Measurements of π − production in 7 Be+ 9 Be collisions at beam momenta from 19 A to 150 A GeV/ c in the NA61/SHINE experiment at the CERN SPS
NA61/SHINE Collaboration, A. Acharya, H. Adhikary, A. Aduszkiewicz, K.K. Allison, E.V. Andronov, T. Antićić, V. Babkin, M. Baszczyk, S. Bhosale, A. Blondel, M. Bogomilov, A. Brandin, A. Bravar, W. Bryliński, J. Brzychczyk, M. Buryakov, O. Busygina, A. Bzdak, H. Cherif, M. Ćirković, M. Csanad, J. Cybowska, T. Czopowicz, A. Damyanova, N. Davis, M. Deliyergiyev, M. Deveaux, A. Dmitriev, W. Dominik, P. Dorosz, J. Dumarchez, R. Engel, G.A. Feofilov, L. Fields, Z. Fodor, A. Garibov, M. Gaździcki, O. Golosov, V. Golovatyuk, M. Golubeva, K. Grebieszkow, F. Guber, A. Haesler, S.N. Igolkin, S. Ilieva, A. Ivashkin, S.R. Johnson, K. Kadija, N. Kargin, E. Kashirin, M. Kiełbowicz, V.A. Kireyeu, V. Klochkov, V.I. Kolesnikov, D. Kolev, A. Korzenev, V.N. Kovalenko, S. Kowalski, M. Koziel, A. Krasnoperov, W. Kucewicz, M. Kuich, A. Kurepin, D. Larsen, A. László, T.V. Lazareva, M. Lewicki, K. Łojek, V.V. Lyubushkin, M. Maćkowiak-Pawłowska, Z. Majka, B. Maksiak, A.I. Malakhov, A. Marcinek, A.D. Marino, K. Marton, H.-J. Mathes, T. Matulewicz, V. Matveev, G.L. Melkumov, A.O. Merzlaya, B. Messerly, Ł. Mik, S. Morozov, S. Mrówczyński, Y. Nagai, M. Naskręt, V. Ozvenchuk, V. Paolone, O. Petukhov, R. Płaneta, P. Podlaski, B.A. Popov, B. Porfy, M. Posiadała-Zezula, D.S. Prokhorova, D. Pszczel, S. Puławski, J. Puzović, et al. (42 additional authors not shown)
EEUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)
Submitted to: Eur. Phys. J. C CERN-EP-2020-150October 12, 2020
Measurements of π − production in Be+ Becollisions at beam momenta from 19 A to A GeV /c in the NA61/SHINE experiment at the CERN SPS The NA61/SHINE Collaboration
The NA61/SHINE collaboration studies at the CERN Super Proton Synchrotron(SPS) the onset of deconfinement in hadronic matter by the measurement of particleproduction in collisions of nuclei with various sizes at a set of energies covering theSPS energy range. This paper presents results on inclusive double-differential spectraand mean multiplicities of π − mesons produced in the 5% most central Be+ Becollisions at beam momenta of 19 A , 30 A , 40 A , 75 A and 150 A GeV /c obtained by theso-called h − method which does not require any particle identification.The shape of the transverse mass spectra differs from the shapes measured in centralPb+Pb collisions and inelastic p+p interactions. The normalized width of the rapiditydistribution decreases with increasing collision energy and is in between the resultsfor inelastic nucleon-nucleon and central Pb+Pb collisions. The mean multiplicity ofpions per wounded nucleon in central Be+ Be collisions is close to that in centralPb+Pb collisions up to 75 A GeV /c . However, at the top SPS energy the result liesbetween those for nucleon-nucleon and Pb+Pb interactions.The results are discussed in the context of predictions for the onset of deconfinementat the CERN SPS collision energies. © 2020 CERN for the benefit of the NA61/SHINE Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license. a r X i v : . [ nu c l - e x ] O c t he NA61/SHINE Collaboration A. Acharya , H. Adhikary , A. Aduszkiewicz , K.K. Allison , E.V. Andronov , T. Antićić ,V. Babkin , M. Baszczyk , S. Bhosale , A. Blondel , M. Bogomilov , A. Brandin , A. Bravar ,W. Bryliński , J. Brzychczyk , M. Buryakov , O. Busygina , A. Bzdak , H. Cherif ,M. Ćirković , M. Csanad , J. Cybowska , T. Czopowicz , , A. Damyanova , N. Davis ,M. Deliyergiyev , M. Deveaux , A. Dmitriev , W. Dominik , P. Dorosz , J. Dumarchez ,R. Engel , G.A. Feofilov , L. Fields , Z. Fodor , , A. Garibov , M. Gaździcki , , O. Golosov ,V. Golovatyuk , M. Golubeva , K. Grebieszkow , F. Guber , A. Haesler , S.N. Igolkin ,S. Ilieva , A. Ivashkin , S.R. Johnson , K. Kadija , N. Kargin , E. Kashirin , M. Kiełbowicz ,V.A. Kireyeu , V. Klochkov , V.I. Kolesnikov , D. Kolev , A. Korzenev , V.N. Kovalenko ,S. Kowalski , M. Koziel , A. Krasnoperov , W. Kucewicz , M. Kuich , A. Kurepin ,D. Larsen , A. László , T.V. Lazareva , M. Lewicki , K. Łojek , V.V. Lyubushkin ,M. Maćkowiak-Pawłowska , Z. Majka , B. Maksiak , A.I. Malakhov , A. Marcinek ,A.D. Marino , K. Marton , H.