of the particle orbit and the non-integerpart of the spin tune is not equal to zero. In the ST-mode the direction of the spin vector is reproduced inany point at every turn, i.e. the magnetic structure of the accelerator ( or the storage ring) is transparentfor the spin – the non-integer part of the spin tune is equal to zero.The main difference between the DS- and ST-mode can be observed while manipulating the spin directionduring physics data taking. In the ST-mode, the spin motion is very sensitive to magnetic field changes,because particles move in the vicinity of the integer resonance. In the case use of the additional ”weak”magnetic field, the rotating spin at small angles Ψ ∼ T × m ,which would introduce negligible distortions to the closed particle orbit in order to produce the necessaryvariation of the spin angle in the NICA collider over the momentum range up to 13.5 GeV/ c . In the caseof the DS-mode similar procedure will require spin rotators based on a strong field, rotating the spins atthe angles of Ψ ∼ 1. Thus, in case of changing the polarization direction from the longitudinal to thetransverse one, it would be necessary to apply the transverse field with the total integral of 20 ÷ T × m ,which would result in strong distortions of the closed particle orbit. The amplitude of the distortionscan reach tens of centimeters at low energies. Thus, efficient polarization control of ions, especiallydeuterons, by means of quasi-stationary weak fields is possible only if the ST-mode is used.The configuration of the NICA collider with two solenoid snakes inserted into its straights allows one tooperate with polarized proton and deuteron beams in the both DS- and ST-modes (see Fig. 3.2).Figure 3.2: Possible operating modes with polarized beams at the NICA collider: a) without snakes, b)with one snake, c) with two snakes.4The stable polarization direction in the NICA collider is vertical at any point of the orbit in the NICAcollider, whereas the spin tune is proportional to the particle energy: ν = γ G , where G is the anomalouspart of the gyromagnetic ratio and γ is the relativistic Lorentz factor. The collider operates in the DS-mode practically over the total energy range, because γ (cid:54) = k / G , where k is an integer. At integer spinresonances γ G = k the collider operates in the ST-mode. After switching one of the two snakes on, thecollider operates in the DS-mode with the spin tune equal to half, whereas if two snakes are switched on,it operates in the ST-mode with the spin tune equal to zero. Different experiments are planned with polarized proton, deuteron, and helium-3 (in the future) beamsto identify and study various observables for multiple physics tasks: Drell-Yan, J / ψ , high- p T hadrons,exotic states, etc. The polarization control system should satisfy the following main conditions:– obtain both longitudinal and transverse polarization in the MPD and SPD detectors with a polar-ization degree not less than 70% and a polarization lifetime of not less than the beam lifetime;– provide collision luminosity of ∼ ÷ cm − s − over the particle momentum range from 2to 13.5 GeV/ c ;– provide the particle energy scan with a step of 1 ÷ ÷ 27 GeVand 0.3 MeV at lower energies. The deuteron beam at ∼ The ST-mode is enabled at the discrete energy points corresponding to the integer spin resonances: γ = k / G . For protons, the number of points corresponding to the ST-mode is 25 starting from theminimal energy E minkin = 108 MeV with a step of ∆ E = 523 MeV. There is only one point E kin = . MPD SPD = G = k SN SN Figure 3.3: General scheme of the polarization control at integer spin resonance points.is presented in Fig. 3.3. Two spin navigator insertions (SN) placed near MPD are used to stabilize theneeded polarization direction at any point of the collider ring, including the collision points, at injection,etc. A detailed scheme of the SN’s is presented in Fig. 3.4. The SN solenoids ( B z and B z ) generating aonceptual design of the Spin Physics Detector 55 MPD B x -B x Bx -B x -B z -B z B z -B z (or SPD) Figure 3.4: Detailed scheme of the spin navigator insertion in the collider in the ST-mode.longitudinal magnetic field ± B z are placed between the collider structural magnets that generate a radialfield ± B x (marked as 3 and 4) deflecting the beams to the collision plane of MPD.The scheme makes the ion polarization control possible in the vertical plane ( yz ) in MPD or SPD ( Ψ isthe angle between the polarization and the particle velocity vectors). The scheme provides the necessaryspin rotation for all discrete points over the NICA energy range provided the integral magnetic fieldreaches 0.6 T × m in each of the four solenoids. If we limit the field maximum to 1.5 T, the magneticlength of the SN solenoid unit will be 40 cm. The real relative scale of the SN solenoid (40 cm long), theradial dipole, and the distances between them are shown in Fig. 3.5.The scheme of the SN solenoids installation in the vertical plane together with the collider lattice ele-ments is presented in Fig. 3.6. The beam convergence angle in vertical plane, which is defined by thedipoles with a magnetic field transverse to the beam axis magnetic fields is a x = . 04 rad. The distancebetween the collider rings in the vertical plane is 32 cm. The distances between the closed particle orbitsin the vertical plane are ∆ y dip = L x a ≈ . ∆ y sol = ∆ y dip + L a ≈ 22 cm. at the output of thecommon radial dipole and at the exits of the control solenoids, respectively. 40 cm L = 263 cm L = 208 cm 40 cm 137 c m 137 c m Radial Dipole Radial Dipole Sol Sol Figure 3.5: Placement of the SN solenoids in the horizontal plane. y sol y sol = 22 cm y dip = 5.5 cm y dip Sol Radial Dipole Radial Dipole Radial Dipole Sol Figure 3.6: Placement of the SN solenoids in the vertical plane together with the radial dipoles. Two solenoidal snakes installed symmetrically relative to both MPD and SPD setups will provide imple-mentation of the ST-mode in the NICA collider (Fig. 3.7).6 MPD SPD S N S N SOL, SOL, SOL, SOL, Figure 3.7: Implementation of the ST-mo in the NICA collider.The configuration makes it possible to turn the spin in the vertical plane ( yz ) of MPD or SPD detector,whereas in the collider magnet arcs the polarization vector is moves in the median plane ( xz ) [365]. TheST scheme with two snakes provides a zero spin tune at any point of the particle energy. It is very impor-tant for optimization of the effective NICA operation at the highest possible luminosity of p - p collisions,due to a necessity of storing particles at an energy level that provides proper conditions for electron cool-ing of the stored beam. Only in this case it is possible to form particle bunches with a high number ofparticles and a high degree of polarization at low energy (about 1 GeV) with further acceleration up tothe experiment energy. The total integral of the longitudinal solenoidal field should reach 4 × 25 T × mper ring at a proton momentum of 13.5 GeV/ c and 4 × 80 T × m for deuterons, respectively. A distributedsystem consisting of short solenoids is possible, i.e. in the case of 6 T solenoids the total length of 4.2m is sufficient to form a half-length snake. It is possible to adopt the collider lattice structure optimizedfor a heavy ion beam for the case of the ST-mode at the protons mode over the total energy range. Weakcontrol solenoids barely distort the orbital motion in the collider, whereas strong solenoids of the snakeslead to a strong betatron tunes coupling. As the longitudinal field of the snakes changes proportionallyto the particle momentum, the collider magnetic optics stays adequate to the stable motion of a polar-ized particle during the beam acceleration phase. Matching the solenoids with the collider structure isprovided by means of a proper choice of the work point by means of structural KF (focusing) and KD(defocusing) quadrupole lenses. A possible scheme of the distributed snake (one half) based on short 6 Tsuperconducting (SC) solenoids is shown in Fig. 3.8. The elements are the following: SOL-SC solenoid,FFQ - final focus triplet of the collider, VB - structural dipole magnets; RB - bending dipoles with atransverse field making for converging bunches in the interaction point. K D K D K F K F K D K D K F VB VB RB RB FFQ IP SOL SOL SOL SOL SOL SOL Figure 3.8: Distributed snake (one half) based on short 6 T SC solenoids.onceptual design of the Spin Physics Detector 57 In the ST-mode precession of the polarization vector is caused by the field of solenoids, field imper-fections of the collider lattice elements, a finite beam emittance and depends on the power of the zerospin tune resonance. To stabilize the polarization during the acceleration process or when controllingthe polarization direction in the ST-mode it will be necessary to maintain the spin tune level caused bythe control solenoids much higher than the power of the zero spin tune resonance. The calculations haveshown that the level of 10 − for protons and 10 − for deuterons would be sufficient. These values imposelimitations on the minimum field integral in each of the weak control solenoids – 0.6 T × m. The spin flipping (SF) system makes it possible to carry out spin physics experiments at a much higherlevel of accuracy [366]. Being equipped with such a system, the SPD setup will have following advan-tages:– no need for reversing the polarization direction at the polarized ion source;– no need for bunch-to-bunch luminosity measurements and a bunch monitoring system;– the possibility of comparing collisions of bunches of any particle spin directions (vertical-longitudinal,vertical-radial, radial-longitudinal, etc.).The SF-system based on quasi-stationary fields is naturally implemented in the ST collider mode. Thepair of SN solenoids provides simultaneous influence on the polarization direction and the spin tune.Thus, the possibility of the spin tune stabilization during the spin flipping appears, preventing both zerospin tune and higher-order spin resonance crossing. The polarization degree will preserve an exponentialaccuracy, provided the field of the SN solenoids changes slowly. A typical flipping time is approximatelyestimated as 1 ms and 10 ms for the proton and deuteron, respectively. Enabling the SF-system in theDS-mode will require inserting an RF-module of a several MHz range and the field total integral of1 T × m, which is a rather challenging technical task. A unique possibility of online polarization control becomes available when the collider operates in theST-mode. Since the field ramp in the SN solenoids ( t change ∼ . t rev ∼ − s), any manipulations with the spin direction at the spintune will occur adiabatically and the polarization degree during the experiment time will be maintainedconstant with an exponent accuracy. The direction of the polarization vector will be a function of the SNsolenoids field and can be defined by means of the SN field measurements. Thus, the ST-mode makes itpossible to carry out experiments at the NICA collider at a new level of accuracy. As it was already mentioned, the stable polarization direction in the Nuclotron is vertical, and the spintune is proportional to the beam energy: ν = γ G , which definitely leads to the crossing of spin resonancesduring particle acceleration and, as a consequence, to resonance depolarization of the beam. There is noproblem with deuterons: the only one integer spin resonance at E kin = . E p π mm × mrad; quadrupolemisalignment errors – 0.1 mm; errors of angular alignment of the structural dipole and quadrupole mag-nets – 0.01 rad; and the relative error of the quadrupole gradients – 0.001. The resonances marked withred circles are dangerous and lead to the beam depolarization after their crossing. To keep the polariza-tion of the proton beam at a proper level, a partial Siberian snake based on a solenoid will be used. Twooptions have been considered: i) using a weak 5% snake with a field integral of 0.65 T × m, which cansave the proton beam polarization up to 3.4 GeV/ c and ii) using a 25% snake ( ∼ 12 T × m). The first oneis efficient if the collider operates in the ST-mode with two snakes and injection of the beam is providedat a low energy (around 1 GeV), whereas the strong enough snake used in the second option could savethe polarization over the total energy range in the Nuclotron and is suitable for the operation at integerresonances. The choice of energy points is limited to the points of integer resonances. The NICA collider with two solenoidal snakes will make the following configurations possible (see Table3.2) [369].If the snakes installed in SPD and MPD sections are switched off, the DS-mode with vertical polarizationat any point of the collider orbit is activated. Certain narrow energy gaps where the ST-mode at integerresonances exist, give possibility of having any direction of the polarization in both detectors. Afteronceptual design of the Spin Physics Detector 59Table 3.2: Polarization in the SPD and MPD interaction points in the DS- and ST-modes.Collider Spin Spin Polarization direction atconfiguration tune mode SPD and MPDWithout snakes γ G (cid:54) = k DS Vertical at SPD and MPDWithout snakes γ G = k ST Any direction at SPD or MPDWith one snake (SPD) 1/2 DS Longitudinal at MPDWith one snake (MPD) 1/2 DS Longitudinal at SPDWith two snakes 0 ST Any direction at SPD or MPDTable 3.3: Features of the operation with polarized protons and deuterons in the NICA collider.Collider Spin SF- Online Energyconfiguration mode system polarimetry energyWithout snakes DS No No NoWithout snakes ST Yes Yes NoWith one snake DS No No YesWith two snakes ST Yes Yes Yesswitching one of the snakes on, the collider will operate in the DS-mode with the spin tune 1/2. Thesnake transforms the spin motion completely, providing a stable longitudinal direction of the polarizationin the collider orbit section opposite the snake.If two dynamic solenoid snakes are switched on, the ST-mode is activated. The spin tune does not dependon the particle energy and is equal to zero, which gives a possibility to obtain any direction of polarizationat any point of the collider orbit. The features of the collider operation in the polarized modes are shownin Table 3.3.It is very important to implement the possibility of polarized beam acceleration in the NICA colliderwithout loosing the polarization degree. The problem of reaching the highest possible luminosity ofpolarized proton collisions is connected with the particle multi-bunch storage in the collider and electroncooling of the stored beam during the process. The optimal proton beam kinetic energy at the beaminjection into the collider is about 1 GeV [361, 370]. The proposed scheme of the ion polarization control in the NICA collider is adapted easily to the collidermagnetic optics at any modes of the polarization control. Significant advantages could be gained byusing the spin transparency mode. A polarization degree of about 70% is provided at the collision points.The polarization lifetime is expected to last for several hours that is comparable with the beam lifetime.We have not mentioned particular measurement and monitoring systems that should be designed at thestage of the technical project preparation, and namely: precise measurement of the luminosity, absolutepolarimeter based on a gas jet, targeting stations, etc. hapter 4 Detector layout The physics tasks presented in Chapter 2 impose general requirements on the concept of the Spin PhysicsDetector. Unlike the case of high-energy collisions where the collision energy √ s is a few orders ofmagnitude higher than a typical hard scale Q of the studied reactions, at the SPD energies for all theprobes planned to be used to access the gluon content of the colliding particles Q ∼ M J ψ ∼ M D ∼ p T γ min is just a few times less that √ s / 2. Therefore, one should expect quite a uniform distribution of all signalparticles (muons from the J / ψ decay, prompt photons, products of D -mesons decay, etc.) over thekinematic range. In other words, there is no preferable range in rapidity, which could be specified foreach probe for the optimal overall performance. Together with relatively small cross-sections of thediscussed probes, this fact leads one to a requirement of ∼ π coverage of the SPD setup.The Spin Physics Detector must have sufficient tracking capabilities and a magnetic system for spec-trometric purposes for the majority of the addressed physics tasks. It has to be equipped with a muonsystem thick enough for effective separation of muons and hadrons to make it possible to deal with thedecay J / ψ → µ + µ − . A precision vertex detector is needed for the recovering of the secondary verticesfrom the decays of D ± / mesons and other short-lived particles. An electromagnetic calorimeter ensurescapability to detect signal and background photons. A low material budget and general transparency ofthe setup should also provide favorable conditions for the photon physics. Hadron identification capabil-ity is needed for any physics task with protons and/or kaons in the final state, in particular, to enforce asignal-to-background ratio for D -mesons selection, and also to improve tracking at low momenta. Sincetiny effects are intended to be investigated, a triggerless DAQ system is planned in order to minimizepossible systematic uncertainties of the measurements.Strict limitations to the SPD detector layout arise from the external conditions, such as the maximalpossible load to the floor of the SPD experimental hall (1500 tons together with the lodgement andthe detector moving system). Together with the requirement to have the overall thickness of the muonsystem not less than 4 nuclear interaction lengths ( Λ I ), this limits the outer size of the SPD detector andthe size of the inner part of the detector. The location of the collider infrastructure, in particular, focusingelements, also defines the size of the SPD setup along the beam axis. More details could be found inChapter 3.The general layout of the SPD is shown schematically in Fig. 4.1. The detailed description of eachsubsystem could be found below. Table 4.1 brings together the elements of the SPD physics programand the requirements to the experimental setup. We would like to emphasize here that the most partof the SPD gluon program can not be performed at MPD [218], another detector at the NICA collider,60onceptual design of the Spin Physics Detector 61optimized for operation at a high multiplicity of charged tracks and relatively low luminosity.Figure 4.1: General layout of the Spin Physics Detector. All dimensions are in millimeters.2Table 4.1: Required setup configuration for each point of the SPD physics program. (+++) - absolutelyneeded, (++) - extremely useful, (+) - useful, (-) - not needed.Program Vertex Straw PID Electromagnetic Beam-beam Rangedetector tracker system calorimeter counter systemGluon content with:charmonia + ++ + ++ + +++open charm +++ ++ ++ + + ++prompt photons + + - +++ + -SSA for π and K + ++ +++ ++ + -Light vector meson production + ++ - + + -Elastic scattering + ++ - - +++ -¯ p production + ++ +++ ++ + -Physics with light ions ++ +++ + ++ ++ + The SPD Magnetic System (MS) should satisfy the following criteria:– minimization of the material inside the detector inner part;– a magnetic field integral of (1 ÷ 2) T · m along the particle tracks, whereas the peak value of thefield should be limited to 0.8 T over the straw tracker volume;– minimization of the total weight, the cross-section of the current coil (coils), and the overall amountof the MS material, i.e. the MS should have perfect mechanics.Several options of MS’s were considered:1. Solenoid – a uniform multi-turn coil placed between the ECal and the muon range (RS) systems;2. Toroidal MS (inside ECal): 3 × × turns and generatethe necessary magnetic field in the detector volume. Some of the SPD 6-coil MS are presented in Table4.2 in comparison with the other detectors.4 Figure 4.2: Geometrical model of the 6-coil magnetic system. All dimensions are in millimeters.(a) (b)Figure 4.3: Field calculation results: (a) B z as function of r , z ; (b). B z as function of z at different r . Alldimensions are in millimeters. A beam pipe separates the detector and high vacuum of the accelerator. It must be mechanically sturdy onthe one hand and thin enough in terms of the number of radiation lengths to minimize multiple scatteringand radiation effects, on the other hand. The diameter of the beam pipe is a compromise between theradial size of the beams and the requirement to put coordinate detectors as close to the interaction pointas possible for better reconstruction of the primary and secondary vertices. A beryllium beam pipe withouter diameter of about 6 cm with 0.5mm wall thickness is proposed to be used.onceptual design of the Spin Physics Detector 65(a) (b)Figure 4.4: Magnetic field in the inner part of the SPD setup (a) z - r section; (b) x - y section at z = ∼ ∼ ∼ ∼ ∼ ∼ ∼ The SPD Vertex Detector (VD) is a silicon-based part of the spectrometer responsible for precise de-termination of the primary interaction point and measurement of secondary vertices from the decaysof short-lived particles (first of all, D -mesons). The Vertex Detector is divided into the barrel and twoend-cap parts (Fig. 4.6). Two different versions of the VD design are discussed: i) five layers based ondouble side silicon detectors (DSSDs) and ii) three inner layers based on Monolithic Active Pixel Sensors(MAPS) and two outer layers based on DSSDs. The VD Barrel consists of five layers based on doubleside silicon detectors (approximately 4.2 m ). The end-cap regions consist of five disks each (approxi-mately 0.4 m ). The VD Barrel covers a radius from 96 to 500 mm (Fig. 4.7). All five cylindrical layersare set with rectangular two-coordinate silicon strip detectors and give information on the coordinates ofthe tracks ( r , φ , z ) (which makes it possible to measure a point in each layer). The end-cup regions detectparticles in the radial region between 96 mm and 500 mm. Each of the five disks is set with a DSSD with6 Figure 4.5: SPD beam pipe inside the setup. All dimensions are in millimeters.Figure 4.6: General layout of the SPD Vertex Detector.concentric ( r ) strips and radial ( φ ) strips. The VD has a length of about 1.1 m and covers the region ofpseudo-rapidity up to | η | < . 