-J. Mathes , T. Matulewicz , V. Matveev , G.L. Melkumov ,A.O. Merzlaya , B. Messerly , Ł. Mik , S. Morozov , , S. Mrówczyński , Y. Nagai ,M. Naskręt , V. Ozvenchuk , V. Paolone , O. Petukhov , R. Płaneta , P. Podlaski ,B.A. Popov , , B. Porfy , M. Posiadała-Zezula , D.S. Prokhorova , D. Pszczel , S. Puławski ,J. Puzović , M. Ravonel , R. Renfordt , D. Röhrich , E. Rondio , M. Roth , B.T. Rumberger ,M. Rumyantsev , A. Rustamov , , M. Rybczynski , A. Rybicki , S. Sadhu , A. Sadovsky ,K. Schmidt , I. Selyuzhenkov , A.Yu. Seryakov , P. Seyboth , M. Słodkowski , P. Staszel ,G. Stefanek , J. Stepaniak , M. Strikhanov , H. Ströbele , T. Šuša , A. Taranenko ,A. Tefelska , D. Tefelski , V. Tereshchenko , A. Toia , R. Tsenov , L. Turko , R. Ulrich ,M. Unger , D. Uzhva , F.F. Valiev , D. Veberič , V.V. Vechernin , A. Wickremasinghe , ,Z. Włodarczyk , K. Wojcik , O. Wyszyński , E.D. Zimmerman , and R. Zwaska National Nuclear Research Center, Baku, Azerbaijan Faculty of Physics, University of Sofia, Sofia, Bulgaria Ruđer Bošković Institute, Zagreb, Croatia LPNHE, University of Paris VI and VII, Paris, France Karlsruhe Institute of Technology, Karlsruhe, Germany University of Frankfurt, Frankfurt, Germany Wigner Research Centre for Physics of the Hungarian Academy of Sciences, Budapest, Hungary University of Bergen, Bergen, Norway Jan Kochanowski University in Kielce, Poland Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland National Centre for Nuclear Research, Warsaw, Poland Jagiellonian University, Cracow, Poland AGH - University of Science and Technology, Cracow, Poland University of Silesia, Katowice, Poland University of Warsaw, Warsaw, Poland University of Wrocław, Wrocław, Poland Warsaw University of Technology, Warsaw, Poland Institute for Nuclear Research, Moscow, Russia Joint Institute for Nuclear Research, Dubna, Russia National Research Nuclear University (Moscow Engineering Physics Institute), Moscow, Russia St. Petersburg State University, St. Petersburg, Russia2 University of Belgrade, Belgrade, Serbia University of Geneva, Geneva, Switzerland Fermilab, Batavia, USA University of Colorado, Boulder, USA University of Pittsburgh, Pittsburgh, USA
This paper presents measurements of inclusive spectra and mean multiplicities of π − mesonsproduced in central Be+ Be collisions at beam momenta of 19 A , 30 A , 40 A , 75 A and 150 A GeV /c ( √ s NN = 6.1, 7.6, 8.8, 11.9 and 16.8 GeV) performed by the NA61/SHINE collaboration. Theseresults are part of the strong interactions studies proposed by the NA61/SHINE collaboration [1]to investigate the properties of the onset of deconfinement and to search for the possible existenceof a critical point in the phase diagram of strongly interacting matter. The first goal of theprogramme is motivated by the observation of rapid changes of hadron production propertiesin central Pb+Pb collisions at about 30 A GeV /c by the NA49 experiment [2, 3] - a sharp peakin the kaon to pion ratio ("horn"), the start of a plateau in the inverse slope parameter forkaons ("step"), and a steepening of the increase of pion production per wounded nucleon withincreasing collision energy ("kink"). These findings were predicted and interpreted as the onset ofdeconfinement [4, 5]. They were recently confirmed by the RHIC beam energy scan programme [6],and the interpretation is supported by the LHC results (see Ref. [7] and references therein).Experimentally the goals of the NA61/SHINE strong interaction programme are persued by a twodimensional scan in collision energy and nuclear mass number of colliding nuclei. The scan allowsto explore systematically the phase diagram of strongly interacting matter [1]. In particular, theanalysis of the existing data within the framework of statistical models suggests that by increasingcollision energy one increases temperature and decreases baryon chemical potential of stronglyinteracting matter at freeze-out [8], whereas by increasing nuclear mass number of the collidingnuclei one decreases the temperature [9, 8, 10].Within this programme NA61/SHINE recorded data on p+p , Be+Be, Ar+Sc, Xe+La and Pb+Pbcollisions. Further high statistics measurements of Pb+Pb collisions are planned with an upgradeddetector starting in 2021 [11]. Results on particle spectra and multiplicities have already beenpublished from p+p interactions [12, 13, 14] which represent the basic reference. This paper reportsNA61/SHINE results from the next step in size of the collision system namely measurementsof π − production for the 5% most central Be+ Be collisions. The data were recorded in 2011,2012 and 2013 using a secondary Be beam produced by fragmentation of the primary Pb beamfrom the CERN SPS [15]. The Be+ Be collisions play a special role in the NA61/SHINE scanprogramme. First, it was predicted within the statistical models [16, 17] that the yield ratio ofstrange hadrons to pions in these collisions should be close to those in central Pb+Pb collisionsand significantly higher than in p+p interactions. Second, the collision system composed ofa Be and a Be nucleus has eight protons and eight neutrons, and thus is isospin symmetric.Within the NA61/SHINE scan programme the Be+ Be collisions serve as the lowest mass isospinsymmetric reference needed to study collisions of medium and large mass nuclei. This is ofparticular importance when data on proton-proton, neutron-proton and neutron-neutron are notavailable to construct the nucleon-nucleon reference [18].3n this paper the so-called h − method is used for determining π − production since it provides thelargest phase space coverage. This procedure utilizes the fact that negatively charged particles arepredominantly π − mesons with a small admixture (of order 10%) of K − mesons and anti-protonswhich can be subtracted reliably.The paper is organized as follows: after this introduction the experiment is briefly describedin Sec. 2. The analysis procedure is discussed in Sec. 3. Section 4 describes the results of theanalysis. In Sec. 5 the new measurements are discussed and compared to model calculations. Asummary closes the paper.The following variables and definitions are used in this paper. The particle rapidity y is calculatedin the collision center of mass system (cms), y = 0 . · ln [( E + p L ) / ( E − p L )], where E and p L are the particle energy and longitudinal momentum, respectively. The transverse component ofthe momentum is denoted as p T , and the transverse mass m T is defined as m T = p m + ( cp T ) where m is the particle mass. The momentum in the laboratory frame is denoted p lab and thecollision energy per nucleon pair in the center of mass by √ s NN .Be+Be collisions can be characterized by the energy detected in the region populated by projectilespectators. Low values of this forward energy are referred to central collision and a selectionof collisions based on the forward energy is called a centrality selection. Although for Be+Becollisions the forward energy is not tightly correlated with the impact parameter of the collision,the terms central and centrality are adopted following the convention widely used in heavy-ionphysics. The NA61/SHINE experiment is a multi-purpose facility designed to measure particle productionin nucleus-nucleus, hadron-nucleus and p+p interactions [19]. The detector is situated at theCERN Super Proton Synchrotron (SPS) in the H2 beamline of the North experimental area.A schematic diagram of the setup during Be+Be data taking is shown in Fig. 1. The maincomponents of the produced particle detection system are four large volume Time ProjectionChambers (TPC). Two of them, called Vertex TPCs (VTPC), are located downstream of the targetinside superconducting magnets with maximum combined bending power of 9 Tm. The magneticfield was scaled down in proportion to the beam momentum in order to obtain similar phasespace acceptance at all energies. The main TPCs (MTPC) and two walls of pixel Time-of-Flight(ToF-L/R) detectors are placed symmetrically to the beam line downstream of the magnets. Thefifth small TPC (GAP-TPC) is placed between VTPC1 and VTPC2 directly on the beam line.The TPCs are filled with Ar:CO gas mixtures in proportions 90:10 for the VTPCs and theGAP-TPC, and 95:5 for the MTPCs.The Projectile Spectator Detector (PSD), which covers the region into which the projectilespectators are emitted is positioned 20.5 m (16.7 m) downstream of the MTPCs at 75 A and150 A GeV /c (19 A , 30 A , 40 A GeV /c ) centered in the transverse plane on the deflected position ofthe beam. The PSD allows to select the centrality of the collision by imposing an upper limit onthe measured forward energy. 