0. Each DSSD has a 300- µ m thickness and a strip pitch in the range from95 µ m to 281.5 µ m. The DSSDs are assembled into detector modules by two detectors per module,forming 18-cm long strips. The detectors and the front-end electronics boards (FEE-PCB) are connectedvia low-mass polyimide microcables and assembled on the extra-light carbon fiber mechanical supportswith a cooling system in the similar way as it was done for the ALICE outer barrel (see Fig. 4.10). Therelevant numbers for the barrel part of the VD for the DSSD configuration are presented in Tab. 4.3.onceptual design of the Spin Physics Detector 67 η = 1.5 η = 1 η = 0.5 η = 0 η = 2 ∅ 64 1106.6553.3 369.2 185.7600 50 90 130 170 210 (a) Beam pipe layerlayerlayerlayerlayer (b)Figure 4.7: Longitudinal (a) and transversal (b) cross-sections of the barrel part of the Vertex Detector.All dimensions are in millimeters.From the general conditions of the SPD setup the VD performance requirements are i) geometry close to4 π ; ii) track reconstruction efficiency for muons greater than 99% at p ≤ 13 GeV/ c (for 0 ≤ | η | ≤ . σ r , φ < µ m, σ z < µ m. Thelifetime of the Vertex Detector is required to be not less than 10 years of NICA running.8 Table 4.3: Relevant numbers for the barrel VD (DSSD configuration).Parameter Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 TotalN DSSD /module 2 2 2 2 2N modules /ladder 2 4 4 6 6N ladders /layer 6 10 14 19 23 72N DSSD /layer 24 80 112 228 276 720N chip /module 10 10 10 10 10N chip /layer 120 400 560 1140 1380 3600N channel /layer 15360 51200 71680 145920 176640 460800 A ( 2 : 1 )A , m a x Capton cable Si - det FEE Figure 4.8: Concept of the barrel DSSD module. All dimensions are in millimeters.Figure 4.9: Conceptual layout of the barrel ladder.onceptual design of the Spin Physics Detector 69Table 4.4: Possible ASIC readout solution for the Vertex Detector.ASIC APV25 VATAGP7.3 n-XYTER TIGERNumber of channels 128 128 128 64 (128)Dynamic range -40fC – 40fC -30fC – 30fC Input current 10 nA, 1–50fCpolarity + and − Gain 25mV/fC 20 µ A/fC 10.35mV/fcNoise 246 e − +36 e − /pF 70e − +12 e − /pF 900 e − at 30pF 2000 e − at 100pFPeaking time 50ns 50ns/500ns 30ns/280ns 60ns/170nsPower consumption 1.15mW/ch. 2.18mW/ch. 10mW/ch. 12mW/ch.ADC No No 16fC, 5 bit 10-bitWilkinson ADCTDC No No 10-bitWilkinson ADC The concept of the barrel DSSD module is shown in Fig. 4.8. The module consists of two silicondetectors wire bonded strip to strip for the p + side (to reduce the number of readout channels), glued tothe plastic frame and connected with two front-end electronic boards via a low-mass polyamide cable.The Silicon Detector is made using a planar double-side technology based on the n-type conductivity6-inch float-zone Silicon wafers (produced by ZNTC, Zelenograd, Russia). Its size is 63x93 mm and itsthickness is 300 µ m thickness. The pitch for the p + side is 95 µ m and for the n + side 281.5 µ m. Thenumber of strips is 640 and 320 for the n + and p + side, respectively. The stereo angle between the stripsis 90 degrees. The excepted spatial resolution for such a detector topology is pitch p ( n )+ / √ = µ m for r − φ and r − z projections, respectively. As mentioned before the barrel DSSD modulecontains two DSSDs ( p + strips wire bonded strip to strip) and has 640 strips at each side.To bring the front-end electronics out of the tracker volume, two thin polyimide cables with aluminumtraces (for each side of the module) will be used. The cable consists of several layers: signal, perforatedor solid dielectric (polyimide), and a shielding layer. Cable pins were designed for the tape-automatedbonding with the detector and the pitch adapter sides. The maximum cable length is 60 cm, and the totalthickness of all cable layers is less than 0.15% of X .Since the DSSDs have a DC topology, it is necessary to supply bias voltage to the detector and electricallydecouple the DC current from the ASICs electronics inputs. For this purpose, an integrated RC circuit(sapphire plates with Si-epitaxial layer Silicon On Insulator (SOI)) Pitch Adapter (PA) will be used foreach side of the module (produced by ZNTC, Zelenograd) designed with different topologies for eachside. After the pitch adapter the detector signal goes to ASIC. Table 4.4 shows a possible ASIC readoutsolution. The optimal choice should be done after the ongoing R&D. The concept of the barrel DSSD ladder is shown in Fig. 4.9. The silicon modules are laying on a carbonfiber support from center to edge. The detectors are connected with the FFE via thin low-mass cables.The front-end electronics is located at the edges of the ladder and is placed in the conical caves as shownin Fig. 4.10 to provide a connection to the voltage supply, DAQ, and the cooling ASIC chips subsystems.0Figure 4.10: Schematic exploded view and cross section of the Outer Barrel module similar to ALICEouter barrel design. To improve the spatial resolution of the vertex reconstruction the two inner layers could be replaced by theMAPS-ALPIDE detectors, designed and produced for the ALICE experiment basing on the TowerJazztechnology [372]. Each chip has the pixel size of 29 µ m × µ m . The scheme of a MAPS pixel is shownin Fig. 4.11. One of the options of the MAPS sensors layout could be based on the current ITS2 InnerBarrel design of ALICE [372], that has achieved the record minimal level of material budget and providesprecise determination of D -meson decay vertices, (see Fig. 4.12). The impact of such replacement to thevertex reconstruction and, in turn, to the proposed physics with D -mesons is discussed in Chapter 9. Themore advanced option like ALICE ITS3 [373] could be also considered for the inner layers of SPD.Figure 4.11: Scheme of a MAPS pixel [372].onceptual design of the Spin Physics Detector 71Figure 4.12: ALICE ITS2 Inner Barrel design [372]. Preliminary cost estimation for the DSSD and DSSD+MAPS configurations of the Vertex Detector ispresented in Tab. 4.5. The total cost of the detecting elements in both cases is about 9.5 M$. As for theFFE, very rough estimation for both variants gives 6.5 and 7 M$, respectively.Table 4.5: Cost estimation for the VD configurations (DSSD / DSSD+MAPS).Layer Number of Number of Barrel End-cup Cost Costsensors ASICs area, m area, m barrel, M$ end-cup, M$1 36 / 440 180 / 0 0.22 / 0.20 0.38 / 0.38 0.40 / 0.36 0.69 / 0.692 80 / 840 400 / 0 0.47 / 0.38 0.86 / 0.693 112 / 1736 560 / 0 0.66 / 0.78 1.20 / 1.424 228 / 228 1140 / 1140 1.34 / 1.34 2.43 / 2.435 368 / 368 1840 / 1840 2.16 / 2.16 3.92 / 3.92Total 824 / 3612 4120 / 2980 4.85 / 4.86 0.38 / 0.38 8.81 / 8.82 0.69 / 0.69 The purpose of Straw Tracker (ST) is to reconstruct tracks of primary and secondary particles with highefficiency, to measure their momenta with high precision based on a track curvature in a magnetic field,and participate in particle identification via energy deposition ( dE / dx ) measurement. A spatial resolutionof ST is expected to be about 150 µm and the drift time is about 120 ns for tubes of 1-cm diameter.The detector is planned to be built of low-mass straw tubes similar to the ones used in many modernexperiments such us NA62 [374], COMET [375], SHiP [376], Mu2e [377], COMPASS [378, 379], andNA64 [380]. The technology is quite well established and a detailed R&D is not needed. The concept ofthe SPD ST is similar to the ATLAS TRT [381–383] and PANDA [384] straw trackers.2 The straw manufacturing process in general follows the procedure developed for NA62 [385]. The tubesare manufactured of PET foil 36 µ m thick, coated on one side with two thin metal layers (0.05 µ m ofCu and 0.02 µ m of Au) in order to provide electrical conductivity of the cathode and to improve the gas(Ar+CO mixtute) impermeability. NA62 has demonstrated that these straws can be operated in vacuum[374]. A leak rate of only about 7 mbar/min for the whole detector (7168 straws) was measured [385].A few straws with a diameter of 10 mm were used for dedicated mechanical tests. They were cut in 20segments of about 25 cm long and tested under overpressure until the breaking point. The other strawswere cut to 5.3 m and the cut ends were preserved for further analysis. The breaking pressure was foundto be 9 bar on average and no one sample broke under 8.5 bar. The quality control procedure was thesame as for NA62 straws. During the ultrasonic welding process the seam quality was verified by adigital microscope (recorded to file for each straw). Furthermore, the seam quality was checked by anoperator in real time. All 50 tubes produced so far have good seams.Several measurements and tests are performed post-fabrication. The seam width and straw inner diameterare measured by an optical method. The cathode electrical DC resistance is measured. The elongationand breaking force are both measured on the test samples (cut straw ends). The straws undergo a long-term overpressure test with temporary end-plugs glued into both ends of each straw. An overpressuretest to ∆ P ≈ ∆ P ≈ + + + + + + + + + - - - - - - - +HV e - Earlier signal propagation Later signal propagation Frontend digitizer board Waveform, time difference ADC TDC TDC Readout Controller (b)Figure 4.13: Individual straw tube of the SPD ST (a). Schematic representation of a 2-side straw readout(b). The mechanical construction of the SPD Straw Tracker is based on engineering solutions which werealready efficiently applied in ATLAS and PANDA experiments. The ST consists of three parts: a barrelpart and two end-caps. The barrel has the external radius of 850 mm and the internal hole with radius of270 mm. It is subdivided azimuthally into 8 modules, each with 30 double layers of straw tubes. Eachtube has a diameter of 10 mm. Four modules are fixed together by a carbon fiber frame, thus forming apair of independent semi-cylinders. This design provides a possibility to assemble and disassemble theST in the presence of the beam pipe.onceptual design of the Spin Physics Detector 73Figure 4.14: Layout of the barrel part of ST which shows 8 modules with 30 double-layers of straw ineach capsule. Straws of adjacent double layers oriented perpendicular to each other. All dimensions arein millimeters.Each module is enclosed in a 400- µ m carbon fiber capsule. The capsule provides the positioning ofindividual straw tubes with 50 µ m accuracy. One side and two ends of the capsule have 5 mm holeswhere straw end-plugs will be fixed. FE electronic boards which will be connected to these plugs willadditionally serve as capsule covers, thereby isolating the inner volume from the external environment.Long straws oriented along the beam line will be read out from both ends in order to obtain an additionalcoordinate along the straw axis via mid-time calculation as shown in Fig. 4.13 (b). While short strawsoriented perpendicular to the beam line will have electronics only on one side. Each capsule containsabout 1500 tubes with parallel and 6000 tubes with perpendicular to the beam orientations. The totalnumber of electronic channels per capsule is 9000. Thus, the total number of channels in the barrel partof ST is 72 000.The rigidity of the structure is assured by the low overpressure of gas inside the tubes and their fixationinside the capsule volume. The anode wire positioning accuracy is achieved by the wire fixation in thecarbon fiber covers. The capsule also serves for thermostabilization of the gas mixture inside detectorvolume and for protection of the straw surface from humidity. The layout of the barrel part of the StrawTracker is shown in Figure 4.14.Each end-cap part of ST comprises 3 modules along the beam axis. Each module consists of 4 identicalhexadecimal cameras (for measurement of the 4 coordinates: X, Y, U and V). By construction, thecameras are divided into halves. Each module has a technological hole Ø = 160 mm for the beam pipe.The mechanical support is provided by carbon fiber frames. The total amount of electronic channels inboth end-caps is 7200. The layout of one straw end-cap is shown in Fig. 4.15. The Straw Tracker is designed for precision measurements which require excellent spatial, angular andtiming resolutions to meet physics goals. Moreover, an amount of charge collected by anode will be usedto identify particles. In view of this, requirements for the straw readout electronics are the following:– to measure time and energy deposit ( dE / dx );– time resolution not worse than 1 ns for the drift measurements and 0.1 ns for the case of the 2 sidereadout to determine the coordinate along the wire;4Figure 4.15: Layout of one end-cap part of the ST. It includes 3 modules along the beam axis where everymodule consists of 4 identical hexadecimal cameras (X, Y, U and V). All dimensions are in millimeters.– low threshold to identify a charge from primary electron-ion clusters;– dynamic range of about 1000;– low power consumption to reduce heating.Two options of electronics are under consideration now. The first one is the front-end electronics de-signed for the NA64 experiment [380]. It is a 32-channel amplifier-discriminator board based on AST-1-1 chip, developed by the Institute of Nuclear Problems of the Belarusian State University. The am-plifier sensitivity is K=100 mV/ µ A (20 mV/fC). The discriminator threshold is adjustable in the range(2 ÷ 20) fC. The delay of LVDS output signal is 6 ns. The amplifier has an ion tail compensation (BLR).The LVDS output signals are sent to the 64-channel time-to-digital converters (TDC).The second option is to take the front-end electronics designed for DUNE experiment [386], which isbased on 64 channel VMM3 a custom Application Specific Integrated Circuit (ASIC), developed byBNL for the LHC experiments at CERN. A low power consumption and a low per-channel cost (about0.9 $/ch) of the chip are valuable futures for a compact multichannel detector readout. Each channel hasADC and TDC circuits. Fast serial outputs are used for readout. Each of the 64 ASIC channels is highlyconfigurable and combines a preamplifier shaping circuit with an ADC to allow independent digitizationof triggered input signals. These digitized signals can be output with four different data readout options,which provides flexibility to accommodate different detector requirements and data rates. Each inputchannel has an individual preamplifier and dedicated digitizing logic. Each channel can be configured toaccommodate a variety of input signal sizes, polarity and capacitance. The preamplifier shaping circuitcan be configured to use one of four different peaking times (25, 50, 100, and 200 ns) and eight gainsettings (0.5, 1, 3, 4.5, 6, 9, 12, 16 mV/fC). A channel-specific discriminator triggers on input signalsabove a configurable threshold to initiate digitization of the amplified pulse with a 10-bit Analogue toDigital Converter (ADC). Discriminator thresholds are adjusted by a global 10-bit Digital to Analogueonceptual design of the Spin Physics Detector 75Converter (DAC) with additional channel-specific 5-bit trimming DACs. These features allow the VMM3to satisfy the SPD TR requirement of measuring the collected charge and signal time in each channel. Anequivalent noise charge of better than 1000 e − can be achieved with input capacitance less than 100 pF.On the basis of this performance, it is reasonable to expect that VMM3 can meet the SPD TR requirementof low charge threshold for the straw tube gain greater than G = and the input capacitance less than100 pF.It was shown that the time resolution better than 1 ns was obtained for 6 pF input capacitance andinput charge greater than 1 fC. A much better time resolution can be achieved for higher input signalamplitudes. This suggests that VMM3 can satisfy the SPD TR requirements for the time resolution withsufficiently high gain and appropriate input capacitance. The channel thresholds are individually adjustedby a global 10-bit DAC and an individual channel 5-bit trimming DAC. This suggests that the requiredlow charge threshold can be achieved. Presently, we estimate the cost of the SPD ST development and construction at 2.4 M$. The calorimeter should meet the criteria imposed by the physical goals of the SPD experiment of dif-ferent nature and importance. The most important criteria arise from the physical requirements to theaccuracies of measurement of energies, trajectories, and timings of photons and electrons. Technologicalpossibilities of modern experimental physics should be taken into account when choosing the calorimetersetup. Price factors should also be considered to ensure the feasibility of the project. High multiplicityof secondary particles leads to a requirement of high segmentation and dense absorber medium witha small Moli`ere radius. It is needed in order to have sufficient spacial resolution and a possibility toseparate overlapping showers. The transverse size of the calorimeter cell should be of the order of theMoli`ere radius. A reliable reconstruction of photons and neutral pions is possible only for small showeroverlaps. Occupancy should not exceed 5%, so that it is possible to determine photon reconstructionefficiency with high precision.The SPD experiment imposes the following requirements on the calorimeter characteristics:1. reconstruction of photons and electrons in the energy range from 50 MeV to 10 GeV;2. energy resolution for the above-mentioned particles: ∼ / √ E [ GeV ] ;3. good separation of two-particle showers;4. operation in the magnetic field;5. long-term stability: 2 ÷ 3% in a six month period of data taking.The energy range requirement follows from the kinematic range of secondary particles, which are pro-duced in a collision of protons with energy up to 27 GeV and emitted into 4 π solid angle. Good energyresolution is required for identification and quantitative measurement of single photon and neutral pionenergies. Good two-particle separation is needed to separate photon showers from the π decay in orderto suppress background events in measurements with prompt photons. Long-term stability is necessaryfor polarization measurements featuring π reconstruction in the calorimeter, especially in the end-caps.Calorimeter instability may result in false asymmetry values. While it is essential to meet the physicsrequirements imposed on the calorimeter design, one should also take into account the cost estimate and6the technical feasibility when choosing its granularity, as the larger number of cells leads to larger costsof the manufacturing technology and readout electronics. The SPD electromagnetic calorimeter is placed between the Range System and the magnet coils, asshown in Figs.1.2 and 4.1. It consists of a barrel and two end-caps, covering a 4 π solid angle. The outerdimensions of the calorimeter are determined by the inner size of the muon system. The thickness of thecalorimeter is determined by the required thickness of the active part and the size of the readout blockconsisting of photodiode and amplifier boards, as well as by the size of the flexible part of the fibers.For efficient absorption of electrons and photons with energies up to 10 GeV, the calorimeter thickness,which is defined by the number of sampling layers, should be at least 18 ÷ 20 X in terms of radiationlengths X . For the sampling structure of a 1.5-mm scintillator and 0.5-mm lead, 200 layers are requiredfor a thickness of 18.6 X , which sets the length of the active part to 400 mm. The period of the structureis set to 2 mm in order to avoid optical contact between the lead and the scintillator, and because ofthe connection technique involving special ”Lego” spikes. The flexible parts of the fibers take up 8 cm.The transverse size of the calorimeter cell should be of the order of the effective Moli`ere radius of thecalorimeter medium, which is, in its turn, defined by the scintillator-to-lead sampling ratio. The selectedstructure has a Moli`ere radius of 2.4 cm. The separation efficiency of two photons with energies from200 MeV to 500 MeV depends on the cell size and reaches a plateau at a cell size of 40 mm, as wasdetermined in the MC simulation. Therefore, we have selected 40 mm cell granularity for both barreland end-caps. Cells in the barrel part of the calorimeter have trapezoidal shape in the azimuthal directionto minimize the gaps between the modules. The vertex angle of the trapezoid equals 1.58 ◦ .A schematic drawing of the calorimeter, which is limited in size by the muon system, is shown inFig.4.16(a). The limits of the calorimeter zone are shown as a thick line. Holes of the size 160 × in the centers of the end-caps for the beam pipe are shown.The inner size of the barrel part is limited by radius of the magnetic coils, whereas the outer size islimited by the dimensions of the muon range system. The thickness of the active part is 400 mm, whichcorresponds to 18.6 X . This corresponds to 200 layers of the scintillator and lead of 1.5 mm and 0.5mm width.The barrel part of the calorimeter has 19712 cells of trapezoidal shape in the azimuthal direction with avertex angle of 1.58 ◦ , and a front face size of 34 mm, and rectangular shape in the direction along thebeam axis with a size of 40 mm (Fig.4.16(b)). The total weight of the barrel part is 40 tons.Each end-cap (one is shown in Fig.4.17) consists of 4 sectors of 1308 cells per sector. The cell cross-section is 40 × 40 mm . There is a hole for the beam pipe in the center of each end-cap. The hole hasa size of 160 × 160 mm , which is equivalent to 16 cells. Each end-cap has 5232 cells. The thicknessof the active part of an end-cap cell is 440 mm (Fig.4.16), which corresponds to 20.4 X . The weight ofone end-cap is 14 tons. The total weight of two end-caps is, therefore, 28 tons. In total, there are 10464cells in both end-caps, each with dimensions of 40 × × 440 mm .The total weight of the calorimeter is 68 = 40 + 28 tons composed of the barrel and two end-caps. Thetotal number of cells of size about 40 × 40 mm is 30176 = 19712 + 10464 for the barrel and the end-caps,respectively.A possibility to use another type of modules in the central part of the end-cups in order to improve energyand spatial resolution of the calorimeter for energetic photons is also under discussion.onceptual design of the Spin Physics Detector 77(a)(b)Figure 4.16: (a) Barrel and end-cap parts of the calorimeter. The holes of size 160 × 160 mm for thebeam pipe can be seen in the centers of the end-caps. (b) Schematic drawing of a cross-section of thebarrel part of the calorimeter. It is sectioned into 224 azimuthal sectors (8 sections, 28 cells per section)with vertex a angle of 1.58 ◦ . All dimensions are in millimeters.8Figure 4.17: The end-cap part of the calorimeter consists of 4 sectors, 1308 cells each. In total, there are5232 cells in one end-cap, and 10464 cells in both end-caps. All dimensions are in millimeters. The initial version of the module, which was made for testing purposes, consisted of alternating layersof polystyrene scintillator and lead with a thickness of 1.5 mm and 0.3 mm, respectively. The selectednumber of layers is 220, setting the number of radiation lengths to 12.6 X . The lead plates are intendedto absorb the particle energy and develop an electromagnetic shower, whereas the scintillator platesproduce an amount of light proportional to the energy of particles. The properties of the absorber andthe scintillator define the Moli`ere radius, which is equal to 3.5 cm for the selected structure. The energyresolution for 1 GeV photons is assumed to depend on the calorimeter sampling fraction and is expectedto be 4.15%. The test results of the present work are given for this particular design of the module.The scintillator plates are made of polystyrene beads with an added luminophore admixture of 1.5%p-Terphenyl and 0.05% POPOP (C H N O ) [387]. It has scintillation time of about 2.5 ns and lightoutput of 60% of anthracene, which are good results. The radiation hardness of the scintillator is suf-ficient for radiation doses up to about 10 Mrad, which is important for operating the calorimeter in theradiation field of secondary particles in the vicinity of the interaction point.The luminophore admixtures re-emit the energy of excitations in polystyrene in the form of visible light.The first admixture (p-Terphenyl) emits light with a wavelength of maximum emission at 340 nm. Thislight is absorbed by the second admixture (POPOP) and is re-emitted into a spectrum with a wavelengthof maximum emission of 420 nm, which is seen as a light blue glow.The light from the scintillator plates is gathered using wavelength shifting fibers (WLS) [388]. Fibers oftype Y-11(200) manufactured by KURARAY are used. The fibers absorb the light from the POPOP andonceptual design of the Spin Physics Detector 79Figure 4.18: Photo of a single module consisting of 4 cells with 220 layers of the scintillator and theabsorber with a thickness of 1.5 mm and 0.3 mm, respectively. Four bundles of fibers for guiding thelight to the multi-pixel photon counters (MPPC) can be seen.re-emit it into a spectrum with a wavelength of maximum emission of 490 nm. Thirty-six WLS fibersgo along each cell, gather in one bundle and transmit light to one multi-pixel 6 × photodiode(multi-pixel photon counter, or MPPC). In this prototype, counters of types S13160-6025, S13160-6050,S14160-6050, and FC-6035 [389] are used.The size of the cell for cosmic ray testing with the purpose of estimating signals from the MIP waschosen to be 55 × 55 mm . It consists of 220 layers of the scintillator and lead with widths of 1.5 mmand 0.3 mm respectively.The module consists of 4 cells with a cross-section of 55 × 55 mm combined into one tower with a cross-section of 110x110 mm and a length of 440 mm. Nine modules of the calorimeter, each consisting of 4cells, were manufactured for testing at the experimental test benches in VBLHEP and outside. Four ofthem were tested on cosmic rays. The test results are shown in Section 6.6.In the photo (Fig.4.18), a module of trapezoidal shape is shown, which is obtained after milling a rectan-gular parallelepiped at a 2 degrees angle. The cell size of 40 × 40 mm at the front face and 55 × 55 mm at the back face allows one to implement projective geometry (if necessary) in the SPD electromagneticcalorimeter. All of the MPPC’s, that are used in this prototype have the same size of 6 × , but have differentdynamic and time characteristics. The S13160-6025 series has the best response speed, low capacitanceand a large number of pixels, but the largest temperature coefficient of K T ∼ . 054 V/°C. The temperaturecoefficient shows a linear dependence of the breakdown voltage on the temperature and leads to a changein signal amplification. To achieve calorimeter stability of about 2%, one needs to ensure the stability ofthe surrounding environment, or use the breakdown voltage compensation scheme U OP = U BR + ∆ U − K T × ∆ T , where U OP and U BR are the operation and the breakdown voltages, respectively, ∆ U is a voltagebias and ∆ T is a deviation of the current temperature from the nominal one, e.g. 20 °C.The S14160-6050 series has high photo detector efficiency, but fewer pixels, which is worse in termsof the dynamic range. This series has a small temperature coefficient. An optimal solution would be to0manufacture a similar photodiode series, but with a smaller pixel size of 15 ÷ µ m, which would makethem more suitable for a calorimeter. Four MPPC’s are surface mounted on a circuit board, as shown in Fig.4.19. A thermistor is also installedto measure the photodiode temperature. The circuit board is connected to a module in such a way thatthe photodiodes are placed at the positions of fiber bundles. There is no optical contact between thephotodiode and the WLS, instead there is an air gap of about 0.1 mm. Optical grease is not used in orderto avoid instability in the conditions of light guiding. A light insulating basket made of black plastic isinstalled on top of the circuit board.