4 z zxyBEAM PSDVTPC-1 VTPC-2 MTPC-LMTPC-RGTPC ToF-LToF-RTarget zyx Figure 1: The schematic layout of the NA61/SHINE experiment at the CERN SPS [19] showing thecomponents used for the Be+Be energy scan (horizontal cut, not to scale). The beam instrumentation issketched in the inset (see also Fig. 2 below). Alignment of the chosen coordinate system as shown in thefigure; its origin lies in the middle of VTPC-2, on the beam axis. The z axis is along the nominal beamdirection. The magnetic field bends charged particle trajectories in the x – z (horizontal) plane. The driftdirection in the TPCs is along the y (vertical) axis. The beam line instrumentation is schematically depicted in Fig. 2. A set of scintillation countersas well as beam position detectors (BPDs) [19] upstream of the target provide timing reference,selection, identification and precise measurement of the position and direction of individual beamparticles.The target was a 12 mm thick plate of Be placed ≈
80 cm upstream of VTPC1. Massconcentrations of impurities in the target were measured at 0.3% resulting in an estimatedincrease of the produced pion multiplicity by less than 0.5% [20]. No correction was applied forthis negligible contamination. Data were taken with target inserted (denoted I, 90%) and targetremoved (denoted R, 10%). Be Beam
The beam line of NA61/SHINE experiment is designed to provide good momentum resolutionand particle identification even with secondary ion beams. The beam instrumentation (see Fig. 2)consists of scintillator counters (S) used for triggering and beam particle identification, vetoscintillation counters (V) with a hole in the middle for rejection of upstream interactions andbeam halo particles, and a Cherenkov charge detector Z built based on quartz glass radiator forthe measurement of the secondary beam charge. Additionally the three Beam Position Detectors(BPDs) are used for determination of the charge of individual beam particles.5 igure 2: The schematic of the placement of the beam and trigger detectors in high-momentum (top) and low-momentum (bottom) data taking configurations showing scintillation counters S, veto counters V,charge Cherekov counter Z and beam position detectors BPD.
This paragraph provides a brief description of the Be beam properties (see [15]). Primary Pb ions extracted from the SPS were steered toward a 180 mm long beryllium fragmentation targetplaced 535 m upstream of the NA61/SHINE experiment. An interaction of a Pb-ion with thefragmentation target produces a mixture of nuclear fragments with a large fraction of so-calledspectator nucleons which originate from the Pb nucleus but did not participate in the collision.Their momenta per nucleon p N are equal to the beam momentum per nucleon smeared by Fermimotion. The field strength in the bending magnets of the beam line define the rigidity of thetransported charged particles: Bρ = 3 . · p beam /Z , where Bρ can be adjusted by setting thecurrent in the dipole magnets and p beam = A · p N is the beam momentum and Z the charge ofthe beam particle. Thus the beam line selects particles with the wanted A/Z ratio. Figure 3shows the charge spectrum of a fragment beam with a rigidity corresponding to fully stripped Be ions with a momentum of 150 A GeV /c measured by the Z detector. A well separated peakfor charge Z equal 4 is visible. In a special run taken at beam momentum of 13.9 A GeV /c it waspossible to also measure the time-of-flight of the beam particles. As demonstrated in Fig. 4 theselected Be fragments are pure Be.