(a) (b)Figure 4.19: Printed circuit board with 4 MPPC diodes: front (a) and back (b) sides.The MPPC are connected to the amplifier board (Fig.4.20) using a 1-meter 17-pair flat twisted-pair cable.Five pairs of wires transmit signals to the amplifiers [390]. Two wires are used to send base voltage of ∼ 40 V and connect the thermistor. Channel voltages are transmitted via signal wires as a small biasfrom 0 to 5 V. This way, the bias voltage can be precisely set in a small range, but with 10-bit precision(i.e. about 5 mV).The voltage control is implemented at a software level, taking into account the temperature from thethermistor installed on the circuit board. This allows for operation without special equipment for tem-perature stabilization. Signal stability of the order of 0.1 ÷ The readout electronics consists of an analog-to-digital converter ADC-64 [391] (Fig.4.20(a)). The ADCreceives continuous-time samples of the input signal with a fixed frequency and provides full digitalrepresentation of signals in time. Samples are received at a 64-MHz frequency, which corresponds to thetime period of 15.625 ns. Each sample is measured with a 12-bit precision. At present, there is an ADC-64-ECal modification, which improves the precision up to 14-bit and significantly extends the range ofthe measured amplitudes. The new ADC modification also allows for operation in strong magnetic fields,which is necessary for experiments at the NICA accelerator complex.onceptual design of the Spin Physics Detector 81(a) (b)Figure 4.20: (a) 16-channel amplifier board is used to control the MPPC High Voltage and transmitsignals to the ADC-64. The power consumption is about 16 mW per 16 channels. (b) 64-channel ADC-64- specifically designed for calorimeter operation in the magnetic field. The power consumption isabout 120 W per one board (64 channels).An Ethernet connector for data transfer can be seen in Fig.4.20 (b), together with a coaxial input forreadout synchronization, which serves as a trigger. The ADC can also operate in streamer mode dueto dedicated firmware. Using the White Rabbit technology provides sub-nanosecond synchronizationaccuracy. For testing on cosmic rays, a small setup of 4 (Fig.4.21) modules (each 11 × 11 cm ), of the total cross-section of 22 × 22 cm , was used. The cells, each 55 × 55 mm , are assembled in a 4 × × . All thephotodiodes are included in a coincidence trigger for the ADC. The trigger includes the signal from thegenerator, which starts the LEDs for control, calibration of calorimeter cells using the estimates of thelight yield, and long-term stability control. Data acquisition is conducted at the ADC using the softwareprovided by the developer. During a data taking period of 5-6 days, statistics of the order of milliontriggers was obtained.The setup allows one to measure energy depositions and trajectories of cosmic ray particles. Relativisticmuons with energy above 250 MeV pierce through the calorimeter and form a peak in the depositedenergy distribution. In order to select straight tracks of particles, which pass vertically through onemodule, only those events are selected, where the number of hits is equal to 1.Signals obtained on cosmic muons are used for amplitudes alignment and calorimeter energy calibration.Only events with exactly one cell hit are selected. The bordering cells have more events with smalleramplitudes due to angled tracks. We perform calorimeter calibration using only vertical tracks. Eachmaximum value in terms of ADC units is mapped to the corresponding energy deposition. The energyscale is determined from the Monte-Carlo simulation as the scale factor between the energy depositionof an electron with a 1-GeV energy, and a relativistic muon with an energy above 1 GeV, in scintillatorplates for the given structure. From this proportion we estimate the MIP signal in this calorimeter tobe 240 MeV. This value divided by the position of the muon peak maximum is used as a calibrationcoefficient for each cell. This calibration procedure involving the MIP energy deposition is not absolute2Figure 4.21: Photo of the calorimeter test setup consisting of 4 modules of the size 11 × 11 cm , with thetotal cross-section of 22 × 22 cm .or conclusive. Primarily, it aligns the amplification coefficients in each cell to ensure equal response ofeach cell. The measured electron or photon energy can be further revised by reconstructing neutral pionsor calibrating the calorimeter using electron or photon beams of the given energy.The electromagnetic calorimeter measures electron or photon energy by summing up signals from all 16cells. Each cell can only contain a fraction of energy deposited by the particle in the calorimeter (if theparticle is not a relativistic muon, or a MIP). If the calorimeter is calibrated with a precision of severalpercent, the total energy weakly depends on the particle angle and the resolution increases only by 1.4%.The energy resolution of the calorimeter for vertical cosmic ray particles is 9.6% (Fig.4.22 (a)). Thisnumber corresponds to energy deposition of 240 MeV. Assuming the resolution depends on the energyas E − / , the energy resolution at 1 GeV is estimated to be 5%.Time resolution for calorimeters of such types is about 175 ps for the MIP (Fig.4.22 (b)) and can beimproved for high-energy electrons. This can be applied to identify particles in the energy range of50 ÷ Cosmic ray testing allows one to obtain dependences of energy and time resolution on the number ofphotoelectrons ( NPE ) produced during the MIP passing through a cell. For each channel, time is cal-culated as zero intersection of the waveform. This method, Constant Fraction Discriminator, is used fordetermining a time value on a constant fraction of the pulse leading edge. The energy and time resolutiononceptual design of the Spin Physics Detector 83 = 10% s (a) / ndf c – – – c – – – (b)Figure 4.22: (a) Total energy deposition in the calorimeter for the MIP obtained by summing up signalsfrom 16 cells while selecting 1-hit events. (b) Time resolution for calorimeter cell E ne r g y r e s o l u t i on , % (a) T i m e r e s o l u t i on , p s (b)Figure 4.23: Dependence of energy (a) and time (b) resolution for different calorimeter cells on thenumber of photoelectrons ( NPE ).of the calorimeter depend on the NPE as 1 / √ NPE .Different conditions of light guiding were used in this 4-module calorimeter. These conditions includedforming reflective surfaces on the edges of the WLS, or using the fibers as U-shaped loops. Differencesin light guiding conditions lead to large variations in the NPE in the range between 1000 and 3000photoelectrons per MIP for different cells. In terms of the amount of deposited energy, this correspondsto 4000 ÷ NPE /GeV.Information on the number of photoelectrons for each cell allows one to obtain dependence of energyand time resolution on the NPE . The presented dependences of energy and time resolution are displayedin Fig.4.23 and show that the limit for large values of the NPE is 6 . 2% and 197 ps for energy and timeresolutions, respectively. Temperature dependence of calorimeter stability was investigated using daily temperature variations inthe range of 18-22 °C. During the measurement of signals from cosmic ray particles over 5 days, signalsfrom LEDs of a 1-Hz frequency were also measured. Photodiode temperature is constantly monitoredusing a high-voltage system. The voltage bias on photodiodes is corrected during a temperature mea-4 Time, h , % L E D A Figure 4.24: Dependence of the sum (average value) of signals from the calorimeter (in % with respect tothe first 5 minutes of the measurement period) on the time of measurement (in hours) with temperature-dependent voltage compensation.Table 4.6: Contributions of separate elements to the cost of the ECal.ECal cell WLS ADC HV MPPC TotalCost per 1 cell, $ 300 270 80 20 30 700Cost for 30.176 cells, M$] 9.1 8.1 2.4 0.6 0.9 21.1surement using a linear dependence: U out = U bias − k × ( − T ) .Daily temperature variations during the measurement were about 5°C. The temperature coefficient k = . 034 V/°C is used for temperature compensation of the operating voltage. After compensation, vari-ations in the signal amplitude are constrained within ± ∼ The cost of the calorimeter is proportional to the number of channels. Mechanical assembly of acalorimeter cell from the scintillator and the lead plates costs 300$ per channel. Another expensiveelement is the wavelength shifting fibers. For a 40 × 40 mm cell, 9 fibers of the total length of 54 m areused. Assuming an average price of 5$/m, the price per channel amounts to 270$. The cost of photodi-odes depends on the quantity. For purchases of tens of thousands of units, their price is about 30$ perunit. The electronics also contributes significantly to the total cost, especially the ADC with a price of80$ per channel. The cost of the supply and voltage control systems is 20$ per channel. The total costof a calorimeter cell is about 700$. Thus, the total cost of a 30176-cell calorimeter is 21.1 M$.onceptual design of the Spin Physics Detector 85 The Range System of the SPD detector serves for the following purposes: (i) identification of muonsin presence of a remarkable hadronic background and (ii) estimation of hadronic energy (coarse hadroncalorimetry). It is important to stress that the system is the only device in the SPD setup, which canidentify neutrons (by combining its signals with the electromagnetic calorimeter and the inner trackers).Muon identification (PID) is performed via muonic pattern recognition and further matching of the tracksegments to the tracks inside the magnets. The precise muon momentum definition is performed by theinner trackers in the magnetic field. The Mini Drift Tubes [392, 393] are used in the Range System astracking detectors providing two-coordinate readout (wires and strips running perpendicularly). Suchreadout is mostly needed for the events with high track multiplicity and also for the reconstruction of theneutron space angle.As for the design and construction of the present system, we assume to capitalize on the experiencegained by the JINR group in the development of the PANDA (FAIR, Darmstadt) Muon System [394].These two systems (PANDA and SPD), dealing with muons of comparable momentum ranges and solv-ing the same PID tasks, should look very similar in their design and instrumentation. The Range System serves as an absorber for hadrons and a ‘filter’ for muons. It also forms the magnetyoke. It consists of a barrel and two end-caps. Each end-cap, in its turn, consists of an end-cap diskand a plug. The schematic 3D view of the system and its main sizes are shown in Fig.4.25 (a). Theabsorber structure is shown in Fig.4.25 (b). The outer 60-mm Fe layers are used for bolting the modulestogether. The interlayer gaps of 35 mm are taken for reliable mounting of the detecting layers comprisingthe MDTs proper, the strip boards and the front-end electronic boards on them. The 30-mm thicknessof the main absorber plates is selected as comparable with muon straggling in steel, thus giving the bestpossible muon-to-pion separation, and also providing rather good sampling for hadron calorimetry.(a) 60 mm / Fe35 mm – gaps for detectors 19 x30 mm / Fe (b)Figure 4.25: 3D view (half cut) of the Range (muon) system: (a) Barrel is shown in grey, End Cap Disks − in green, and End Cap Plugs − in yellow; (b) absorber structure.The Barrel consists of eight modules, and each end-cap disk consists of two halves divided vertically.6Such subdivision of the system (14 pieces in total) is chosen to optimize its further assembly and tosatisfy the constructional requirements of the SPD experimental hall (cranes capability and floor load).The total weight of the system is about 810 tons, including 30 tons of detectors. The total number ofMDT detectors is about 8000 units. The MDTs are deployed in the following way: along the beamdirection in the Barrel, and perpendicular to the beam (horizontally) in the end-caps.The absorption thicknesses of the barrel and end-caps are selected to be equal to 4 nuclear interactionlengths ( λ I ) each. It provides uniform muon filtering in all directions. Together with the thickness of theelectromagnetic calorimeter ( ∼ λ I ) the total thickness of the SPD setup is about 4.5 λ I . The Mini Drift Tubes (MDT) detector was initially developed and produced at JINR for the Muon Systemof the D0 experiment at FNAL [395]. Later on, an MDT-based muon system was also produced for theCOMPASS experiment at CERN [396]. Developed two-coordinate readout modification of the MDTwith open cathode geometry and external pickup electrodes was proposed to and accepted by the PANDAcollaboration at FAIR for the muon system of their experimental setup. This new version of the MDTis proposed for the SPD project, as it has all the necessary features – radiation hardness, coordinateresolution and accuracy, time resolution, robustness, as well as advanced level of already conductedR&D within the PANDA project. External board with strips perpendicular to MDT wires MDT with open cathode geometry and external pickup electrodes (strips)cross-section Wire support Figure 4.26: Mini Drift Tube with open cathode geometry cross-section (left) and layout (right).The cross-section and layout of the MDT with open cathode geometry are shown in Fig.4.26. The detec-tor consists of a metallic cathode (aluminum extruded comb-like 8-cell profile), anode wires with plasticsupports, and a Noryl envelope for gas tightness. The comb-like profile of the cathode provides each wirewith an opening left uncovered to induce wire signals on the external electrodes (strips) perpendicular tothe wires. The strips are applied to obtain the second coordinate readout. The shape of the induced signalrepeats the initial one, having the opposite polarity, but the amplitude is about 15% of the wire signal (seeFig.4.27). Thus, the strip signal readout requires higher signal amplification and proper electromagneticshielding.onceptual design of the Spin Physics Detector 87Figure 4.27: Oscillograms of single signals: from the anode wire (1) and the strip (2, inverted); theconversion factors are 60 and 480 mV/ µ A, respectively.Application of an open cathode leads to the loss of the electric field symmetry in each of the 8 detec-tor cells, resulting in lower gas gain for the applied voltage comparing to the standard MDT (cathodeopenings closed with stainless steel lid). The conducted R&D proved that the MDT with open cathodegeometry easily achieves the parameters of the one with a closed cathode at higher voltages. The com-parative plots of the counting rate, efficiency, and gas gain for both detector types (see Fig.4.28) showthat the MDT with open cathode geometry repeats the standard MDT performance at a high voltage shiftof +100 V. The drift time and the amplitude spectra of both detector variants also match, if we set thisvoltage shift between their operating points.According to the results of the MDT (open cathode geometry) ageing tests, accumulation of a 1 C/cmtotal charge does not produce any significant effect on the detector performance. To monitor the ageingeffects, measurements of the counting rate curves (Co-60 source) together with oscilloscopic observa-tions of the MDT average signals (256 events) for Co-60 and X-rays were made twice a week over thewhole period of intense irradiation (see Fig.4.29). Later on, this measurement (with X-rays) was con-ducted up to 3.5 C/cm of irradiation without any visible degradation of the MDT performance. It shouldensure stable MDTs performance for the lifetime of the SPD project.All R&D studies were made with a gas mixture of 70% Ar + 30% CO at atmospheric pressure, the oneto be used in the proposed SPD Muon System. It is inflammable, radiation hard and fast enough (150-200 ns drift time). The wire pitch in the present design equals 1 cm, and a 3-cm strip width is selectedfor the second coordinate. These spatial parameters provide the Range System with coordinate accuracywell enough for identification of muons and give the system the features of a digital hadron calorimeter. We plan to use the analog front-end electronics (with probable minor modifications) developed forthe D0/FNAL and COMPASS/CERN experiments and also accepted by PANDA/FAIR. It is based ontwo ASIC chips: 8-channel amplifier Ampl-8.3 [397] and 8-channel comparator/discriminator Disc-8.3[398].8 C o un t i n g r a t e , s - Anode voltage, kV MDT with closed cathodeMDT with open cathode00,20,40,60,811,2 1,8 1,9 2 2,1 2,2 2,3 2,4 E ff i c i e n c y Anode voltage, kV MDT with closed cathodeMDT with open cathode 234567891011 2 2,1 2,2 2,3 2,4 G a s g a i n , Anode voltage, kV MDT with the closed cathodeMDT with the open cathode Figure 4.28: Comparative plots of the counting rate, efficiency, and gas gain versus the supply voltagefor the MDT with closed and open cathode geometry. C o un t i n g r a t e , H z MDT HV, V A v e r a g e a m p li t u d e , V Charge, C/cm Co-60X-rays Figure 4.29: Counting rate curves for different accumulated charges (0.16 ÷ Mezzanine board Motherboard Artix 7 FPGA XC7A200T Interface board Programming Module for Xilinx FPGA (DIGILENT) SMT1 Threshold LVDS Threshold LVDS Threshold LVTTL JTAG CONFIG. DATA 3 3 3 96 96 ch 96 ch USB JTAG (stand Config) Remote Config RS-485 DAQ HotLink interface Consist of 3 boards: (192 channel, VME 6U, double width) DIGITAL 6U VME R/O UNIT STRUCTURE A n a l o g E l ec t r on i c s Figure 4.31: Block-diagram of the MFDM module.Tests performed at CERN with the Muon System prototype on cosmic muons gave encouraging results.The further tests will be conducted with a prototype of the SPD range system ( ∼ The evaluation of the main parameters of the proposed Range System is being performed with big pro-totype installed at CERN within the PANDA program. The prototype (see Fig.4.33) has a total weightof about 10 tons (steel absorber and detectors with electronics) and comprises 250 MDT detectors with4000 readout channels (2000 for the wires and 2000 for the strips, 1 cm wide). It has both samplings(3 cm and 6 cm) present in the system (Barrel and End Caps), thus providing an opportunity for directcalibration of the response to muons, pions, protons, and neutrons.Fig.4.34 gives the examples of the prototype response to different particles. The patterns demonstrateexcellent PID abilities of the Range System. The data were taken during the May and August runs of2018 at the T9/PS/CERN test beam. The beam particles hit the prototype from the top of the picture.The beam momentum for all the particles is 5.0 GeV/c. Neutrons were generated by a proton beam on aonceptual design of the Spin Physics Detector 91 Analog electronics Digital electronics MFDM-192 FPGA-based, 5ns time resolution, 5 Byte/Hit VME 6U 2M, 550 pcs/system, 62 VME crates Compass FPGA-based MUX VME 6U 2M, 37 pcs/system 15 (S-Link) -> 1 (S-Link), TCS input, IPBus MDT Detector LVDS S-Link S-Link Threshold (analog) Figure 4.32: Data flow diagram – from the RS to the DAQ.carbon target placed in the very vicinity of the first detecting layer. The points on the pictures representhit wires, thus giving the impression of a typical device response with an accuracy ∼ The preliminary cost estimate for the Range System is presented in Tab. 4.7. This Section describes detectors providing identification of particle types such as π , K , p . The particleidentification system of SPD will include a time-of-flight detector (TOF) and a Cherenkov thresholddetector with aerogel used as a radiator. Their data will be used in conjunction with the energy loss dataregistered by the straw tubes. The latter will serve to identify mainly soft particles which cannot travelmore than a meter in the radial direction because of either decays or interactions. Whereas particleswith longer trajectories will be able to reach and therefore can be identified using the TOF and aerogelcounters.The barrel part of the PID system will be located inside the magnet coils which will limit the radial2 Figure 4.33: Range System prototype (10 ton, 4000 readout channels) at CERN.(a) (b) (c)Figure 4.34: Demonstration of PID abilities: patterns for - (a) muon, (b) proton and (c) neutron.flight distance for particles to 108 cm. The detectors will occupy a maximum radial thickness of 20 cmbetween the coils and the Straw Tracker (see Fig. 4.1). Spatial constraint for the end-caps is weaker.In this section, two technologies for the TOF and one for the Cherenkov aerogel counter are described.The choice for the baseline option will be made after comparing the respective performances, costs andavailability of group which will be able to build the detector. The purpose of the time-of-flight (TOF) system is to discriminate between charged particles of differentmasses in the momentum range up to a few GeV/ c . A short distance of 108 cm between the collisionpoint and the TOF dictates the requirement for the time resolution of the TOF to be better than 70 ps. Inonceptual design of the Spin Physics Detector 93Table 4.7: Cost estimate for the RS. Cost, M$MDT detectors with strip boards 2.35Analog front-end electronics (including cabling) 2.78Digital front-end electronics (including VME crates and racks) 3.05Yoke/absorber (without supporting structure and movement system) 6.00Total 14.18Figure 4.35: Two technologies are being considered for the time-of-flight system of SPD: the multigapTiming Resistive Plate Chamber, mRPC (left) and the plastic scintillator option (right). Barrel and oneof two end-cap parts are shown for both options. One of six magnet coils limiting the volume of TOF isshown in red.view of the uncertainty related to the length of the interaction region (about 60 cm), the time t whichcan be assigned to the collision vertex will only be on the order of 1 ns, so it is useless for identificationpurposes. Therefore the particle identification (together with the t determination) can only be done formulti-track events, where several particles emerged from a same primary vertex hit active elements ofthe TOF. A certain mass hypothesis will have to be applied in this procedure. For details of this analysissee Section 1.4 of Chapter 9. In addition to the particle identification, the detector will also provide astart time to the straw drift tubes.The TOF system will consists of a barrel and two end-cap parts with an overall active area of 27.1 m . Thecharge particle rate that detector will have to withstand is 0.1 kHz/cm for the barrel. The rate increasesrapidly when moving closer to the beam axis. Thus, for the TOF elements located in the end-caps 20 cmoff the beam axis, the rate of about 1 kHz/cm is expected (see Fig. 9.3 for details). Two alternativetechnologies are being considered for the detector: a multigap Timing Resistive Plate Chamber (mRPC)and a plastic scintillator with Silicon Photomultiplier (SiPM) reading. Both are shown in Fig. 4.35. Thesetwo technologies, in general, can provide about the same efficiency and time resolution, require similarreadout electronics and have about the same cost per channel. Main features as well as pros and cons ofboth options are listed below:– The multigap Timing Resistive Plate Chamber. It is a stack of resistive glass plates with highvoltage applied to external surfaces. Pickup electrodes are located inside the chamber separating4 MPRC Plastic scintillatorActive area:barrel + 2 × end-cap 19.8 m + 2 × = 27.1 m Area of readout element: strip tilepitch × length 1.25 cm × 40 cm = 50 cm × Size of chamber or tile: chamber (24 strips) tileW × L × H 33 cm × 40 cm × × × × end-cap 160 + 2 × 30 = 220 7.3k + 2 × × × 25 mm which corresponds to a PCB with 24 readout strips, each 10 mm wide and400 mm long. The detector is composed of 220 chambers: 160 and 30 chambers for the barreland each end-cap, respectively. Adjacent mRPCs will be positioned in such a way as to create anoverlap of 1 strip at the edge of the active area. This will ensure the inter-calibration of the mRPCsusing tracks crossing both chambers. A rectangular shape of each chamber, which is quite largeand can not be modified, creates a certain inconvenience for covering the end-cap parts of detector.Contributions of all parts of the TOF to the radiation length is about 0 . X in average [401].– The plastic scintillator option. The basic element of the detector is a plastic scintillator tile withdimensions of 90 mm × 30 mm × The required time resolution for SPD is better than 70 ps while the efficiency of particle registrationat high rate (few kHz/cm ) should be above 98%. Based the experience of building similar systems insuch experiments as ALICE [402], HARP [403], STAR [404], PHENIX [405] and BM@N [406], a glassonceptual design of the Spin Physics Detector 95multigap Resistive Plate Chamber could be used as base time detector. For example, the ToF-700 wall inthe BM@N experiment, placed at a distance of 8 m from the target, provides one the π / K separation upto 3 GeV/ c and p / K separation up to 5 GeV/ c under the assumption that the time resolution of the starttiming detector is < 40 ps.Figure 4.36: Schematic view of the twelve-gap mRPC [407].The design of the BM@N ToF-700 wall is based on experimental results obtained during multiple tests ofvarious modifications of the glass mRPC exposed in charge particles beam. The count rate for a standardglass mRPC is limited to several hundreds Hz/cm due to the use of conventional float glass plates with abulk resistivity in the range 10 − Ω · cm. Therefore, the extension of the counting rate capabilitiesof the mRPC has become an important issue.One of the ways to increase the mRPCs performance at high rates is to use the low resistivity glass(less than 10 − Ω · cm) [408–410] or ceramics [411] as the electrode materials. For instance,time resolutions below 90 ps and efficiencies larger than 90% were obtained for particle fluxes up to 25kHz/cm for the 10-gap mRPC [412]. An alternative method is to reduce the glass stack resistance byminimizing the used electrode thickness and increasing a temperature of the glass [413, 414]. It wasshown that such method can provide high time resolution at continuous rate up to 20 kHz/cm [415].Schematic cross-section of the mRPC used at BM@N is shown in Fig. 4.36. It consists of two identical6-gap stacks with anode strip readout plate in between. The size of mRPC is 473 × × 17 mm withthe working area of 351 × 160 mm . Each mRPC has 3210 × 160 mm readout strips with 1 mm gapsbetween them.Each stack is formed by seven glass plates with the 2 × Ω · cm bulk resistivity. The 0.22-mm gapbetween the glasses is fixed by spacers – usual fishing-lines, which ran directly through the RPC workingarea. The graphite conductive coating with surface resistivity of ∼ Ω is painted to the outer surfacesof the external glass plates of each stack to distribute both the high voltage and its separate ground toform a uniform electrical field in the stack sensitive area. The anode readout strips plate is a one-sidedprinted PCB with the thickness of 100 mm. The thickness of the copper layer is 35 µ m. Signals aretaken from the both ends of the anode strips. The entire mRPC assembly is put into a gas-tight box.The bottom of box is made of a double-sideed PCB (motherboard) with a thickness of 2.5 mm, the sideframe of the box is made of aluminum profile, the top of box is closed by the 1.5-mm aluminum cover.The paper [416] presents the performance of the 12-gap mRPC in the range of the counting rate from6Figure 4.37: Left: schematic view to the plastic scintillator tile and a photo of the 4 SiPM board ofPANDA [417]. Right: time resolution obtained from a position scan of a 90 × × EJ-232scintillator tile read out by Hamamatsu SiPMs attached to opposite sides, 4 SiPMs in series per side[417].0.45 kHz/cm up to 10 kHz/cm obtained using the secondary muon beam from the U70 accelerator atProtvino. The measurements at different rates were performed in the temperature range 25-45 o C withthe step of 5 o C. The time resolution is reached up to 50-60 ps with good and stable efficiency under thetemperature of 40-45 o C.Since the particle flux in the SPD experiment is expected to be up to 1 kHz/cm , a similar approach couldbe used to build the mRPC-based high-speed TOF with time resolution of about 50 ps. This option was inspired by the TOF system of the MEGII [418] and PANDA [417] experiments. Thesurface of the TOF is segmented into many small scintillator tiles made of a fast scintillating organicmaterial. The optical readout is performed by Silicon Photomultipliers (SiPM) attached to the ends ofevery tile. A typical number of optical photons produced by a minimum-ionising particle crossing a 1 cmplastic scintillator is ∼ . A resulting number of detected photons depends on a signal propagationand photosensor efficiencies. Nowadays, large-area SiPMs have appeared on the market at relativelymoderate cost and offer several advantages over PMTs: magnetic field tolerance, a much smaller volumeand footprint allowing a compact design for bars without light-guides, low operation voltage and highphoton detection efficiency (PDE). Thus, they ideally meet the requirements dictated by a thousand tilesystem of the TOF/SPD.The choice of the scintillator material is primarily driven by the requirement for a short emission time.Organic scintillators based on a plastic matrix of polyvinyl-toluene, such as EJ-228 (BC-420) or EJ-232(BC-422), have an attenuation length of about 10 cm, rise time of 0.5 ns and wavelength of maximumemission in UV region of 391 nm. They are commonly used for applications as the one discussed in thisSection. Note that, contrarily to the mRPC, the time resolution of a plastic scintillator detector degradesexponentially with increase of distance between the interaction point and photosensor. It is especiallycrucial for UV photons. Therefore the choice of scintillator is all the time a compromise between theattenuation length (visible light) and fast emission (UV region).In the case of the TOF/PANDA, a scintillator tile with dimensions of 90 × × was read out by4 Hamamatsu SiPMs coupled to opposite sides as shown in Fig. 4.37 (left). Each SiPM has its sensitivearea of 3 × , thus the array of four can detect about a quoter of photons reaching the edge of tile.This configuration was chosen as a baseline for estimates for the TOF system of SPD. The time resolutionobtained from a position scan is shown in Fig. 4.37 (right). One can see that the resolution varies fromonceptual design of the Spin Physics Detector 9750 ps in the near-to-SiPM region to 60 ps in the center of tile. The resolution of 100 ps around the end oftile is, presumably, due to tracks only partially crossing the volume of scintillator.Summarizing the advantages of the plastic scintillator option versus the mRPC, one can say that theassembling is faster, easier and does not require clean enviroment; it is easier to maintain the detector (nogas flow, only LV); the detector can be squeezed within 5 cm radially, thus leaving space for the aerogeloption which is described in the next section; the circular cross-section of the barrel can be approximatedexactly matching the magnet coils from the outside; the radiation length is only 2% of X . The weakpoints of the plastic option are: an exponentially drop of the resolution vs distance, which will requirelarger number of SiPMs for the case of longer tile; a smaller surface of a single tile, 26 cm vs 50 cm of a mRPC’s strip, doubles the number of read channels; the organic material is sensitive to radiation.Although this option is promising it will require a detailed study before being accepted.(a) (b) c m ∅ =202 с m π K KEDR (c) p [GeV/c] R e f r e c t i v e i nde x , n p K /K) p KEDR ( /K) p SPD ( -1 nm = th p (d)Figure 4.38: (a) Principle of ASHIPH operation. (b) KEDR aerogel counters: two barrel counters ina single housing (left), end-cap counter (right) [419]. (c) Possible arrangement of barrel and end-capcounters in SPD. (d) Momentum intervals of KEDR and SPD where the π /K separation is possible. Another option for the system of particle identification is aerogel Cherenkov counters. Aerogel is a syn-thetic porous ultralight material which has found an application, in particular, as a radiator in Cherenkovcounters. Aerogel may have a refractive index in the range between 1.0006 and 1.2, the exact value ofthe refractive index being specified at the production stage. In fact, aerogel fills the gap in the refrac-tive index values between gases and liquids. This feature of aerogel allows one to use it in Cherenkovcounters for particle identification in conditions when other Cherenkov radiators are not applicable, for8instance, for π /K separation at the momenta from few hundred MeV/ c to about 3 GeV/ c . The selectionof the refractive index value defines the region of momenta where the separation is effective.There exists a good experience of using threshold aerogel Cherenkov counters, in particular, in exper-iments KEDR (BINP, Novosibirsk) [419], [420], BELLE (KEKB, Tsukuba) [421]. In the BELLE ex-periment a threshold aerogel Cherenkov counter with refractive index from 1.010 to 1.030 provided π /Kseparation in the momentum region up to 3.5 GeV/ c . In the KEDR detector the aerogel counters withrefractive index 1.05 provided π /K separation in the range from 0.6 to 1.5 GeV/ c .Aerogel has a short scattering length of light, 12-40 mm depending on wavelength. Therefore, directivityof Cherenkov light cannot be used because directivity disappears soon after emission. For this reasondiffusive reflectors are used at the walls. No scintillation has been observed in aerogel. Aerogel samplessuffered from hygroscopicity for a long time, but in the 1990s the technology of hydrofobic aerogel hasbeen developed.In KEDR, the aerogel counters received the name ASHIPH (Aerogel, SHIfter, PHotomultiplier). InFig. 4.38 (a) a principle scheme of the counter is shown. Cherenkov light from aerogel is captured by awavelength shifter (WLS). PMMA light guide doped with BBQ dye is used as wavelength shifter, cross-section of WLS is 3 × 17 mm . WLS absorbs Cherenkov photons at short wavelengths where Cherenkovradiation is more intensive and re-emit photons at large wavelength bringing them to a light sensor. InFig. 4.38 (b) the counters of KEDR are shown. The microchannel plate photomultipliers served as lightsensors in KEDR, but for later developments the APD were used (BELLE-II), also SiPM are proposedfor aerogel detectors in PANDA (GSI) and FARICH (for Super Charm-Tau Factory in Novosibirsk).If a particle crosses WLS, it produces a much higher signal than the particle traversing aerogel. To avoidmisidentification, two-layer structure in KEDR is used with shifted layers with respect to WLS position,so that a particle cannot cross WLS in both layers. The thickness of one layer is 74 mm, a total amountof material in both layers is 0.24 X .For relativistic cosmic muons that cross both counter layers of KEDR the average number of photoelec-trons was 9 . ± . 4, and the detection efficiency 99 . ± . 1% at the threshold that equals to 2 photoelec-trons. For under-Cherenkov-threshold muons (200 < p µ < 300 MeV/ c ) the efficiency was 3 ± a la ASHIPH can be inserted between the Straw tracker and ECAL. Possiblearrangement of barrel and end-cap counters in SPD is shown in Fig. 4.38 (c). The barrel of SPD is afactor of 2 longer and 50% wider as compared to the one of KEDR. Thus the amount of aerogel willhave to be three times larger in volume: 1 m and 3.2 m for KEDR and SPD, respectively. The numberof counters will also increase by about the same value.The value of refractive index can be selected for the momentum region where π /K separation is the mostimportant. As will be shown in Fig. 9.10, this separation up to 1 GeV/c can be provided by the TOF.Aerogel will be employed for momenta above this value which corresponds to the refractive index equalto 1.02 as shown in Fig. 4.38 (d). One can see from the figure that kaons begin generating a signal in thecounters having momenta above 2.5 GeV/ c , which defines the region of detector applicability.The detector is thin (in terms of X ), fast and rather simple in operation. We estimate its cost to be ofabout 5 M$. Two Beam-Beam Counters (BBCs) are planned to be located just in front of the PID system in the end-cups of the SPD setup. The detector should consist of two parts: the inner and the outer one, which arebased on different technologies. The inner part of the BBC will use fast segmented MicroChannel Plateonceptual design of the Spin Physics Detector 99(MCP) detectors and should operate inside the beam pipe, while the BBC outer part will be producedfrom fast plastic scintillator tiles. The inner part covers the acceptance 30 ÷ 60 mrad and should beseparated into 4 layers consisting of 32 azimuthal sectors. The outer part covering the polar anglesbetween 60 and 500 mrad will be divided into 5 or 6 concentric layers with 16 azimuthal sectors in theeach of them. The final granularity is the matter of further optimization for the entire energy range ofcollisions at SPD. The concept of the BBC is shown in Fig.4.39. The magenta part represents the MCPdetector while the internal layer of the outer part is shown in red.The main goals of the Beam-Beam Counters are: i) the local polarimetry at SPD basing on the measure-ments of the azimuthal asymmetries in the inclusive production of charged particles in the collisions oftransversely polarized proton beams, ii) the monitoring of beam collisions and iii) participation in theprecise determination of the collision time t for events in which other detectors can not be used for that(for instance in case of elastic scattering). R R . R . . . Figure 4.39: Beam-Beam Counter: azimuthal and polar angle segmentation [422]. All dimensions are inmillimeters.Another important goal of the BBCs is fast preselection of different types of events for monitoringpurposes. The Monte Carlo simulation shows that in the p - p collisions at √ s =27 GeV at least one BBCshould have a signal in 79% of events (51% of events has a signal in the both BBCs). However, for thehard processes, in 97% of events the only one BBC will be hit, while hits for both counters could beexpected in 68% of cases. Therefore, the requirement of the BBC signals allows one to preselect hardprocesses. The concept of the MCP-based Fast Beam-Beam Collision (FBBC) monitor is described in details in[423]. Two ring beam-beam collision detectors (FBBC-left and FBBC-right) could be located inside thevacuum beam line together with two 2D position-sensitive beam imaging detectors (BPMs) (see Fig.4.40). The FBBC uses the concept of the isochronous multi-pad fast readout and the precise timingdetermination of short ( ∼ µ m) channels, low resistivity(100 ÷ 500 M Ω ), high gain ( ∼ ), short fast rise-time ( ∼ Ω signal andHV feedthroughs (the latter are not shown).Figure 4.41: A typical MCP signal the detector prototype. The scintillation part of the BBC will consist of tiles viewed by the SiPMs. The measurement of thesignal amplitude is required for time-walk correction to improve the time resolution.onceptual design of the Spin Physics Detector 101 GND C1 GND C2 C4 GND R2 GND HV+5-5 1234P6R1HVD1 GNDGND GND P3 BNCC5C3 GND R3 GND P2 BNCPhoto Sen AMPLIFIER TOT Function NIM ShaperLVDS Shaper (a) 500 1000 1500 2000 2500 3000 3500 4000 ToT, Channels (25 ps) (b)Figure 4.42: (a) Schematic view of the front-end electronics with a ToT function, (b) Distribution of theToT for LED signal. (a) (b)Figure 4.43: (a) dT ( T SiPM − T SiPM ) correlation on the ToT. (b) Result after the time-walk correctionfor the dT ( T SiPM − T SiPM ) correlation on the ToT.With a single-channel prototype of the detector we will be able to measure the amplitude using the devel-oped FEE based on the Time-over-Threshold (ToT) technique. This technique is a well-known methodthat allows us to measure the energy deposited in the material by reconstructing the given property ofthe output current pulse – the total charge collected, the pulse amplitude, etc. The ToT method convertsthe signal pulse height into a digital value in the early stage of the FEE, which greatly simplifies thesystem in comparison to analog detectors with serial readout through ADCs. The measurement of theToT is composed of two measurements of time for the signal going above (leading) and returning below(trailing) the given threshold. The first version of the prototype includes a power supply and electronics(Fig.4.42(a)) made on a separate PCB. This PCB is used for each cell of the SiPM. The power supplyfor the SiPM provides a voltage of up to 65 V with an individual channel adjustment within 0-10 V,manual tuning, and a built-in voltmeter for the voltage monitoring It is possible to connect eight cellssimultaneously. The amplifiers used for that do not change the leading edge of the signal. This allows usto get a time stamp of the event. Afterwards, the signal is integrated and transmitted to the comparator.The response of the Hamamatsu S12572-010P SiPM [425] with the FEE to the LED has been studied.The electrical signal from a LEMO output of the LED was used as a trigger. The illumination wasperformed by uniform light in a light-isolated box. In addition to the ToT information (Fig.4.42(b)),02 850 900 950 1000 1050 1100 1150 1200 Channels (25ps) . ~600 ps (a) 850 900 950 1000 1050 1100 1150 1200 Channels (25ps) ~400 ps (b)Figure 4.44: (a) dT ( T SiPM − T SiPM ). (b) Result after the time-walk correction for the dT ( T SiPM − T SiPM ).the time stamp of the event for each SiPM cell was investigated. The distribution (Fig.4.43(a)) showsthe correlation of these values and that the signal in the region of small amplitudes comes later in time.This is due to signal latency (the so-called time-walking effect). This delay occurs due to the differencebetween the time when a photon or a charged particle passes through the detecting element and thetime when the electronics registers this signal. This leads to deterioration in the time resolution. Afterperforming the correction (see Fig.4.43(b)), the time-walking effect has been removed [426].The time resolution was defined as the RMS and was approximately 600 ps. Taking into account thenon-Gaussian waveform (Fig.4.44(a)) and the fact that the time resolution is not the maximum allowedfor this type of the detector, the time-walk correction has been applied. The most important result of thecorrection was a time resolution of approximately 400 ps (Fig.4.44(b)), which is 1.5 times better than theresolution before the correction.The first version of the prototype using developed front-end electronics based on the Time-over-Thresholdmethod was tested. After the time-walk correction, the time resolution improved up to 400 ps. Takinginto account the SiPM suboptimal for precise time measurements, the result is promising. Further devel-opment of the FEE with a ToT function allows using standard TDCs for timing measurements. 10 Zero degree calorimeter A zero degree calorimeter (ZDC) will be installed in the beam separation areas on both sides of the SPDinteraction point as it is shown in Fig. 4.45, where all charged particles originating from the interactionregion are swept out by the strong magnetic field. Main goals of the ZDC are:– luminosity measurement;– local polarimetry with forward neutrons (see Chapter 5);– spectator neutron tagging;– time tagging of the events for event selection.The ZDC is a standard system used for the purposes mentioned above in many collider experiments. Thestrong magnetic field before a ZDC efficiently removes all charged particles allowing clean measure-ment of neutrals, so the device can work till very high luminosities. Scattering at zero angle is insensitiveonceptual design of the Spin Physics Detector 103 QFF5W IP QFF4W QFF6W BV4W BV3W2 SPD BV3W1 MC1W2 MC2W MC31W1 ZDC RF3 RF3 Figure 4.45: ZDC placement at the collider. All dimensions are in millimeters.to transverse polarization and provides offset-free luminosity measurement, very useful for luminositycrosschecks. The device could provides an additional time stamp for an event. Standard usage of ZDCincludes local polarimetry with forward neutrons [427]. The main purpose is the verification of longi-tudinal polarization settings. One can expect 1 ÷ ÷ 200 ps;– energy resolution for neutrons 50 ÷ / √ E ⊕ ÷ × × 17 mm for the first layer to 28 × 28 mm at the lastlayer. Each tile is covered by a chemically produced thin white reflective layer with a small transparentwindow for optical readout, done by HAMAMATSU SiPMs S13360-3050PE directly coupled to thetiles. Output signals are digitized by 500 MHz flash ADC 16 channel boards. A fast output for SPDtrigger system is also produced. The ZDC will be placed inside the beam separation magnet and its sizeis limited to 88 × 88 mm at front side and 140 × 140 mm at rear side. The length is limited to 650 mm.Table 4.9: The parameters of the ZDC layers.Parameter Electromagnetic Hadronpart partNumber of layers 10 26Scintillator thickness, mm 5 10Absorber thickness, mm 5 10Total absorber thickness, mm 45 260Part thickness, X 13 75Part thickness, λ I × × 30 mm plastic, SiPM board and support board;b) the prototype assembly in a box before wrapping in black paper; c) the box in place for cosmic muontests.The expected energy resolution for neutrons is about 50% / √ E ⊕ 30% while the energy resolution forphotons is about 20% / √ E ⊕ L ∼ 10 m distancefrom the interaction point. For neutrons, the space resolution is 10 ÷ 13 mm within energy range 1 ÷ × × 30 mm in size and is chemically covered with a thin light reflectinglayer. A numerical simulation has shown the mean number of cells hit in an event is more than 20 foronceptual design of the Spin Physics Detector 105both photons and neutrons. It means the total thickness of scintillator plates of the order of 15 cm (5times more than for tested prototype). The test results obtained for the prototype wre extrapolated to thefull ZDC. Thus the expected time resolution has to be about 150 ps.The proposed design of the ZDC calorimeter satisfies most of its physics goals in the limited space insidethe magnet. The exception is the energy resolution for neutrons, which is reached by larger calorimeteronly. Nevertheless even this goal could be achieved by more elaborated analysis taking advantage fromthe calorimeter fine granularity. hapter 5 Local polarimetry The main goal of the local polarimetry at SPD is the permanent monitoring of the beam polarizationduring data taking to reduce the systematic error coming from the beam polarization variation. Anothertask is beam polarization monitoring independent on the major polarimeters (CNI and the absolute one),as well as possible usage of this tool to tune the beam polarization axis. Since the SPD energy rangeis relatively new for spin physics, there is a lack of precise polarization data allowing one to find theexplicit solution for the local polarimetry. One of the tools to control the proton beam polarization is the measurement of the azimuthal asymmetryin inclusive production of charged particles in collisions of transverse polarized proton beams. Sucha method is well adopted at the STAR detector. Two Beam-Beam Counters (BBCs) are used for thispurpose. Each BBC consists of two zones corresponding to different rapidity range. The inner and outerzones cover 3.3 < | η | < < | η | < pC CNI polarimeter [429, 430] and theSTAR BBCs is demonstrated in Fig.5.1. One can see that the measurements by BBCs are sensitive tothe transverse polarization of the colliding beams. The value of the effective analyzing power A N forinclusive production of charged particles at √ s = 200 GeV is about ( ÷ ) × − . At NICA energies itwill have, in principle, the same magnitude, or even a larger one due to a larger analyzing power for the p - p elastic scattering. Therefore, the BBCs can be used for the local polarimetry at SPD. The design ofthe SPD BBCs is described in the previous section. π production One of the reactions to measure and to monitor the vertical component of the polarized proton beam is theinclusive pp → π ± , X reaction. Fig.5.2(a) demonstrates the single transverse spin asymmetries A N ob-tained in the p - p collision for π + , π and π − inclusive production at 200 GeV ( √ s ∼ 20 GeV)[175, 176].The data demonstrate large values of the single transverse spin asymmetries with their signs followingthe polarization of the valence quarks in the pions. This regime occurs already at 22 GeV [431] corre-sponding to √ s NN ∼ pp → π X reaction is almost twice smaller than106onceptual design of the Spin Physics Detector 107(a) (b)Figure 5.1: Correlation of the beam asymmetries measured by the RHIC pC CNI polarimeter [429, 430]and left (a) and right (b) STAR BBCs (in arbitrary units).