The schematic of the placement of the beam and trigger detectors can be seen in Fig. 2. Thetrigger detectors consist of a set of scintillation counters recording the presence of the beamparticle (S1, S2), a set of veto scintillation counters with a hole used to reject beam particlespassing far from the centre of the beamline (V0, V1), and a charge detector (Z). Beam particleswere defined by the coincidence T1 = S1 · S2 · V1 · Z(Be) and T1 = S1 · V0 · V1 · V1’ · Z(Be) for6 igure 3: Charge of the beam particles measured by the Z detector.Figure 4: Mass of fragments of Z/A with momentum of 13.9 A GeV /c . Left: carbon ions show doubleGaussian structure due to two isotopes of carbon in the beam. Right: beryllium ions show single Gaussiandistribution, indicating isotopic purity of the beryllium in the beam. Charge of the beam particle wasselected by the measurement of scintillation counters. low and high momentum data taking respectively. In addition, for the two lower energies aninteraction trigger detector (S4) was used to check whether the beam particle changed chargeafter passing through the target. Central collisions were selected by requiring an energy signalbelow a set threshold from the 16 central modules of the PSD. The event trigger condition thuswas T2 = T1 · S4 · PSD and T2 = T1 · PSD for the lower and higher energies, respectively. The PSDthreshold was set to retain from ≈
70% to ≈
40% of inelastic interactions at beam momenta from19 A to 150 A GeV /c , respectively. The statistics of recorded events are summarised in Tab. 1.7 able 1: Basic beam properties, number of events recorded, and number of events selected for the analysisfor Be+ Be interactions of 5 % most central collisions at incident momenta of 19 A , 30 A , 40 A , 75 A and150 A GeV /c . p beam ( A GeV /c ) √ s NN (GeV) Recordedevents (alltriggers) Number ofselectedevents19 6.1 3 . · . ·
30 7.6 5 . · . ·
40 8.8 3 . · . ·
75 11.9 5 . · . ·
150 16.8 2 . · . · at y0 2 4 ( G ev / c ) T p c GeV/ A - π dE/dxtof-dE/dx h- method y0 2 4 ( G ev / c ) T p c GeV/ A - π at h- method dE/dxtof-dE/dx Figure 5: Acceptance in y and p T of analysis techniques used by NA61/SHINE to obtain multiplicities of π − produced in Be+Be collisions at 30 A ( left ) and 150 A GeV /c ( right ). Acceptance for the h − method is shownas gray area, for the d E/ d x identification technique as black boxes and for the tof -d E/ d x identification asred hatching. In this paper the so-called h − method is used for determining π − production utilizing the fact thatnegatively charged particles are predominantly π − mesons with a small admixture (of order 10%)of K − mesons and anti-protons which can be subtracted reliably. Compared to the other analysisstrategies used by NA61/SHINE, aiming at identifying particles based on measuring energy lossin the TPCs and time-of-flight, the h − method provides the largest phase space coverage. Theacceptance of the h − analysis technique for π − produced in Be+Be collisions is shown in Fig. 5for 30 A and 150 A GeV /c . It covers almost the full forward and part of the backward hemisphereof y and p T down to zero.This section gives a brief overview of the data analysis procedure and the applied corrections. Italso defines to which class of particles the final results correspond. A description of the calibration8nd the track and vertex reconstruction procedure can be found in Ref. [12].The analysis procedure consists of the following steps:(i) application of event and track selection criteria,(ii) determination of spectra of negatively charged hadrons using the selected events and tracks,(iii) evaluation of corrections to the spectra based on experimental data and simulations,(iv) calculation of the corrected spectra and mean multiplicities,(v) calculation of statistical and systematic uncertainties.Corrections for the following biases were evaluated:(i) contribution from off-target interactions,(ii) bias of selection procedure of central collisions,(iii) geometrical acceptance,(iv) contribution of particles other than primary (see below) negatively charged pions producedin Be+Be interactions,(v) losses of produced negatively charged pions due to their decays and secondary interactions.Correction (i) was not applied due to insufficient statistics of the target removed data. Thecontamination of the target inserted data was estimated from the z distribution of fitted vertices(see Fig. 9) and found to be very small ( ≈ central interactions. Correction(ii) was estimated to be small and was therefore included in the systematic uncertainty (seeSec. 3.1). Corrections (iii)-(v) were estimated by simulations, see Sec. 3.3 below.The final results refer to π − produced in central Be+Be collisions by strong interaction processesand in electromagnetic decays of produced hadrons. Such hadrons are referred to as primary hadrons. The definition and the selection procedure of central collisions is given in Sec. 3.1.The analysis was performed independently in ( y , p T ) bins. The bin sizes were selected takinginto account the statistical uncertainties and the resolution of the momentum reconstruction [12].Corrections as well as statistical and systematic uncertainties were calculated for each bin. Central collisions