(a) , GeV gg m = 13.3 MeV m s (b)Figure 5.2: (a) Single transverse spin asymmetry A N for inclusive pion production in p - p collisions at200 GeV [175, 176].. (b) The π reconstruction in the SPD ECal end-cup with (blue) and without (red)vertex position information.for the charged pions production. However, the π selection can be done more easily, since it does notrequire track reconstruction.For online local polarimetry one can use the parts of the ECal end-cups placed around the beam pipe. Fast π reconstruction algorithms will not include the information on the vertex position along the beam axis,therefore, the width of the π peak will increase. The Monte-Carlo results obtained for √ s NN ∼ 27 GeVand presented in Fig.5.2(b) demonstrate such enlargement. However, one can see that the selection of π is good enough for the local polarimetry purposes. The effective analyzing power (cid:104) A N (cid:105) for the kinematicrange of produced π p T > . c and x F > . π decays reconstructed08in the end-caps of the calorimeter provides statistical accuracy of the beam polarization estimation at afew-percent level after 10 minutes of data taking at 10 GeV < √ s ≤ 27 GeV. The corresponding accuracyof the spin direction reconstruction is about a few degrees. The energy dependence of the single transverse spin asymmetry, A N , for neutron production at veryforward angles was measured in the PHENIX experiment at RHIC for the polarized p - p collisions at √ s =200 GeV [427]. The neutrons were observed in the forward detectors covering an angular rangeof up to 2.2 mrad. The observed forward neutron asymmetries are large, reaching A N = − ± x F =0.8; the measured backward asymmetries, for negative x F , are consistent with zero. The results ofthe x F dependence of A N for neutron production in the (upper) ZDC trigger sample and for the (lower)ZDC ⊗ BBC trigger sample are shown in Fig.5.3(a). The error bars show statistical uncertainties, and thebrackets show the p T -correlated systematic uncertainties. The data were obtained for 2 types of triggers:the first one is the ZDC trigger for neutron inclusive measurements, requiring an energy deposit in theZDC to be greater than 5 GeV. The other one was a ZDC ⊗ BBC trigger, a coincidence trigger of the ZDCtrigger with the BBC hits defined as one or more charged particles in both of the BBC detectors.The observed large asymmetry for forward neutron production was discussed within the pion exchangeframework, with interference between the spin-flip amplitude due to the pion exchange and the non-flipamplitudes from all Reggeon exchanges. The numerical results of the parameter-free calculation of A N are in excellent agreement with the PHENIX data (see Fig.5.3(b)). One can see that A N is increasingalmost linearly as a function of the neutron transverse momentum q T . One can expect the A N value of ∼ − . 02 at √ s =27 GeV. Therefore, the pp → nX reaction with neutron emission at very forward anglescan be used at SPD at least at high energy.Very forward neutrons are detected by two zero-degree calorimeters (ZDCs) [433] placed in the gapsbetween the ion tubes of the colliding beams on the left and right from the center of the detector. TwoZDCs will be also placed at SPD. These ZDCs can be considered as an additional tool for the localpolarimetry for pp-collisions at the highest NICA energy.onceptual design of the Spin Physics Detector 109(a) -0.2-0.15-0.1-0.0500.050 0.1 0.2 0.3 0.4 q T (GeV) A N s=62 GeVs=200 GeVs=500 GeVTheory (b)Figure 5.3: (a) x F dependence of A N for neutron production in the (upper) ZDC trigger sample and for the(lower) ZDC ⊗ BBC trigger sample. (b) Single transverse spin asymmetry A N in the reaction pp → nX measured at √ s = 62, 200, 500 GeV at PHENIX as a function of the transferred momentum q T . Theasterisks show the result of the theoretical calculations [432]. hapter 6 Detector control system The SPD detector control system (DCS) is designed to control the basic operating modes of the detectorparts and the detector as a whole, and to continuously monitor slowly changing parameters of the detec-tor, engineering means which provide the detector operation, and the environment. The DCS is synchro-nized with the basic operating modes of the NICA accelerator complex by means of a synchronizationsubsystem shared between the DCS and the SPD DAQ. The DCS provides parameterization of the man-aged object (i.e. the SPD detector), implements algorithms for normalization, parameters measurementand control based on these parameters, and generates the necessary sets of abstractions and options forpresenting these abstractions to the operator in an intuitive manner. Critical values of the parametersgoing beyond the predefined limits in predetermined situations cause emergency events and initiate pro-cedures for handling such events, including the procedure for an automatical detector shutdown in orderto prevent its damage. Parameter values are archived in a database for long-term monitoring of the detec-tor operation and identify possible failures in the operation of the equipment and emergency situations.The configurations of the detector parameters saved in the database make it possible to start the detectorpromptly and use it with various preset parameters and in various operating modes in accordance with therequirements of a particular physics experiment. The DCS allows autonomous operation of each detectorsubsystem at the stage of the initial start-up as well as its periodic maintenance, calibration sessions, andplanned upgrades. The number of parameters in the system is expected to be significant, therefore, it isassumed that the system should be extendable and flexibly configurable. Architectural and software so-lutions based on the event-driven model [434] and client-server and producer-consumer [435] interactionmodels should be preferred for communication, when building the general DCS and the control systemsof each part of the detector. Centralized systems operating in the master-slave polling mode should beavoided. Most of high-energy physics detectors include parts consisting of similar systems built from devices,sensors, and actuators with similar or identical functionality. This determines parameterization of theentire detector as a managed object. Such systems include:1. high voltage (HV) power supply system for powering gas detectors and light (photon) sensors(PMT and SiPM);2. low voltage (LV) power supplies for powering magnets, digital and analog electronics;3. cryogenic systems; 110onceptual design of the Spin Physics Detector 1114. gas supply and mixing systems;5. vacuum systems;6. front-end electronic LV powering control and temperature monitoring;7. different cooling and temperature control systems;8. DAQ system;9. accelerator interface and synchronization;10. general external electricity and water cooling stations, etc.The SPD detector is no exception and includes almost all of these systems spread among different partsof the detector, as shown in the layout diagram, Fig. 6.1. Each part of the detector refers to one or moresubsystems. The composition of the systems will be refined, as the individual parts of the detector aredeveloped. Figure 6.1: SPD detector control system layout.All the systems can be similarly parameterized and shown to the operator in an intuitive presentation inorder to simplify the operator’s decision-making algorithm. However, the physical implementation at thehardware level of these elements may vary significantly in different parts of the SPD, because:12– the parts inherit the experience of their developers gained in previous experiments;– hardware and software components are selected based on their cost and availability;– parts of the detector are manufactured at different times.Nevertheless, in order to optimize financial and human resources costs for the creation of the entiredetector and the DCS, in particular, it is necessary to recommend the developers of the detector parts tostrive for standardization of the used hardware and embedded software. This will significantly reducethe efforts put into developing, deploying, and operating the detector and will result in significant costsavings. To achieve these goals, at the stage of prototyping the detector systems it is advisable to workout not only the detector itself, the front-end electronics and the DAQ, but also the slow control systems.This work can be carried out in the beam test zone (BTZ), for which the BTZ slow control system mustbe made as similar to the final DCS version as possible. Figure 6.2: SPD detector control system architecture.The detector control system is divided into three logical levels (Fig. 6.2). The lower level includesmeasurement channels built into the Front End Electronics (FEE) and Data Acquisition (DAQ) of thedetector parts, various stand-alone sensors, I/O devices, and low and high voltage power supplies. Themiddle level is represented by programmable logic controllers and integrated ready-made and custom-made subsystems (vacuum posts, gas consoles, multichannel ready-made power subsystems, etc.). Theinterfaces to the FEE and DAQ that provide data for the detector control system are also on this level.The upper level is designed to provide a human-machine interface for operators, implement a database ofdetector parameters and configurations, communicate with the external world (accelerator, engineeringsupport systems, access system, etc.), and implement macro-control algorithms common for the entiredetector. All these levels are connected in a hierarchical network using fieldbuses between the first andthe second level, for example, a CAN-bus with a CANopen protocol. An Ethernet LAN is used betweenthe middle and the upper levels. At the top level, special software, such as SCADA (Supervisory ControlAnd Data Acquisition), is used, which provides control, collection and storage of data in real time. It isonceptual design of the Spin Physics Detector 113proposed to use the WinCC OA system common at CERN, as a SCADA system. We understand that forsmooth and reliable communication with the control system of the Nuclotron, a gateway to the TangoControls [436, 437] system should be developed and deployed. WinCC OA (ex PVSS-II) [438, 439] is a commercial SCADA system. It is a software component con-structor that allows one to use both preinstalled prototypes and templates, and software modules andsystem components developed in C. This system is actively used in many experiments at CERN and hassupport and safety certificates in the Russian Federation. The following properties make WinCC OA anattractive solution to be used in the DCS SPD:– object-oriented approach built into the system ensures an efficient development process and theability to flexibly expand the system;– capability to create distributed systems - up to 2048 WinCC OA servers;– scalability from a simple single-user system to a distributed redundant network system with > WinCC OA Figure 6.3: SCADA structural scheme of the WinCC OA software.– in the xml format with the ability to display in any external tool for working with reports (EclipseBIRT, Crystal Reports, SYMATIC Information Server etc.), SOAP (Simple Object Access Proto-col) protocol is also supported.Project development for the WinCC OA system is based on an object-oriented approach. In the WinCCOA data model, objects are represented as data points that characterize the image of a specific physicaldevice or process. For each data point (called tag) element, properties and actions, such as signal pro-cessing (smoothing, setting limits, etc.), communication with external systems, archiving, generation ofalarm messages (alarms), etc. can be defined in accordance to it. Typing and inheritance are supported,therefore arbitrary hierarchical data structures can be created. Similarly, the principles of inheritance andreusability are implemented for graphical objects. The WinCC OA IDE includes the PARA configurationeditor and the GEDI graphical editor of the User Interface Manager (UI) (includes a data model editor,mass configuration tools, administration tools, an interface to version control systems, a debugger, etc.).Changes to data structures and graphics are applied without restarting the project. Writing custom scriptscan be done using CONTROL++ (a programming language, the syntax of which is similar to C/C++).Such scripts can be both event handlers associated with the elements of the graphical interface, and dataprocessing procedures. The system includes a standard graphical objects library; it can be extended bydeveloping user objects or using the Qt Toolkit widgets. It is also possible to use the JavaScript librariesavailable on the market or included JavaScript scripts. Thanks to the open API (C++ / C hapter 7 Data acquisition system The data acquisition system of the SPD should provide continuous data taking, including data readoutfrom the front-end electronics, data consistency check, event building and writing events to a storage.The system should have no dead time or minimal dead time. These features will be implemented with theDAQ operating in a free-running (triggerless) mode. Other important tasks of the DAQ are:– initialization of hardware;– control and monitoring of the data taking process: control of the status of all hardware devicesincluding front-end electronics, status of software, quality of collected data;– monitoring of the parameters characterizing the detector performance (accumulation of time, am-plitude and hit distribution histograms, detector rates, etc.);– logging of information and errors;– distribution of data over computing nodes for further online analysis;– etc.The data acquisition system of SPD should withstand the data flux from p - p , p - d or d - d interactions atthe extreme conditions of high luminosity. At the highest NICA energy and luminosity, √ s = 27 GeVand L = cm − s − , the interaction rate within the SPD aperture will be 3 MHz, and the averagemultiplicity of about 15. This drastically differs from the conditions of another NICA experiment, MPD,where the collision rate of heavy ions is orders of magnitude less, but the multiplicity is much higher.The structure of DAQ will be similar to recently modernized DAQ of the COMPASS experiment at CERN[440–446]. The COMPASS DAQ extensively uses logical programmable integrated circuits FPGA atdifferent levels of the system. This allows one to handle large data streams with minimal latency andprovides very good flexibility. Unlike the COMPASS experiment, which uses the beam of the CERNSPS with a spill time structure, the SPD DAQ will deal with a continuous beam.The DAQ of SPD will operate in a free-running mode, when the readout is not controlled by a triggersystem, but occurs with a fixed frequency. It requires all front-end electronics running in a self-triggeredmode, and the readout happens synchronously with a common clock distributed by the precise timing11516Table 7.1: Summary of detectors outputs to DAQ. Information type: T means time, A – amplitude (orcharge).Sub-detector Information Number Channels Numbertype of channels per FE card of outputsVertex detector 5 DSSD T + A 460800 640 720Vertex detector 3 MAPS+ 2 DSSD T + (T + A) (3024 + 596) ∗ 864 + 596Straw tracker T + A 79200 64 1238Calorimeter T + A 30176 64 472PID-ToF T 20200 32 632PID-Aerogel T + A 320 32 10BBC (inner+outer) T + (T + A) 256 + 192 32 8 + 6Range system T 106000 192 553ZDC T + A 250 + 650 16 57Total (max) 698044 ∗∗ ∗ – number of sensors, see Section 4 of Chapter 4 ∗∗ – for DSSD versionsystem. All the data received between the acts of readout are accumulated in the memories implementedin the front-end electronics modules and are stored there until the next readout. The readout frequencyvalue will be chosen depending on the detector rates and memory depths available in the front-end cards.The width of the time slice between the successive readouts should be much larger than the responsetime of the sub-detectors in order to minimize the probability of separating an event into two slices.Digitization of data and zero suppression occur in the front-end electronics. It is expected that theso-called ”feature extraction algorithm” will be implemented in the front-end electronics of the ver-tex detector and the calorimeter. This algorithm, which is under development in several collaborations(in particular, PANDA [447], COMPASS [448–450]), allows transferring only the extracted time andamplitude, instead of many samples of the digitizer, thus greatly decreasing the amount of data to betransferred.For now the expected data flux in the hardest conditions of the experiment (maximum energy and lumi-nosity) has been estimated without detailed simulations, but using the current knowledge of the sub-detector structure, particle multiplicity per event, hit multiplicity in different detectors, expectationsabout the front-end electronics parameters and, where relevant, results of the beam tests at other ex-periments (MPD, PANDA). The total number of channels to be read out is about 700 thousand, with themajor part coming from the vertex detector ( ∼ 460 thousand for the VD strip option). The full numbersare given in Table 7.1. Preliminary estimation for the data flow is about 20 GB/s including some marginof safety. The scheme of the DAQ is presented in Fig. 7.1. The data from the front-end electronics cards cometo the detector interface cards (FE concentrators). Now the existing electronics card with 12 input isconsidering as FE concentrators [442]. The Data-Handler multiplexers (UDHmx) are configured on thebase of FPGA. The multiplexer has 48 high speed input and up to 8 output interfaces. They verify theonceptual design of the Spin Physics Detector 117consistency of data and store them until receiving the readout signal.The two Data-Handler Switches (UDHSw) function as a 10 × 10 switch and perform event building with amaximum throughput rate of 10 GBytes/second. The UDHSw’s perform the final level of event buildingand distribute the assembled events to 20 readout computers. The Data-Handler Switches and Data-Handler multiplexers are implemented on the same electronics cards by means of different firmware.Each readout computer is equipped with a dedicated PCIe buffer card for data collection. These cards arebuilt on a FPGA chip and are commercially available. The current version of the card used in COMPASShas a bandwidth close to 1 GB/s [445]. Finally, the continuous sequence of slices is formed below theNetwork Switch in each of on-line computers to be used for on-line filtering and event monitoring.The slow control software accesses the front-end electronics via the FE concentrators using the UDP-based IPBus protocol [451]. The interface cards retransmit control and clock signals provided by thetime distribution system to the corresponding front-end electronics, and convert the detector informationfrom the detector specific interfaces to a common high-speed serial interface running over optical fiber.It is foreseen to use UCF [452] as a standard high speed link protocol within the DAQ.The White Rabbit system [453, 454] is planned to be used at NICA for time synchronization. It providessynchronization for large distributed systems with a time-stamping of 125 MHz, sub-nanosecond accu-racy and ∼ 10 ps precision. Signals from the White Rabbit system will be used as an input for the TimeControl System (TCS) [455] which will distribute clock signals through the whole electronic system. The time structure of the expected data flow during a run is shown in Fig. 7.2. All processes are syn-chronized with a 125-MHz clock coming from the White Rabbit system. A Run is started after the resetprocedure which includes all initialization processes. Afterwards, the continuous date flow is dividedinto a sequence of time slices. The proposed time slice duration can be selected in the range from 1 µs to8.3 ms and will be chosen according to the data flux and capacity of the whole chain of data collection.Longer slices are preferable, because the longer the slice, the less the probability an event falling intotwo adjacent slices. The slices have a continuous numbering within a frame, a wider time interval, whichcan extend from 65 ms to 549.7 s. The slice numbering is reset in every frame by the Start of the framesignal.The proposed formats of the collected data are shown in Figs. 7.3–7.7. The data are formatted at allstages of transfer from the Front-End Concentrators to the Data-Handler Switches. The required headersand checksums are added at all stages.In Fig. 7.3, the structure of a Run is shown. The Run consists of a sequence of Frames (Fig. 7.4)numbered from 0 to N, where N, the maximum number of frames in the Run, is assigned by the TCScontroller. The Frame consists of a sequence of slices numbered from 0 to K, the maximum number ofslices in the Frame, which is also assigned by the TCS controller.Fig.7.5 shows the structure of the Slice. The Slice contains a sequence of Data Blocks from the DataConcentrators (Fig. 7.6). Finally, the lowest unit in the Data Format chain is the Data Block of FEConcentrators (Fig. 7.7) which contains Physical Data from several ports the amount of which dependson the FE card type.The proposed format provides a unique connection of the physical information to the detectors geometryand the event time.18 SPD Detectors Frontend cards (~700k channels) SPD Experimental Hall FPGAUDHsw FPGAUDHsw 20 Data Links(1 GB/s) 20 ReadoutComputers20 x 25GbpsEthernet Links NICAWhite Rabbit TCS TCS Controller:- Reference Clock;- Time Stamps;- Bunch Crossing (??) TCSTCSTCS TCSIPBUS IPBUSIPBUS IPBUSIPBUS Supervisor Computer:- IPBUS Server;- Con fi g Server;- File Server;- Con fi g DB Server;- etc. IPBUS Online Computers:- online fi lter;- monitoring;- temporary data storage;- data recording;- online data analysis;- etc. Transfer toFinal Storage FrontendConcentrator FrontendConcentrator FrontendConcentrator FrontendConcentrator ... ~3500 FE Cards FrontendConcentrator ~6000 UCF Links(<10 MB/s/link) ~300 FEConcentrators ~300 Data Links(<100 MB/s/link) TCS IPBUS FPGAUDHmx FPGAUDHmx FPGAUDHmx FPGAUDHmx FPGAUDHmx 10 UDHmx Online Computers ... Figure 7.1: General structure of DAQ-SPD.onceptual design of the Spin Physics Detector 119 Start of RunStart of Frame Start of SliceReset Procedure(N1 clocks) End of SliceStart of Slice End of SliceStart of Slice Start of Slice End of SliceEnd of FrameEnd of RunEnd of SliceEnd of FrameStart of FrameSlice( M clocks ) Reset Procedure(N2 clocks) Command to stop RunSlice( M clocks ) Slice( M clocks ) 125 MHz Figure 7.2: Time diagram of a sequence of clocks, Slices and Frames within the Run. 31 24 23 16 15 0Start of Run Run NumberStart of Run Time in seconds since DATEFrame 0Frame 1 · · · Frame KEnd of Run LSB of Run Number Run NumberStart of Run Run NumberEnd of Run Time in seconds since DATE Figure 7.3: Data Format: Run structure. 31 24 23 16 15 0Start of Frame LSB of Run Number Frame NumberStart of Frame Time in seconds since DATESlice 0Slice 1 · · · Slice KEnd of Frame LSB of Run Number Frame NumberEnd of Frame Time in seconds since DATE Figure 7.4: Data Format: Frame structure.20 31 24 23 16 15 0Start of Slice Slice NumberLSB of Run Number Frame NumberTotal size of all data blocks in 32-bit words or Number of BlocksBlock 0Block 1 · · · Block XEnd of Slice Slice Number Figure 7.5: Data Format: Slice structure. 31 28 27 24 23 16 15 0Block Size in 32-bits wordsVersion Reserved Block Type Concentrator IDFrame Number Slice NumberData blocks from low level Data Concentrators with the same data strutructure or physicaldata FE electronics for lowest Data ConcentratorsCheckSum Figure 7.6: Data Format: structure of Data Blocks of High Level. 31 28 27 24 23 16 15 0Block Size in 32-bits wordsVersion Reserved Block Type Concentrator IDFrame Number Slice NumberPhysical Data from port 0Physical Data from port 1 · · · Physical Data from port ZCheckSum Figure 7.7: Data Format: structure of Low Level Data from FE Concentrators.onceptual design of the Spin Physics Detector 121Table 7.2: Cost estimation of the DAQNumber Cost Total(k$) (k$)FE concentrators 380 3.5 1330UDHmx modules 12 17.5 210UDHsw modules 3 17.5 52Case for UDHmx modules 6 2.3 14Time Distribution 1 35 35Online Computers 20 12 240VME crates 45 6 270Consumables 100Contingencies ≈ 350 (15%)Total 2600 The numbers of modules and their preliminary cost estimation are summarized in Table 7.2. hapter 8 Computing and offline software Expected event rate of the SPD experiment is about 3 MHz ( pp collisions at √ s = 27 GeV and 10 cm − s − design luminosity). This is equivalent to the raw data rate of 20 GB/s or 200 PB/year, assumingthe detector duty cycle is 0.3, while the signal-to-background ratio is expected to be in order of 10 − .Taking into account the bunch crossing rate of 12.5 MHz, one may conclude that pile-up probability willbe sufficiently high.The key challenge of the SPD Computing Model is the fact, that no simple selection of physics events ispossible at the hardware level, because the trigger decision would depend on measurement of momentumand vertex position, which requires tracking. Moreover, the free-running DAQ provides a continuous datastream, which requires a sophisticated unscrambling prior building individual events. That is the reasonwhy any reliable hardware-based trigger system turns out to be over-complicated and the computingsystem will have to cope with the full amount of data supplied by the DAQ system. This makes amedium-scale setup of SPD a large scale data factory 8.1.The continuous data reduction is a key point in the SPD computing. While simple operations like noiseremoval can be done yet by DAQ, it is an online filter that is aimed at fast partial reconstruction of eventsand data selection, thus being a kind of a software trigger. The goal of the online filter is to decrease thedata rate at least by a factor of 50 so that the annual upgrowth of data including the simulated samplesstays within 10 PB. Then, data are transferred to the Tier-1 facility, where full reconstruction takes placeand the data is stored permanently. Two reconstruction cycles are foreseen. The first cycle includesreconstruction of some fraction of each run necessary to study the detector performance and derivecalibration constants, followed by the second cycle of reconstruction of full data sample for physicsanalysis. The data analysis and Monte-Carlo simulation will likely run at the remote computing centers(Tier-2s). Given the large data volume, a thorough optimization of the event model and performance ofreconstruction and simulation algorithms are necessary.Taking into account recent advances in the computing hardware and software, the investment in theresearch and development necessary to deploy software to acquire, manage, process, and analyze thedata recorded is required along with the physics program elaboration and the detector design. While thecore elements of the SPD computing system and offline software now exist as prototypes, the system asa whole with capabilities such as described above is in the conceptual design stage and information willbe added to SPD planning documents as it is developed.122onceptual design of the Spin Physics Detector 123 Event size (Bytes) ) - L T r i gg e r R a t e ( s 10 COMPASS CMS ATLASALICELHCbKTeV D0CDFOPAL BaBarH1BELLE ISPD Figure 8.1: Expected event size and event rate of the SPD setup after the online filter compared withother experiments [456]. The SPD online filter facility will be a high-throughput system which will include heterogeneous com-puting platforms similar to many high performance computing clusters. The computing nodes will beequipped with hardware acceleration. The software framework will provide the necessary abstraction sothat common code can deliver the selected functionality on different platforms.The main goal of the online filter is a fast reconstruction of the SPD events and suppression of thebackground ones at least by a factor of 50. This requires fast tracking and fast clustering in the electro-magnetic calorimeter, followed by reconstruction of event from a sequence of time slices and an eventselection (software trigger). Several consecutive time slices shall be considered, tracker data unpackedand given for a fast tracking. The result of the fast track reconstruction is the number of tracks, an es-timate of their momentum and an estimate of primary vertex (to distinguish between tracks belongingto different collisions). Using this outcome, the online filter should combine information from the timeslices into events and add a trigger mark. The events shall be separated in several data streams using thetrigger mark and an individual prescale factor for each stream is applied.One of the most important aspects of this chain is the recognition of particle tracks. Traditional trackingalgorithms, such as the combinatorial Kalman filter, are inherently sequential, which makes them ratherslow and hard to parallelized on modern high-performance architectures (graphics processors). As aresult, they do not scale well with the expected increase in the detector occupancy during the SPD datataking. This is especially important for the online event filter, which should be able to cope with theextremely high data rates and to fulfill the significant data reduction based on partial event reconstruction‘on the fly’. The parallel resources like multicore CPU and GPU farms will likely be used as a computingplatform, which requires the algorithms, capable of the effective parallelization, to be developed, as wellas the overall cluster simulation and optimization.Machine learning algorithms are well suited for multi-track recognition problems because of their abil-24ity to reveal effective representations of multidimensional data through learning and to model complexdynamics through computationally regular transformations, that scale linearly with the size of input dataand are easily distributed across computing nodes. Moreover, these algorithms are based on the linearalgebra operations and can be parallelized well using standard ML packages. This approach was alreadyapplied successfully to recognize tracks in the BM@N experiment at JINR and in the BESIII experimentin IHEP CAS in China [457, 458]. In the course of the project an algorithm, based on recurrent neuralnetworks of deep learning, will be developed to search for and reconstruct tracks of elementary particlesin SPD data from the silicon vertex detector and the straw tube-based main tracker. The same approachwill be applied to the clustering in the SPD electromagnetic calorimeter, and fast π reconstruction. Thecaution is necessary, though, to avoid possible bias due to an inadequacy of the training data to the realones, including possible machine background and the detector noise. A dedicated workflow that includescontinuous learning and re-learning of neuron network, deployment of new versions of network and thecontinuous monitoring of the performance of the neural networks used in the online filter is necessaryand needs to be elaborated.Besides the high-level event filtering and corresponding data reduction, the online filter will provide inputfor the run monitoring by the shift team and the data quality assessment, as well as local polarimetry. The projected rate and amount of data produced by SPD prescribe to use high throughput computingsolutions for the processing of collected data. It is the experience of a decade of the LHC computing thatalready developed a set of technologies mature enough for the building of distributed high-throughputcomputing systems for HEP. The ’online’ part of computing systems for the SPD experiment, namely the online filter described above,is an integral part of experimental facilities, connected with the ’offline’ part using a high throughputbackbone network. The entry point to ’offline’ facilities is a high capacity storage system, connectedwith ’online facility’ through a multilink high-speed network. Data from high capacity storage at theLaboratory of Information Technologies will be copied to the tape-based mass storage system for longterm storage. At the same time, data from high capacity storage will be processed on different computingfacilities as in JINR as in other collaborative institutions.The hierarchy of offline processing facilities can be introduced:– Tier 1 level facilities should provide high capacity long term storage which will have enoughcapacity to store a full copy of primary data and a significant amount of important derived data;– Tier 2 level facility should provide (transient) storage with capacity that will be enough for storingof data associated with a period of data taking;– optional Tier 3 level are opportunistic resources, that can be used to cope with a pile-up of pro-cessing during some period of time or for special analysis.Offline data processing resources are heterogeneous as on hardware architecture level so by technolo-gies and at JINR site it includes batch processing computing farms, high performance (supercomputer)facilities, and cloud resources. A set of middleware services will be required to have unified access todifferent resources.onceptual design of the Spin Physics Detector 125Figure 8.2: Scheme of the SPD computing system Computing systems for NICA at JINR are naturally distributed. Experimental facilities and main dataprocessing facilities placed across two JINR sites and, inter alia, managed by different teams. That causessome heterogeneity not only on hardware systems but also on the level of basic software: different OSs,different batch systems etc.Taking into account the distributed nature and heterogeneity of the existing infrastructure, and expecteddata volumes, the experimental data processing system must be based on a set of low-level services thathave proven their reliability and performance.It is necessary to develop a high-level orchestrating system that will manage the low-level services.The main task of that system will be to provide efficient, highly automated multi-step data processingfollowing the experimental data processing chain.The Unified Resource Management System is a IT ecosystem composed from the set of subsystem andservices which should:– unify of access to the data and compute resources in a heterogeneous distributed environment;– automate most of the operations related to massive data processing;– avoid duplication of basic functionality, through sharing of systems across different users (if itpossible);– as a result - reduce operational cost, increase the efficiency of usage of resources;– transparent accounting of usage of resources.Many distributed computing tools have already been developed for the LHC experiments and can be re-used in SPD. For the task management one can use PANDA [459] or DIRAC [460] frameworks. For the26 Figure 8.3: Distributed SPD computing servicesdistributed data management RUCIO [461] package has been developed. For the massive data transferFTS [462] can be used. Evaluation of these tools for the SPD experiment and their implementationwithin the SPD Unified Resource Management System is planned in scope of the TDR preparation. Offline software is a toolkit for event reconstruction, Monte-Carlo simulation and data analysis. Linux ischosen as a base operating system.Currently, the offline software of the SPD experiment – SpdRoot – is derived from the FairRoot soft-ware [463] and it is capable of Monte Carlo simulation, event reconstruction, and data analysis and visu-alization. The SPD detector description is flexible and based on the ROOT geometry package. Proton-proton collisions are simulated using a multipurpose generator Pythia8 [464]. Deuteron-deuteron colli-sions are simulated using a modern implementation of the FRITIOF model [465, 466], while UrQMD [467,468] generator is used to simulate nucleus-nucleus interactions. Transportation of secondary particlesthrough the material of the SPD setup and the simulation of detector response is provided by Geant4toolkit [469–471]. Track reconstruction uses GenFit toolkit [472] and KFparticle package [473] is usedto reconstruct primary and secondary vertices. The central database is going to be established to keepand distribute run information, slow control data and calibration constants.Recent developments in computing hardware resulted in the rapid increase of potential processing capac-ity from increases in the core count of CPUs and wide CPU registers. Alternative processing architectureshave become more commonplace. These range from the many-core architecture based on x86 64 com-patible cores to numerous alternatives such as other CPU architectures (ARM, PowerPC) and specialco-processors/accelerators: (GPUs, FPGA, etc). For GPUs, for instance, the processing model is verydifferent, allowing a much greater fraction of the die to be dedicated to arithmetic calculations, but at aprice in programming difficulty and memory handling for the developer that tends to be specific to eachprocessor generation. Further developments may even see the use of FPGAs for more general-purposetasks.onceptual design of the Spin Physics Detector 127Table 8.1: Required SPD computing resourcesCPU [cores] Disk [PB] Tape [PB]Online filter 6000 2 noneOffline computing 30000 5 9 per yearCost estimate [kUSD] 4000 8000 4500 per yearThe effective use of these computing resources may provide a significant improvement in offline dataprocessing. However, the offline software should be capable to do it by taking advantage of concurrentprogramming techniques, such as vectorization and thread-based programming. Currently, the SPDsoftware framework, SpdRoot, cannot use these techniques effectively. The studies of the concurrent-capable software frameworks (e.g. ALFA [474], Key4Hep [475]) are needed to provide input for theproper choice of the offline software for Day-1 of the SPD detector operation, as well as a dedicatedR&D effort to find proper solutions for the development of efficient cross-platform code.A git-based infrastructure for the SPD software development is already established at JINR [476]. For the online filter we assume the CPU consumption of 1000 SPD events/core/second. This requires3000 cores simultaneously for the fast tracking. Taking into account additional expenditures to the eventunscrambling and data packing and including a real efficiency of CPU which will be lower than 100%,one derives the CPU resources for the online filter as 6000 CPU cores. This number sets the upper limitand the required computing power may decrease substantially if an efficient way to use GPU cores isimplemented for the event filtration. As for the data storage, a high performance disk buffer of 2 PBcapable to keep data of about one day of data taking is needed.For the offline computing, the data storage is determined by the data rate after the online filter, or 4PB/year of raw data. Besides that, we may expect the comparable amount of simulated data and estimatethe long term storage as 10 PB/year, assuming two cycles of data processing and possible optimizationof the data format and data objects to be stored permanently. We assume that a half of the annual datasample ( ∼ hapter 9 Physics performance The total cross-section of the p - p collisions in the full energy range of SPD operation is a constantand equals about 40 mb. The main contributions to that cross-section, i. e. the elastic scattering, thediffractive and non-diffractive processes, are shown in Fig. 9.1. The cross-section of ”hard” processes,the QCD processes with partonic transverse momentum ˆ p T > c , is also shown as a part of the non-diffractive cross-section. The beam particle collisions in the interaction point are the source of numeroussecondary charged and neutral particles in the SPD setup that fully defines our experimental conditions(the load of the detector, radiation environment, etc.). The fluxes of different kinds of the charged andneutral particles produced in the interaction point as a function of the polar angle are shown in Fig.9.2(a) and (b) for √ s = 27 and 13.5 GeV, respectively. Table 9.1 shows the total cross-section of the p - p 10 12 14 16 18 20 22 24 26 28, GeVs0510152025303540 , m b s TOTALNon-diffractiveDiffractive Elastic"Hard" Figure 9.1: Main contributions to the total cross-section of p - p interaction as a function of √ s . The”hard” cross-section is a part of the non-diffractive one.128onceptual design of the Spin Physics Detector 129 q -1 sr -1 , s F pp, - p , + p - p , + p nn, - , K + K g = 27 GeVs -2 cm -1 s L = 10 (a) q -1 sr -1 , s F pp, - p , + p nn, - , K + K g = 13.5 GeVs = 13.5 GeVs -2 cm -1 s L = 10 (b)Figure 9.2: Fluxes of p + ¯ p , π ± , K ± , n + ¯ n and γ as a function of the polar angle θ for (a) √ s = 27 GeVand (b) 13.5 GeV.collisions and the multiplicity of charged and neutral particles for different collision energies √ s .The secondary interactions in the material of the setup, the multiple scattering, the decays of unstableparticles, and the influence of the magnetic field modify the radiation environment inside the SPD setupsignificantly. All these factors are taken into account in Figure 9.3 that illustrates the fluxes of the chargedparticles, photons, and neutrons at different points of the SPD setup for √ s = 27 GeV and L = cm − chargedphotons > 1 MeV kin neutrons Ethermal neuterons Z = 1.3 m -1 s -2 Rate, cm -1 s -2 cm L = 10 = 27 GeVs (a) chargedphotons > 1MeV kin neutrons Ethermal neutrons -1 s -2 Rate, cm -1 s -2 cm L = 10 = 27 GeVs Z = 1.5 m (b) - - - chargedphotons > 1 MeV kin neutrons Ethermal neutrons R = 1 m -1 s -2 Rate, cm -1 s -2 cm L = 10 = 27 GeVs (c) - - - chargedphotons > 1 MeV kin neutrons Ethermal neutrons R = 3.5 cm = 27 GeVs -1 s -2 Rate, cm -1 s -2 cm L=10 (d)Figure 9.3: Flux of charged particles, photons, and neutrons in the radial direction at (a) Z=1.3 m, (b)Z=1.5 m, (c) R=1 m, and (d) R=3.5 cm.30s − : Z=1.3 m (a), Z=1.5 m (b), R=1 m (c), and R=3.5 cm (d).Table 9.1: Total cross-section and the average multiplicity of the charged and neutral particles producedin the p - p collisions as a function of √ s . √ s , GeV σ tot , mb Charged Neutral ( γ )multiplicity multiplicity13 38.4 5.9 4.6 (3.8)20 38.9 7.2 6.0 (5.0)26 39.7 7.8 6.5 (5.5) Traditionally, the track reconstruction procedure is divided into two separate tasks: track finding (orpattern recognition) and track fitting. Since the track multiplicity in the p - p collisions is low enough(see Tab. 9.1) the occupancy of the coordinate detectors is not really a problem. Thus, we hope to havethe efficiency of the track finding to be not less than 90% in the most of our acceptance and we are notpaying too much attention to the pattern recognition algorithms now. However, high multiplicity willlimit the SPD performance in the case of NICA operation with heavy-ion beams.The SPD magnetic system provides the conditions for measurement of the charged particle momenta.The track length in the SPD tracking system for charged particles of different momenta emitted fromthe interaction point at different polar angles as well as the trajectories for muons with momentum of0.25 GeV/ c emitted at different polar and azimuthal angles θ = φ are presented in Fig. 9.4 (a) and (b),respectivly.The track fitting procedure uses measured hits in the tracking detectors (or simulated points for MonteCarlo events) as an input, and calculates the most probable track parameters at any given point along thetrack, together with the corresponding covariance matrix. The fitting procedure also takes into consider-ation such effects related to the particle interaction in the material as multiple scattering, energy losses,and magnitude and configuration of the magnetic field. For the track fitting at SPD the well-knownKalman filter [477] implemented within the GenFit2 package [472] is used. The GenFit2 extrapolates(a) (b)Figure 9.4: (a) Track length in the SPD tracking system for charged particles of different momentaemitted from the IP at different polar angles. (b) Trajectories for muons with momentum of 0.25 GeV/ c emitted from the IP at different polar and azimuthal angles θ = φ .onceptual design of the Spin Physics Detector 131 T p0.511.522.533.54 , % T / p T dp (a) - m + m M(0200400600800100012001400 E n t r i e s ~ 33 MeV s ~ 77 MeV s Dimuon mass spectrum fitted with the double Gaussian shape (b)Figure 9.5: (a) Expected resolution for the transverse momentum σ p T / p T of muons with momentum0.75, 1.5, 3, 6, and 12 GeV/ c . (b) J / ψ peak from the dimuon decay.tracks using the standard Runge-Kutta-Nystr¨om method [478] modified by Bugge and Myrheim to carryalong the Jacobian matrix [479, 480].The expected transverse momentum resolution σ p T / p T for muons with different momenta for the max-imal magnetic field 1.0 T at the beam axis is shown in Fig. 9.5(a). The corresponding resolution formuons emitted at the polar angle θ = ◦ could be expressed as σ p / p (cid:12)(cid:12) θ = ◦ = . + . × p + . × p . (9.1)The width of the J / ψ peak shown in Fig. 9.5(b) is a good indicator of the tracking performance. TheSPD tracking system demonstrates the width at the level of 40 MeV. It is 1.5 times better than at thefixed-target COMPASS experiment with the open setup ( ∼ 60 MeV [481]) and much better than in thefixed-target beam dump experiments like NA3 (80 ÷ 120 MeV [482]), COMPASS ( ∼ 200 MeV [186]),SeaQuest ( ∼ 150 MeV [483]), which worked successfully on the study of the partonic structure of thenucleon at the discussed energy range. The only subsystem that defines reconstruction of primary vertices is the silicon vertex detector. Its im-pact on the accuracy of the vertex reconstruction depends on the baseline (the radial distance betweenlayers), the amount of passed material producing the multiple scattering effects, and the spatial reso-lution of the detector. The latter is a rather complex function of the number of fired strips (or pixels).We estimate the effective spatial resolution of the DSSD layer as σ φ = µ m, σ z = µ m, while theresolution of the MAPS layer is σ φ , z = µ m. σ φ here denotes the resolution in the direction perpen-dicular to the beam line. The effective values are about two times smaller than the corresponding pitchdivided by √ 12. The amount of the material corresponds to 300 µ m and 50 µ m of silicon per one layerof the DSSD and MAPS, respectively. Figure 9.6(a) shows the accuracy of the primary vertex positionreconstruction as a function of the number of outgoing tracks for two configurations of the vertex de-tector: (i) 5 layers of the DSSD, (ii) 3 layers of the MAPS and 2 layers of the DSSD. In both cases theaccuracy becomes better with an increasing number of outgoing tracks, as expected. The DSSD+MAPSconfiguration demonstrates a 1.5 times better precision.The silicon vertex detector is also fully responsible for reconstruction of the decay vertices of short-lived( c τ < D → K + π − decay as an example (see the sketch in Fig. 9.6 (b)),but all the conclusions are also valid qualitatively for the decays like D + → K − π + π − , Λ + c → p π + K − Spatial resolution for primary vertices m ] m [ s (DSSD) x s (DSSD) z s (MAPS+DSSD) x s (MAPS+DSSD) z s (a) D V V + K - p (b)Figure 9.6: (a) Accuracy of the primary vertex position reconstruction as a function of the number ofoutgoing tracks for two configurations of the vertex detector. (b)Sketch of D -meson production anddecay. decay vertices Spatial resolution for secondary D m ] m [ s (DSSD) x s (DSSD) z s (MAPS+DSSD) x s (MAPS+DSSD) z s (a) mass resolution D ] [ G e V / c s DSSDMAPS+DSSD (b)Figure 9.7: (a) Accuracy of the D -decay vertex reconstruction as a function of the D momentum. (b) D peak width as a function of the D momentum.etc. The accuracy of the D -decay vertex reconstruction as a function of the D momentum is shownin the Fig. 9.7 (a). The Gaussian width of the D -meson peak in the K + π − mass spectrum determinedby the tracking accuracy (mainly by the momentum resolution) is 27.2 and 25.0 MeV for the DSSD andDSSD+MAPS configurations, respectively. The constrained fit of the D -decay, where the angle betweenthe reconstructed D momentum and the line connecting the primary and secondary vertices is forced tobe zero and the found vertex is included in the track fitting, reduces the width to 21.4 and 18.0 MeV. Thatimproves, respectively, the signal-to-background ratio by the factor of 1.3 and 2.4. The D -peak widthobtained from the constrained fit as a function of D momentum is shown in Fig 9.7 (b). The impact ofthe secondary vertex reconstruction procedure on our expectations for the asymmetries measurement isdiscussed in Sec. 2.The decays of relatively long-lived unstable particles like Λ , K , Σ − etc. occur mainly within the strawtracker. The Λ → p + π − peak is presented in Fig. 9.8(a) as an example. The effective π /K/p separation is required first of all for such physics tasks as the open charm production(identification of kaons form D ± , decays, see Fig. 9.8 (b)); measurement of the SSA for charged kaons,onceptual design of the Spin Physics Detector 133 + π p M0100200300400500 =2 MeV σ (a) , GeV/c K p + p - K fi D + p + p - K fi + D (b)Figure 9.8: (a) Λ peak in the p π mass spectrum. (b) Kaon spectra from the decays D → K − π + (red)and D + → K − π + π + (blue) produced at √ s = 27 GeV/ c .and the study of the antiprotons yield. The proposed SPD setup has three instruments for identificationof charged hadrons. The energy deposit dE / dx in the straw tubes of the ST can be used for particleidentification at lowest momenta. The TOF system could extend the separation range up to 1.5 GeV/ c and ∼ c for π / K and K / p , respectively. The separation for the higher range of hadron momentacould be provided only by the aerogel detector. dE / dx The energy deposit dE / dx in the straw tubes is plotted in Fig 9.9 (a) for the particles emitted at θ = ◦ in respect to the beam axis as a function of their momenta. The truncated mean approach, where 20%of the measurement results from the individual straw tubes is discarded, was applied. The straw trackeris able to provide π / K and K / p separation up to 0.7 GeV/ c and 1.0 GeV/ c , respectively. With respectto the TOF method (see below), the efficiency of the dE / dx method does not degrade at the low polarangles, since the end-cup part of the ST has enough layers for the precision measurement of the energydeposit. Particle identification with a TOF detector is based on comparison between the time of flight of theparticle from the primary vertex to the TOF detector and the expected time under a given mass hypothesis.For particle identification, the presence of only one plane of the TOF detector requires precise knowledgeof the event collision time t . It can be estimated by the TOF detector on an event-by-event basis, usingthe χ minimization procedure for the events with two and more reconstructed tracks. Having N tracks inthe event, which are matched to the corresponding hits on the TOF plane, it is possible to define certaincombinations of masses (cid:126) m i , assuming the p, K, or p mass for each track independently. The index i indicates one of the possible combinations ( m , m , . . . , m N tracks ) among the 3N-track ones [484].To each track the following weight is attributed W i = σ TOF + σ t exp . i . (9.2)Here σ TOF and σ t exp . i are the time resolution of the TOF detector and the uncertainty of the expectedtime of flight under a given mass hypothesis t exp . i , respectively. The latter is defined by the uncertaintyof the momentum and track length measurements.34The following χ function has to be minimized χ ( (cid:126) m i ) = ∑ N W i (( t TOF − t ( (cid:126) m i )) − t exp . i ) . (9.3)Here t ( (cid:126) m i ) = ∑ N ( t TOF − t exp . i ) ∑ N W i . (9.4)The mass vector (cid:126) m i that minimizes χ in Eq. 9.3 can be used in Eq. 9.4 for determination of the eventcollision time t . For unbiased particle mass determination, each track has to be subsequently excludedfrom the t calculation procedure.Figure 9.9 (b) illustrates the accuracy of t reconstruction as a function of the number of tracks for σ TOF = 70 ps. One can see that σ t is proportional to 1 / √ N and for the track multiplicity 10 (typicalfor hard interaction events) is about 30 ps. Pion, kaon, and proton separation with the TOF detector isshown in Fig. 9.10. The π / K and K / p separation power as a function of the particle momenta and theemission angle θ in the primary vertex is presented in Fig. 9.11 (a) and (b), respectively, for the timeof flight ( t TOF − t ) resolution equal to 80 ps. It is mostly defined by the time measurements, while theaccuracy of the momentum reconstruction becomes sizable only for θ < ◦ .(a) N tracks , p s t s N90 ps (b)Figure 9.9: (a) Energy deposit dE / dx at the ST for particles emitted at θ = ◦ in respect to the beamaxis. (b) Accuracy of the t reconstruction as a function of the number of tracks in the primary vertex. The electromagnetic calorimeter is one of the main detectors for the SPD gluon program. Its functionsare: (i) to measure the energy and the position of the hard prompt photons, and the photons from theradiative decays of π - and η -mesons; (ii) to reconstruct the soft photons ( ∼ χ c , → J / ψγ ; (iii) to provide identification of the electrons and positrons by comparing the energydeposit in the ECal and their momentum measured in the tracking system. The end-cup part of the ECalparticipates also in the online polarimetry with the inclusive π production at high x F (see Sec. 2).The transparency of the SPD setup allows us to detect photons produced in the interaction point in a widekinematic range. The efficiency of photon detection as a function of the production angle θ with respectto the beam direction and as a function of the transverse momentum p T is shown in Fig. 9.12(a) and (b),respectively. The expected energy resolution of the ECal obtained from the Geant4-based Monte Carlosimulation for the normal incidence of photons and for the angle of 30 ◦ with respect to the normal lineis shown in Fig. 9.13(a). Such effects as the individual cell energy threshold at the level of 50 MeV, theonceptual design of the Spin Physics Detector 135 , GeV rec m p , G e V / c p K p Figure 9.10: Reconstructed mass vs. the particle momentum for pions, kaons, and protons. , deg q p , G e V / c s s s s (a) , deg q p , G e V / c s s s s (b)Figure 9.11: π / K (a) and K / p (b) separation power of the TOF system as a function of the particlemomenta and the emission angle.light absorption in the optic fibers, and the fluctuation of the number of photons are taken into account.The fitted curve has the shape: σ E / E = A ⊕ B (cid:112) E / GeV ⊕ CE / GeV , (9.5)where the parameters A , B , and C are 0.9%, 5.9%, 1.7% and 0.0%, 6.0%, 2.2%, respectively, for 0 ◦ and 30 ◦ of the incidence angle. The superconducting coils of the magnetic system (about 1.2 X of thematerial) placed in front of the calorimeter practically do not reduce its acceptance for the hard photonsand do not produce any sizable impart on the energy resolution. For instance, the average resolution forthe 1 GeV photons passing through the coil changes from 6.1% to 6.3%.As long as the internal longitudinal and transverse size of the ECal is small, there is a probability forphotons from the high-energy pions decay ( E π (cid:38) acce p t a n ce , [rad] q (a) T p00.20.40.60.81 A cce p t a n ce (b)Figure 9.12: Efficiency of photon detection as a function of (a) polar angle θ and (b) transverse momen-tum p T . / E E s o o (a) E ff i c i en cy o f doub l e - pho t on c l u s t e r r e j e c t i on (b)Figure 9.13: (a) Energy resolution of the ECal for the normal incidence of photons and for the angle of30 ◦ . (b) Purity of the double-photon clusters rejection vs. the efficiency of the single-photon reconstruc-tion for 6 GeV photons and two 3 GeV photons separated by a distance of 4 cm, based on the clustershape analysis.program. However, it is possible to identify such clusters with a certain precision performing the clustershape analysis. The cluster shape can be characterized using such variables as dispersion or the second-order moment (in one or two dimensions), the fourth-order moment, the ratio of the major and the minorsemiaxes of the cluster ellipse, etc. Machine learning classification techniques are planned to be applied(the multilayer perceptron, the k-nearest neighbors, etc.), using these variables as an input to distinguishbetween single- and double-photon clusters. Figure 9.13(b) illustrates the purity of the double-photonrejection vs. the efficiency of the single-photon reconstruction for 6 GeV photons and two 3 GeV photonsseparated by a distance of 4 cm (exactly the ECal cell size), based on the cluster shape analysis.The impact of the ECal energy resolution on the reconstruction of such states as π , η is shown in Fig.9.14(a). The relative width of the π and η peaks is 7.3% and 6.9%, respectively, for E γ > . χ c , , via their radiative decays is presented in Fig. 9.14(b). The χ c and χ c peaks cannot be fully resolved ( ∆ M / σ M ≈ . gg m050001000015000 = 9.8 MeV p s = 38 MeV h s (a) - m + m ) - M( - m + mg M(05001000150020002500300035004000 E n t r i e s >0.35 GeV g Ecal FastReco + tracking, E Entries 28939 / ndf c – – – c1 c c2 c >0.35 GeV g Ecal FastReco + tracking, E (b)Figure 9.14: (a) π -peak in the γγ mass spectrum. (b) Mass resolution for χ c , reconstructed via theirdecay into J / ψγ final state. The results presented in this section illustrate general possibilities of the SPD setup to deal with spinasymmetries and should be treated as preliminary. The most of them require further optimization of theselection criteria and could be significantly improved.The single transverse ( A N ) and the double longitudinal and transverse ( A LL and A T T ) spin asymmetriesare the main observables to be accessed at SPD. The asymmetry A N is denoted as A N = σ ↑ − σ ↓ σ ↑ + σ ↓ , (9.6)where σ ↑ and σ ↓ denote the inclusive production cross-sections with the opposite transverse polarizationof one of the colliding particles. In practice, taking into account the 2 π coverage of the SPD setup inazimuthal angle φ , the A N can be extracted from the azimuthal modulation amplitude of the differentialcross-section d σ / d φ d σ / d φ ∝ + PA N cos ( φ − φ ) , (9.7)where P and φ are the beam polarization and its direction. All estimations for the accuracy of the SSAmeasurement are performed under assumption that only one of the two beams is transversely polarized.In the case of two polarized beams the statistical uncertainty could be reduced by the factor of √ N ++ )and the opposite ( N + − ) spin orientations of colliding protons: A LL = σ ++ − σ + − σ ++ + σ + − = P P × N ++ − RN + − N ++ + RN + − . (9.8) σ ++ and σ + − denote the cross-sections with the same and the opposite proton helicity combinations,respectively. P and P are the absolute values of proton beams polarizations and R = L ++ / L + − is theratio of the integrated luminosities for the samples with the same and the opposite spin orientations.Assuming the same amount of data collected with both spin orientations Eq. 9.8 can be rewritten as: A LL = P P × N ++ − N + − N ++ + N + − . (9.9)The aforesaid is also valid for the A T T asymmetry.38 According to the modern theoretical approaches, the charmonia production at the SPD energies (10 GeV ≤√ s ≤ 27 GeV) is dominated by the gluon-gluon fusion process. The inclusive J / ψ production has a largecross-section (200 ÷ 250 nb at the maximum energy) and clear experimental signature in the dimuon de-cay mode, and thus is a powerful probe of the internal structure of proton and deuteron. At the same time,the distinct J / ψ signal allows us to reconstruct excited charmonia states in the decays χ c , → γ J / ψ and ψ ( S ) → π + π − J / ψ . There is also a possibility to reconstruct J / ψ from the e + e − final state, but it looksless promising due a much larger background, a larger observed J / ψ width, and a more complicatedshape of the peak, which will significantly affect both statistical and systematic errors. The study of the η c production properties in the p ¯ p and Λ ¯ Λ decay modes may also be feasible.Muons are identified in the RS. The system is expected to separate showers from strongly interactingpions and muon tracks (using standard or machine learning techniques). The main background is muonsfrom pion decays and pions that passed a large distance in the RS. The pion decays result in a smallkink of the charged track (about 2 ◦ ), and the decay muon retains from 60% to almost 100% of the initialpion energy. There is a possibility that a fraction of decay muons can be suppressed by the search for akink in the tracker or by considering the correlation between the particle momentum and the amount ofmaterial it crossed. However, the results in this section are based on a simplified model (gives a lowerperformance boundary). A particle is identified as a muon based on the amount of material it passes in theactive part of the RS, this amount is given as a number of proton nuclear lengths ( n λ ). Two possibilitiesare considered: a particle from the initial interaction and a muon from a pion decay (the pion must befrom the initial interaction). In the latter case, if the pion decays in the RS, the amount of material isadded for the pion and muon.It is clear that higher running energies are preferable for the physics with charmonia due to larger pro-duction cross-section, a stronger boost for pions and more energetic muons. All estimates in this sectionassume a pp collision energy of 27 GeV, 10 s time of data taking (one year) with the maximum lu-minosity and a polarization P of 0.7. At these conditions one expects about 12 million J / ψ → µ + µ − decays in the SPD detector.The J / ψ events are simulated using Pythia8 and their number is normalized to a production cross-sectionof 200 nb. For the background minimum bias events generated with Pythia6 and Pythia8 are considered(giving almost the same predictions around the J / ψ peak). Approximately half of the background eventsare produced in the hard interaction, but a sizable fraction also comes from the diffraction processes. Itappears that significant amount of background events can be suppressed by the requirement on the polarangle of a muon candidate. The µ + µ − invariant mass spectrum for the muon candidates with n λ > | cos θ | < . J / ψ peak are two decay muons, the other half mostly consists of one decaymuon and one pion that passed a large distance in the RS, and the rest are two pions misidentified as µ + and µ − . The selection efficiency can be estimated to be around 35 ÷ θ ,resulting in 4 ÷ J / ψ events: for more than 50% of J / ψ events one lepton is reconstructed in thebarrel and the other one in the end-caps, more than 35% of events are reconstructed solely in the barrelpart of the detector. The statistical errors for observables can be estimated using a linear LSM fit [31]. Asan example, the estimated statistical precision for the J / ψ polarization λ as a function of the transversemomentum p T is shown in Fig. 9.15 (b). The estimation was done under the assumption λ (cid:28) d σ / d cos θ µ ∝ + λ θ cos θ µ , (9.10)where θ µ is the angle between the muon momentum and the J / ψ momentum in the helicity frame.onceptual design of the Spin Physics Detector 139 ) (GeV) - m + m M( · E v en t s / M e V Total signal y J/ (a) (GeV/c) T p - - ls (b)Figure 9.15: (a) Dimuon candidate spectrum and the J / ψ peak after one year of data taking. (b)Expected statistical precision for polarization λ θ as a function of the J / ψ transverse momentum.The transverse single-spin asymmetry A N in J / ψ production probes the Sivers function. At √ s = 200 GeV it was measured by the PHENIX Collaboration and found consistent with zero [18, 19]. Toestimate our statistical precision, 8 bins in φ are considered (see Eq. 9.7). The same linear fit is usedto, firstly, estimate the error in the bins based on the expected J / ψ number and, secondly, to extract A N .The projected statistical uncertainties for A N as a function of x F are compared to the GPM model pre-dictions from Ref. [485] in Fig. 9.16 (preliminary CGI-GPM calculations indicate lower asymmetries).Compared to the PHENIX measurement, we expect a much better precision and a much wider kinematicrange in x F . Our rapidity range is approximately | y | < A N J / ψ x F ψ NRQCDICEM SPD NICAp ↑ p → J/ ψ (1S)+X √ S = GeV (a) A N J / ψ x F ψ NRQCDICEM SPD NICAp ↑ p → J/ ψ (1S)+X √ S = GeV (b)Figure 9.16: Projection of the estimated statistical uncertainties for A N compared to the GPM predictionsfrom Ref. [485] for SIDIS1 (a) and D’Alesio PDF parameterizations (b).The statistical error of the longitudinal double spin asymmetry A LL sensitive to the polarized gluon dis-tribution was estimated basing on Eq. 9.8 and 9.9. In these formulas, we neglect the uncertainties ofthe measurement of the relative integrated luminosities and the beam polarizations. The projection ofthe statistical uncertainties as functions of p T and | y | are shown in Fig 9.17. Compared to the previousresults obtained by the PHENIX Collaboration at √ s = 510 GeV [120], we have a much better precisionand probe a wider kinematic range.40 (GeV/c) T p LL A s case 1case 2case 3 (a) LL A s case 1case 2case 3 (b)Figure 9.17: Estimated statistical precision of A LL as a function of p T (a) and rapidity (b). Three differentcuts on the polar angle of muon candidates are considered.The study of the associated J / ψ production will be strongly restricted by the insufficient expected statis-tics. The double J / ψ production cross-section was measured by the NA3 Collaboration [486] and wasfound to be 27 ± 10 pb in the proton-nucleus interaction at √ s ≈ 27 GeV. Optimistically, such a cross-section would result in 50 ÷ 100 reconstructed events, if both e + e − and µ + µ − modes are used to recon-struct J / ψ . It may be enough to determine low- p T cross-section dependence, but the study of any angularmodulation will not be possible. The study of γ J / ψ production will be challenging experimentally dueto a lack of statistics and a high expected background. Reasonable statistics might be expected for J / ψ D production.The ψ ( S ) → µ + µ − decay is suppressed, as compared to J / ψ → µ + µ − by approximately a factor of50 and its reliable extraction may not be feasible. At the same time, the decay ψ ( S ) → π + π − J / ψ canbe reliably identified as a narrow (about 10 MeV / c wide) peak in the M π + π − µ + µ − − M µ + µ − distribution.This distribution is shown in Fig. 9.18 (a). The expected statistics is about 1 × selected events. ) (GeV) - m + m )-M( - p + p - m + m M( · E v en t s < 3.2 GeV mm (a) ) (GeV) - m + m )-M( g - m + m M( · E v en t s / M e V Total c2 c c1 c background > 0.35 GeV g ) < 3.2 GeV, E - m + m (b)Figure 9.18: (a) ψ ( S ) signal in the M π + π − µ + µ − − M µ + µ − distribution. (b) Preliminary estimation of thebackground for the χ c and χ c reconstruction. For this plot a feed-down fraction of 15% is assumed forboth states.The χ c and χ c states have a large partial width of decay to J / ψγ and can be reconstructed usingit. The production properties of these states at low energies are poorly known (e.g. see the review ofthe experimental results in Ref. [32]). The identification of these decays at SPD relies on the ECalperformance. The result of the MC simulation for M γµ + µ − − M µ + µ − is shown in Fig. 9.14(b). It willnot be possible to separate χ c from χ c , but their relative fractions should be well-measurable. For theonceptual design of the Spin Physics Detector 141expected statistics of approximately 0.5 million reconstructed decays per year (for both states together)it should be possible to measure the cross-section kinematic dependencies of these states. The majordifficulty in the studying of these states is the high expected background. Its very rough estimation isshown in Fig. 9.18 (b).The η c production cross-section is highly uncertain. At √ s = 24 GeV it is estimated that σ η c · B ( η c → p ¯ p ) = . + . − . nb [487] or 6 × events per year. The typical momenta of p and ¯ p is 1.5 – 2 GeV/ c ,where these particles should be well-identified by the TOF system (see Fig. 9.10). The feasibility ofthe differential cross-section measurements requires detailed MC-simulations due to the high expectedbackground. A very limited statistics, but a clearer signal may be also expected in the Λ ¯ Λ decay mode. As it was already mentioned in Chapter 2, two hard leading-order processes determine the production ofprompt photons in the p - p collisions in the leading order: gluon Compton scattering gq ( ¯ q ) → γ q ( ¯ q ) andquark-antiquark annihilation: q ¯ q → g γ . The contribution of the latter process to the total cross-sectiondoes not exceed 20% in the discussed energy range. That is what makes the prompt photons a convenientprobe for gluons inside the nucleon. The energy and angular distributions for prompt photons with p T > c are shown in Fig. 9.19. There we do not take into consideration fragmentation photons,whose contribution is significant in the discussed range of p T , and which should also be treated as apart of the signal. Figure 9.20 (a) gives one an idea concerning the relative fraction of the fragmentationphotons contribution with respect to the leading-order one. In the ultrarelativistic approximation theFigure 9.19: Expected uncertainty of the unpolarized cross-section Ed σ / d p measurement as a functionof polar angle θ .minimal value of the longitudinal momentum fraction of a struck parton x min accessible by detection ofthe prompt photon with the normalized transverse momentum x T = p T / √ s and the rapidity y can beexpressed as [488] x min = x T e − y − x T e y . (9.11)For fixed x T , the minimal x min = x T is reached at y = − ln ( x T ) . The value x min as a function of rapidity y and p T of photon for √ s = 27 GeV is shown in color in Fig. 9.20(a). One can see that the possibilityof accessing the low- x region is limited by our capability to detect the prompt-photon signal at a low p T y correspond to the blind area near the beam pipe.The huge rate of decay photons makes the determination of the prompt photon production cross-sectionrather difficult. The main source of the decay photons is the two-body decay π → γγ . The second mostimportant source is the decay η → γγ . In the kinematic range p T > c at √ s = 27 GeV there areabout 0.18 photons from the η -decay per one photon from the π decay. The relative contribution of allother decay photons ( ω , ρ , φ decays) does not exceed 0.03. F r ag / M a i n p T (cid:1) s=27 GeV (cid:1) s=13.5 GeV (cid:1) s=20 GeV 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 2.5 3 3.5 4 4.5 5 5.5 6 6.5 -3.0 27 GeV.The p T spectra for the prompt and decay photons expected at SPD after one year of running at √ s = 27 GeV are presented in Fig. 9.21 (a). The result was obtained using the Pythia8 generator with theparameters tuned to reproduce the high- p T spectra of the π and prompt photons measured at similarenergies by the WA70 ( √ s = . 96 GeV) [489, 490] and the UA6 ( √ s = . p T spectrum of the decay photons goes down with the growth of the p T faster than for the prompt photons and their rates become comparable at p T ≈ c . The fittedfunctions presented on the plot have the shape N ( p T ) = A ( − x T ) n ( p / p ) − m . (9.12)Each cluster of the energy deposition in the ECal with the energy above the threshold E = 100 MeV thatis not associated with any reconstructed tracks is treated as the prompt photon candidate. The momentumof such a photon is reconstructed under the assumption of its production in the primary vertex. In orderto reject photons from the π → γγ decay the invariant mass of each two photons is calculated. If thedifference between the reconstructed mass and the nominal mass of π is smaller than 10 MeV, bothphotons are removed from the list of candidates. Nevertheless, this procedure removes just about 40%of false candidates. The photons from the π → γγ decay, whose partner was not reconstructed dueto conversion in the material, too low energy or the acceptance issue, remain on the list of candidates.The photons from the radiative decays of other particles are also in the list. The list of candidates alsoincludes photons associated with two or more overlapping clusters, first of all, the clusters from the decayof energetic π s. A significant part of such false candidates could be rejected by a sophisticated analysisof the cluster shape. The clusters produced by the charged particles whose tracks are lost, the clustersdeposited by the photons originated from the elements of the setup and the clusters induced by the neutralhadrons are also taken into account as the background. The typical contributions of each source of thebackground mentioned above are presented as a function of p T in Fig. 9.21(b).onceptual design of the Spin Physics Detector 143 , GeV/c T p s / . G e V / c E v en t s / = 27 GeVsPrompt photonsMinimum bias photons (a) (b)Figure 9.21: (a) p T spectra of the produced prompt (red) and the decay or minimum bias (blue) pho-tons in p - p collisions at √ s = 27 GeV. Distributions are scaled to one year of data taking (10 s). (b)Contributions of different background components for the prompt photon production in p - p collisions at √ s = 27 GeV (events per year of data taking) [492].As one can see, the photons from the unreconstructed decays of neutral pions are the main source ofthe background. The fraction of such unreconstructed decays can be estimated from the Monte Carlosimulation and is about 50%. Based on the number N π of the reconstructed π → γγ decays, the corre-sponding number of the remaining background photons k × N π should be subtracted from the numberof prompt-photon candidates N γ in order to get an estimation of a true number of prompt photons: N prompt = N γ − k × N π . (9.13)Here k ≈ . π → γγ decay reconstruction, but also the overall contribution of all other backgroundphotons including the photons from the radiative decays of η , ω , ρ , φ , etc. The described subtractionprocedure has to be performed for each bin of p T and x F ranges. One should keep in mind that the back-ground of the decay photons is also spin-dependent, since there is an indication of non-zero asymmetries A LL and A N in the inclusive π and η production [111–113, 175, 176, 493].The expected accuracy of the unpolarized cross-section Ed σ / d p measurement after one year (10 s)of data taking is shown in Fig. 9.21(b). At a low p T range the main contribution to the total uncertaintycomes from the systematics of the π background subtraction procedure while at high p T the statisticaluncertainty dominates. To estimate the systematics dk / k = 1% is assumed as a realistic value.To estimate the A N asymmetry the function f ( φ ) = C + P × A N cos φ (9.14)is fitted to the expected acceptance-corrected azimuthal distribution of the prompt-photon events. Here φ is the azimuthal angle of the photons produced in the laboratory frame in respect to the direction ofthe proton beam polarization. The expected accuracy of the A LL and A N measurement as a function of x F is shown in Fig. 9.22 (b). The statistical part is shown in red, while the total error that also includesthe systematics related to the background subtraction ( dk / k = π -, and η -mesons.44 T p00.020.040.060.080.10.120.14 s / s d sysstat total (a) x F q(pol) qbar->yg (QSF annihil)[q(pol) qbar->yg] + [q(pol) g -> qy] (QSF all)g(pol) q -> yq (GSF)Sum 0 0.02 0.04 0.06 0.08 0.1-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 T <6 GeV, sqrt S=27 GeV, SIDIS1 , µ = p T Stat. Stat+syst (b)Figure 9.22: (a) Expected uncertainty of the unpolarized cross-section Ed σ / d p measurement as afunction of p T . (b) Expected accuracy of the A N measurement for the prompt photons with p T > c at √ s = 27 GeV as a function of x F . The theoretical predictions are also shown. In spite of the relatively large cross-section of the open charm production, most of the D -meson decayscannot be reconstructed easily. The ”golden” decay channels are: D → K − π + and D + → K − π + π + (BF=3.95% and 9.38%, respectively). The momentum distributions for D ± and D / D produced in p - p collisions at √ s = 27 GeV are shown in Fig. 9.23(a). The difference between the red and blue curvesreflects the fact that the probability for the c -quark to hadronize into the neutral D -meson is 2 times higherthan into the charged one. Since the decay length c τ is 311.8 and 122.9 µ m, respectively, which is largerthan the spatial resolution of the vertex reconstruction, the VD allowing one to reconstruct the secondaryvertex of the D -meson decay is the key detector for the open charm physics at SPD. The distribution forthe spatial distance between the primary (production) and secondary (decay) vertices for D ± / mesons ispresented in Fig. 9.23(b). D/ D – D (a) – D D/ D (b)Figure 9.23: (a) Momentum distributions for D ± and D / D produced in p - p collisons at √ s = 27 GeV.(b) Spatial distance between the production and the decay vertices for D -mesons.We demonstrate the ability of the SPD setup to deal with the open-charm physics using the D / D signal. The following quantities can be used as selection criteria in order to suppress the combinatorial π K background together with the kaon identification by the PID system:– the quality of the secondary vertex reconstruction ( χ );– the distance between the primary and secondary vertices (spatial or in projections) normalized toonceptual design of the Spin Physics Detector 145the corresponding uncertainty;– the angle between the reconstructed momentum of the π K pair and the line segment connectingthe primary and secondary vertices;The kinematics of the π K pair (the angular and momentum distributions) could also be used for discrim-ination.Figure 9.24 (a) presents the K − π + invariant mass spectrum obtained as the result of such a selection forthe D -signal in the kinematic range | x F | > . D → K − π + events were lost, while the combinatorial backgroundunder the D -meson peak was suppressed by 3 orders of magnitude. The signal-to-background ratio for D is about 1.3% for the DSSD configuration and about 3.9% for the DSSD+MAPS one. Improvingthe signal-to-background ratio is the subject of further optimization of the selection criteria, as well asthe reconstruction algorithms. The corresponding statistical accuracy of the SSA A N measurement isillustrated by Fig. 9.24 (b), where both signals, D and D , are merged. Similar or even better results(due to a larger c τ value) could be expected for the charged channel D ± → K ∓ π ± π ± . K p M15202530354045 · DSSDDSSD + MAPS |>0.2 F |x (a) A N ( x F ) x F SIDIS1SIDIS2GSF 0 0.02 0.04 0.06 0.08 0.1-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 p p -> DX, sqrt S=27 GeV, 1
27 GeV, | x F | > . A N measurement for the D + D mesons. The expectedSivers contribution to the SSA is also shown.Another way to improve the signal-to-background ratio is tagging the D -mesons by their origin from thedecay of a higher state D ∗ → D π . The complexity of this approach lies in the need for detection of thesoft pion ( p π ∼ . c ).One more possibility to reduce the background is the tagging a leptonic decay of the second D -meson inthe event via reconstruction of the corresponding muon in the RS. The corresponding branching fractions( µ + anything) are 6 . ± . 6% and 17 . ± . 2% for D and D ± , respectively. hapter 10 Integration and services According NICA TDR [494] the SPD area is allocated in the southern point of beam collisions. TheNICA complex with the SPD location is shown in Figure 10.1.Figure 10.1: Schematic layout of the NICA facility with SPD.The design of the SPD experimental hall is very similar to that of the MPD [495]. The top and side views of the SPD building are shown in Figures 10.2, 10.3, respectively. The buildingis divided into production and experimental sites with total area of about 2000 m . Since the productionsite has a gate, it will be used to unload materials. The main gate for trucks is 4 m × × Helium refrigerators have to be close to the detector to provide cryogenic fluids and gases for the magnetoperation (see chapter 3.2). Presumably, they will be installed on a platform that will be located on topof the detector, as shown in Figure 10.4. Crates with electronics for the data acquisition systems and48power supplies of the detector subsystems should also be placed in the vicinity of the detector. They willbe located on a special platform next to the detector. The platform will be attached to the detector, thusmoving along the same rails as the detector itself. Bottles with with Ar and CO for suppling the RS andST detectors, the corresponding gas recirculation compressors and monitoring systems, will be locatedon a similar platform from the opposite side of the detector (not shown in Figure 10.4). A dedicatedradiation shielding can be installed between the detector and the platforms in order to provide access tothe racks with the detector electronics and the gas system during data taking.(a) (b)Figure 10.4: The 3D view of the SPD building. The detector assembly position (a) and the beam positionof the detector (b) are shown. The beam line is highlighted in blue.The total weight of the SPD detector is close to the maximum permissible limit of 1200 ton. The weightof each detector subsystem is presented in Table 10.1. The power consumption of subdetectors is cur-rently under study. It is assumed that the maximum power supply capacity of the SPD hall should notexceed 1.2 MW.Table 10.1: Technical requirements of the SPD detector subsystems (to be completed).Subsystem Weight, t Power, kW SpecialrequirementsVD < . ÷ ECAL 58 63RS 800 31 Ar+CO TOF (sci) 0.4 4BBC 0.1 12Magnet 50 < 100 cryogenicsSupportingstructure 200 -Total ∼ ∼ hapter 11 Beam test facilities Two dedicated beam test facilities are planned to be operated for the benefit of the SPD project. The firstone using secondary beams from the Nuclotron is foreseen to be constructed in building 205 (LHEP).It will be used for testing and certification of detector elements, electronics, data acquisition and slow-control systems under conditions close to those anticipated at NICA. Some elements can be studied usingthe SPD straight section of NICA before the Spin Physics Detector construction at the early phase of thecollider running. The beam test facilities will be also used for training young specialists for the SPDproject. Two specialized channels for secondary particles (electrons, muons, pions, kaons, protons, neutrons,light nuclei) will be organized: the Low Momentum Channel (LMC) and the High Momentum Chan-nel (HMC) in the region of focus F4 of extracted Nuclotron beams. The LMC is designated for sec-ondary beams with a momentum range from 100 MeV/ c to 2 GeV/ c , while the momentum range ofsecondary particles at the HMC is from 1 GeV/ c to 10 GeV/ c . After upgrading, the existing channel ofthe MARUSYA installation [496–499] will be used in the LMC construction. It is advantageous that thereexists positive experience in working with extracted polarized beams at MARUSYA [500]. This wouldensure physical measurements at the extracted beams using the existing experimental installation andinfrastructure. The installation MARUSYA is well-suitable for the applied studies with secondary beamsat the maximum possible intensity of the primary beam extracted to building 205 up to 10 protonsper acceleration cycle. The development of the HMC requires two new magnetic elements; therefore,it is considered as an independent installation to be put in operation at the second stage of upgrade inaccordance with the existing regulations for the commissioning of experimental facilities. The layout ofthe main elements of the SPD test zone is shown in Fig. 11.1.It is planned to use the SP12 magnet of the VP1 extraction channel situated directly in front of theF4 focus in order to turn the primary extracted beam toward the HMC. The calculations show that theprimary beam can be turned to the required angle in a proton momentum range of 1 ÷ c . Forhigher-energy particles, it is necessary to use a target in the F4 focus. In this operation mode, secondarybeams are formed at the LMC and HMC simultaneously. Note that this operation mode is possible withparallel operation of the other installations at the VP1 extraction channel, in particular, the BM&N setup.For the primary 5 GeV/nucleon deuteron beam extracted to carbon targets with a thickness from 0.005to 5 g/cm , the typical intensities for different species available at the LMC and HMC are shown inTab. 11.1. There is also a possibility of forming a secondary quasi-monochromatic neutron beam viainteraction of a deuteron beam in a target and deflecting out the charged component.14950 5 9 8 35 8 2520 Experimental room Experimental room HMC Technical area MARUSYA Figure 11.1: Layout of the main elements of the SPD test zone. All dimensions are in millimeters.Table 11.1: Beam intensities feasible at the channel of the LMC and the HMC.Channel p, MeV/ c d p,n π ± K + K − µ ± e ± LMC 400 10 LMC 800 10 LMC 1500 10 HMC 2000 10 HMC 7000 10 Each channel-spectrometer provides spatial registration, identification, and tagging of each particle hit-ting the detector, provided the electronic registration system of the installation matches the tested de-tector or the data acquisition system element. A prototype time-of-flight system based on scintilla-tion hodoscopes demonstrated reliable identification of protons, pions, kaons in a momentum range of600 ÷ c for the LMC. TOF scintillation hodoscopes providing a momentum resolution of 0.5%and a time resolution at a level of 100 ps are capable of online detection and identification of secondarypions, kaons, and protons at the HMC. In order to extend the testing capabilities of the SPD test zone, itwill be equipped with new coordinate detectors, a Cherenkov counter, and a BGO-based electromagneticcalorimeter. We also suppose, that the beam test experiments and preparation for getting a luminosity of 10 cm − s − at √ s = 27 GeV, including the proton polarization control will be demonstrated by the SPD commis-sioning. For that reason we propose to install of the diagnostic and control equipment at the SPD straightsection (see Fig. 11.2).onceptual design of the Spin Physics Detector 151Figure 11.2: The SPD straight section equipped with the diagnostic and control units. All dimensionsare in millimeters. hapter 12 Running strategy We consider the strategy of the SPD operation as chain of successive experimental works with polarizedproton and deuteron beams aimed at the obtaining of the ultimate polarized proton beam parameters atthe collider and the use of the unique existing polarized deuteron beam for physics experiments fromthe early beginning of the collider commissioning. Polarized deuterons were first accelerated at theold LHEP proton accelerator Synchrophasotron in 1986 and much later at the new superconductingsynchrotron – Nuclotron in 2002 (see Fig. 12.1).Polarized protons were first obtained in 2017. The first test was performed after the analysis of protonspin resonances in 2018. The first dangerous proton spin resonance in Nuclotron corresponds to thebeam momentum of about 3.5 GeV/c, whereas in the deuteron case the spin resonance will occur at theparticle kinetic energy of 5.6 GeV/nucleon. This limit is practically equal to the maximum achievableenergy corresponding to the magnetic rigidity of the Nuclotron dipoles.Figure 12.1: View of the Nuclotron ring.The existing polarized proton and deuteron ion source SPI provides up to a 3-mA pulse current over t ≈ µ s. Thus, up to 1 . × particles can be injected in the Nuclotron during the injection time (8 µ s). The spin modes (pz, pzz): ( , ) , ( , − ) , ( / , ) , and ( − / , + ) were adjusted. The polarization152onceptual design of the Spin Physics Detector 153Figure 12.2: View of the SPI (left) and the existing RFQ (right).degree of 80 % was achieved.The existing pre-accelerator of RFQ-type gives the limit on the achievable proton energy in the nextelement of the injector chain - linac LU-20. We can obtain only 5 MeV at its output instead of 20MeV that we have had in the past years. The new proton and light ion linac “LILAc” is now beingmanufactured [501]. The LILAc output energy will be 12 MeV. Its commissioning is scheduled for2025–2026. The photos of the SPI and the existing RFQ are presented in Fig. 12.2.The following tasks for the period of 2021–2025 are reasonable and necessary to start the SPD operationat the ultimate beam parameters:– continuation of operation and further improvement of the polarized ion source SPI, waiting beamtime at the Nuclotron – 2021–2022;– upgrade of the polarimeters: linak output; coasting beam; extracted beam; new polarimeter for aproton energy of above 6 GeV – 2020–2023;– manufacturing of the 6T SC-solenoid model for the SPD test bench – 2021–2022;– design and manufacturing of the equipment for the SPD test bench at the collider – 2020–2023;– LILAc manufacturing and tests – 2020–2025;– analysis of the He (2+) polarized ion source based on the SPI upgrade. The physics program proposed in Chapter 2 covers at least 5 years of the SPD running. A tentativerunning plan is shown in Tab. 12.1.54 Table 12.1: Tentative running plan for the Spin Physics Detector.Physics goal Required time Experimental conditionsFirst stageSpin effects in p - p scattering 0.3 year p L , T - p L , T , √ s < p - d scattering, 0.3 year d tensor - p , √ s < p yieldSpin effects in d - d scattering 0.3 year d tensor - d tensor , √ s < p T - p T , √ s = 27 GeVSSA for light hadronsTMD-factorization test, SSA, 1 year p T - p T , 7 GeV < √ s < 27 GeVcharm production near threshold, (scan)onset of deconfinment, ¯ p yieldGluon helicity, 1 year p L - p L , √ s = 27 GeV...Gluon transversity, 1 year d tensor - d tensor , √ s NN = d tensor - p T , √ s NN = 19 GeV”Tensor porlarized” PDFs hapter 13 Cost estimate The estimated cost of the Spin Physics Detector at current prices is 94.9 M$. Taking into account thegeneral uncertainty of the project timescale and that at the moment the SPD project is in the early stagesof implementation, this value should be treated as a very preliminary estimation. This value does notinclude the construction of the SPD Test zone and possible R&D expanses. Any expanses related withdevelopment and construction of an infrastructure for polarized beams at NICA are also out of thisestimation. The detailed contribution to the total cost is presented in Tab. 13.1.Table 13.1: Preliminary cost estimate of the SPD setup.Subsystem Option Cost, M$SPD setup Vertex detector:– DSSD VD1 9.5+6.5 (FE)– DSSD+MAPS VD2 9.5+7.0 (FE)Straw tracker 2.4PID system:– RPC-based TOF PID1 5– Scintillator-based TOF PID2 4– Aerogel PID system PID3 5Electromagnetic 21.1calorimeterRange system 14.2ZDC 2BBC 0.4Magnetic system 10Beam pipe 2General infrastructure 5Slow control system 0.8Data acquisition system 2.6Computing 10TOTAL COST VD2+PID2+PID3 96.0155 hapter 14 Participating institutions and author list National Science Laboratory, Armenia Akopov N., Movsisyan A. Institute of Applied Physics of the National Academy of Sciences of Belarus, Minsk,Belarus Shulyakovsky R. Research Institute for Nuclear Problems of Belarusian State University, Minsk, Belarus Korjik M.V., Lobko A.S., Makarenko V.V., Solin A.A., Solin A.V. Universidad Andr´es Bello, Santiago, Chile Kuleshov S., Zamora J. China Institute of Atomic Energy, Beijing, China Chen Lei, Jia Shi-Hai, Li Pei-Yu, Li Xiao-Mei, Song Jin-Xin, Sun Hao, Sun Peng-Fei, Zhang Yun-Yu,Zhang Jun-Wei, Zhao Ming-Rui, Zhi Yu Higher Institute of Technologies and Applied Sciences (InSTEC), Havana University,Havana, Cuba Guzman F., Gars´ıa Trapaga C.E. Charles University, Prague, Czech Republic Finger M., Finger M. (jr.), Prochazka I., Slunecka M., Sluneckova V. Czech Technical University in Prague, Czech Republic Havranek M., Jary V., Lednicky D., Marcisovsky M., Neue G., Popule J., Tomasek L., Virius M.,Vrba V. University of Turin and INFN Section, Turin, Italy Alexeev M., Amoroso A., Chiosso M., Denisov O.Yu., Kotzinian A., Maggiora A., Panzieri D.,Parsamyan B., Tosello F.156onceptual design of the Spin Physics Detector 157 Warsaw University of Technology, Warsaw, Poland Buchowicz A., Dygnarowicz K., Gali´nski G., Klekotko A., Kurjata R., Marzec J., Pastuszak G., RychterA., Zaremba K., Ziembicki M. Joint Institute for Nuclear Research, JINR, Dubna, Russia Directorate Lednick´y R. Laboratory of High-Energy Physics Akhunzyanov R.R., Alexakhin V.Yu., Anosov V.A., Azorskiy N.I., Baldin A.A., Baldina E.G.,Barabanov M.Yu., Beloborodov A.N., Belyaev A. V., Bleko V.V., Bogoslovsky D.N., Boguslavsky I.N.,Burtsev V.E., Dunin V.B., Enik T.L., Filatov Yu.N., Gavrishchuk O.P., Galoyan A.S., Glonti L.,Golubykh S.M., Grafov N.O., Gribovsky A.S., Gromov S.A., Gromov V.A., Gurchin Yu.V., GusakovYu.V., Ivanov A.V., Ivanov N.Ya., Isupov A.Yu., Kasianova E.A., Kekelidze G.D., Khabarov S.V.,Kharusov P.R., Khrenov A.N., Kokoulina E.S., Kopylov Yu.A., Korovkin P.S., Korzenev A. Yu.,Kostukov E.V., Kovalenko A.D., Kozhin M.A., Kramarenko V.A., Kruglov V.N., Ladygin V.P., LysanV.M., Makankin A.M., Martovitsky E.V., Meshcheriakov G.V., Moshkovsky I.V., Nagorniy S.N.,Nikitin V.A., Parzhitsky S.S., Pavlov V.V., Perepelkin E.E., Peshekhonov D.V., Popov V.V., ReznikovS.G., Rogachevsky O.V., Safonov A.B., Salamatin K.M., Savenkov A.A., Sheremeteva A.I., ShimanskiiS.S., Starikova S.Yu., Streletskaya E.A., Tarasov O.G., Terekhin A.A., Teryaev O.V., Tishevsky A.V.,Topilin N.D., Topko B.L., Troyan. Yu.A., Usenko E.A., Vasilieva E.V., Volkov I.S.,Volkov P.V., YudinI.P., Zamyatin N.I., Zemlyanichkina E.V., Zhukov I.A., Zinin A.V., Zubarev E.V. Laboratory of Nuclear Problems Abazov V.M., Afanasyev L.G., Alexeev G.D., Balandina V.V., Belova A.P., Bobkov A.V., BoltushkinE.V., Brazhnikov E.V., Datta A., Denisenko I.I., Duginov V.N., Frolov V.N., Golovanov G.A., GridinA.O., Gritsay K. I., Guskov A.V., Kirichkov N.V., Komarov V.I., Kulikov A.V., Kurbatov V.S., KutuzovS.A., Maltsev A., Mitrofanov E.O., Nefedov Yu.A., Pavlova A.A., Piskun A.A., Prokhorov I.K.,Rezvaya E.P., Romanov V.M., Rudenko A.I., Rumyantsev M.A., Rybakov N.A., Rymbekova A.,Samartsev A.G., Shaikovsky V.N., Shtejer K., Sinitsa A.A., Skachkov N.B., Skachkova A.N.,Tereschenko V.V., Tkachenko A.V., Tokmenin V.V., Uzikov Yu.N., Verkheev A.Yu., Vertogradov L.S.,Vertogradova Yu.L., Vesenkov V.A., Zhemchugov A.S., Zhuravlev N.I. Laboratory of Theoretical Physics Anikin I.V., Efremov A.V. , Goloskokov S.V., Klopot Ya., Strusik-Kotlozh D., Volchansky N.I. Laboratory of Information Technologies Goncharov P.V., Oleynik D.A., Ososkov G.A., Petrosyan A.Sh., Podgainy D.V., Pelevanyuk I.S.,Polyakova R.V., Uzhinsky V.V., Zuev M.I. St. Petersburg Nuclear Physics Institute, Gatchina, Russia Barsov S.G., Fedin O.L., Kim V.T., Kuznetsova E.V., Maleev V.P., Shavrin A.A., Zelenov A.V. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia Andreev V.F., Baskov V.A., Dalkarov O.D., Demikhov E.I., Gerasimov S.G., L’vov A.I., NegodaevM.A., Nechaeva P.Yu., Polyansky V.V., Suchkov S.I., Terkulov A.R., Topchiev N.P. Skobeltsin Institute of Nuclear Physics of the Moscow State University, Moscow, Russia Aleshko A.M., Belov I.N., Berezhnoy A.V., Boos E.E., Bunichev V.E., Chepurnov A.S., Gribkov D.Y.,Merkin M.M., Nikolaev A.S.58 Institute for Theoretical and Experimental Physics, Moscow, Russia Akindinov A.V., Alekseev I.G., Golubev A.A., Kirin D.Yu., Luschevskaya E., Malkevich D.B.,Morozov B., Plotnikov V.V., Polozov P., Rusinov V., Stavinskiy A.V., Sultanov R.I., Svirida D.N.,Tarkovskyi E.I., Zhigareva N.M. Institute for High-Energy Physics, Protvino, Russia Vorobiev A. Samara National Research University, Samara, Russia Karpishkov A.V., Nefedov M.A., Saleev V.A., Shipilova A.V. St. Petersburg Polytechnic University, St. Petersburg, Russia Berdnikov A.Ya., Berdnikov Ya.A., Borisov V.S., Larionova D.M., Mitrankov Yu.M., Mitrankova M.M. St. Petersburg State University, St. Petersburg, Russia Feofilov G.A., Kovalenko V.N., Valiev F.F., Vechernin V.V., Zherebchevsky V.Yo. Tomsk State University, Tomsk, Russia Chumakov A., Lyubovitskij V., Trifonov A., Zhevlakov A. Belgorod State University, Belgorod, Russia Kaplii A., Kishchin I., Kluev A., Kubankin A., Kubankin Yu. University of Belgrade, Institute of Physics Belgrade, Belgrade, Serbia Jokovic D., Maletic D., Savic M. V.N. Karazin Kharkiv National University, Kharkiv, Ukraine Kovtun V.E., Lyashchenko V.N., Malykhina T.V., Reva S.N., Sotnikov V.V. Institute for Scintillation Materials National Academy of Sciences of Ukraine (Kharkiv,Ukraine) Boyarintsev A.Yu., Eliseev D.A., Grinyov B.V., Zhmurin P.N. Individual contributors: Abramov V. (IHEP, Russia), El-Kholy R. (Cairo University), Haidenbauer J. (IAS and IKP,Forschungszentrum J¨ulich), Konorov I. (Technical University of Munich), Richard J.-M. (Universit´e deLyon), Strikman M. (Penn State University), Temerbayev A. ( L.N. Gumilyov Eurasian NationalUniversity, Nur-Sultan), Tomasi-Gustafsson E. (DPhN, IRFU, CEA, Universit´e Paris-Saclay), TsenovR. (University of Sofia), Wang Q. (South China Normal University, Guangzhou), Zhao Q. (Institute ofHigh Energy Physics, CAS, Beijing)We are also grateful to Kukhtin V. V., Nagaytsev A.P., Savin I.A., Shevchenko O. Yu. , andSisakyan A.N. for their invaluable contribution to the SPD project at earlier stages of itsimplementation. Acknowledgements. This work is supported by the RFBR research projects No. 18-02-40097 and 18-02-40061. hapter 15 Conclusion The proposed physics program and the concept of the SPD facility presented in the document, are openfor exciting and challenging ideas from theorists and experimentalists worldwide. The Conceptual De-sign Report of the Spin Physics Detector was presented and discussed at the 54th meeting of the JINRProgram Advisory Committee for Particle Physics on January 18, 2021. The following recommendationswere obtained: The PAC thanks the SPD (proto-)collaboration for the preparation of the comprehensiveCDR and recommends the NICA management to appoint an appropriate Detector Advisory Committeefor a thorough review of the CDR and its subsequent evolution into an SPD TDR (Technical Design Re-port). The PAC encourages the team to pursue every effort to form an international collaboration, findadequate resources and attract students and young scientists. hapter 16 List of abbreviations ADC – Analogue-to Digital ConverterASIC – Application-Specific Integrated CircuitBBC – Beam-Beam CounterBF – Branching FractionBPM – Beam Position MonitorCCR – Constituent Counting RulesCEM – Color Evaporation ModelCM – Center-of-MassCPM – Collinear Parton ModelCPQ – Chromomagnetic Quark PolarizationCR – Cosmic RaysCT – Color TransparencyDAC – Digital-to-Analogue ConverterDAQ – Data AcQuisitionDIS – Deep Inelastic ScatteringDS(-mode) – Distinct Spin modeDSSD – Double-Sided Silicon DetectorDY (process) – Drell-Yan processECal – Electromagnetic CalorimeterExEP – Extended Equivalence PrincipleFBBC (monitor) – Fast Beam-Beam Collisions (monitor)FEE – Front-End ElectronicsFF – Fragmentation FunctionGF – Gluon FusionGPD – Generalized Parton DistributionsGPM – Generalized Parton ModelGSF – Gluon Sivers FunctionGTMD (PDF) – Generalized Transverse Momentum Dependent (PDF)HMC – High Momentum ChannelICEM – Improved Color Evaporation ModelIP – Interaction PointISM – InterStellar MediumLDME – Long-Distance Matrix ElementLMC – Low Momentum Channel 160onceptual design of the Spin Physics Detector 161MAPS – Monolithic Active Pixel SensorMCP – MicroCannel PlateMDT – Mini Drift TubesML – Machine LearningMIP – Minimum Ionizing ParticleMPD – MultiPurpose DetectorMPPC - MultiPixel Photon CounterMRPC - Multigap Resistive Plate ChamberMS – Magnetic SystemNICA – Nuclotron-based Ion Collider fAcilityNPE – Number of PhotoElectronsNPQCD – Non-Perturbative QCDNRQCD – Non-Relativistic QCDPDF – Parton Distribution FunctionPGF – Photon-Gluon FusionPID – Particle IDentificationpQCD – perturbative QCDPRA – Parton Reggeization ApproachQGP – Quark Gluon PlasmaQSF – Quark Sivers FunctionRMS – Root Mean SquareRS – Range SystemSF – Spin FlippingSIDIS – Semi-Inclusive Deep-Inelastic ScatteringSiPM – Silicon PhotoMultiplierSN – Spin Navigator (solenoid)SPD – Spin Physics DetectorSRC – Short Range CorrelationsST(-mode) – Spin Transparency (mode)SSA – Single Spin AsymmetryST – Straw TrackerSTSA – Single Transverse Spin AsymmetriesTMD (PDF) – Transverse Momentum Dependent (PDF)TMDShF – TMD Shape FunctionTOF (system) – Time-Of-Flight (system)VD – Vertex DetectorWLS - WaveLength ShifterZDC – Zero Degree Calorimeter ibliography [1] SPD web site http://spd.jinr.ru .[2] Aram Kotzinian. 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