The term centrality of the collision is related in the simplest models to the impact parameter b or the number of wounded nucleons W . Neither quantity is experimentally measurable andone uses instead the number N of produced particles or the energy emitted into the forwardspectator region to characterise the centrality of the collision. The first choice may bias themeasurements of particle production probabilities whereas such a bias is avoided by the secondchoice. Therefore final results presented in this paper refer to the 5% of Be+Be collisions withthe lowest value of the forward energy E F ( central collisions). The quantity E F is defined asthe total energy in the laboratory system of all particles produced in a Be+Be collision viastrong and electromagnetic processes in the forward momentum region defined by the acceptancemap in Ref. [21]. Results on central collisions defined as above allow a precise comparison with9redictions of models without any additional information about the NA61/SHINE setup andused magnetic field. Using this definition the mean number of wounded nucleons h W i and themean collision impact parameter h b i were calculated within the Wounded Nucleon Model [22]implemented in Epos , see Sec. 3.1.3.Negatively charged pion production was studied in event ensembles the centrality of which wasselected by upper limits of the energy E P SD measured by a subset of PSD modules. This subsetwas optimised for best sensitivity to projectile spectators (see Sec. 3.1.1 for details). For eachcollision energy the upper limit value was adjusted to select 5% of all inelastic interactions.The forward momentum acceptance in the definition of E F corresponds to the acceptance ofthe optimised subset of PSD modules. Based on simulations the results for the E P SD selectedcollisions were corrected to correspond to the E F selected results.The details of the described procedures are given below. In order to optimize the sensitivity to projectile spectators, only a subset of PSD modules wasincluded in the calculation of E P SD [23]. Figure 6 ( top ) shows the impact points of projectilespectator nucleons on the front face of the PSD obtained from the internal Glauber modelof
Epos [24] including Fermi motion. Figure 6 ( bottom ) depicts the modules selected for thesummation of E P SD . Online event selection by the hardware trigger (T2) used a threshold onthe sum of energies over the 16 central modules of the PSD.Measured distributions of E P SD for minimum-bias and T2 trigger selected events, calculatedin the offline analysis, are shown in Fig. 7 at beam momenta of 19 A GeV /c and 150 A GeV /c ,respectively. Also drawn are vertical lines which define the E P SD corresponding to the 5% and20% of events with the lowest E P SD values. A minimum-bias distribution was obtained using thedata from the beam trigger T1 with offline selection of events by requiring an event vertex in thetarget region and a cut on the ionisation energy detected in the GTPC to exclude Be beams. Aproperly normalized spectrum for target removed events was subtracted. E F selected results Comparison of presented experimental results with other data require a realistic implementationof described centrality selection. This is more easily realized using a quantity "forward energy"( E F ) instead of E P SD , since the latter requires detailed knowledge of its response. The acceptancemap provided in Ref. [21] gives the recipe for the computation of E F . Both E F and E P SD were calculated in simulations using the
Epos model, which employed a dedicated softwarepackage which tracks particles through the magnetic fields and simulates the response of thePSD modules. A global factor c cent was then calculated as the ratio of mean multiplicities ofnegatively charged pions obtained with the two selection procedures in the 5% most central events.A possible dependence of the scaling factor on rapidity and transverse momentum was neglected.The resulting factors c cent range between 1.00 and 1.03 (see Table 2) corresponding to only asmall correction compared to the systematic uncertainties of the measured π − multiplicities. Thecorrection was therefore not applied but instead included as a contribution to the systematicuncertainties. 10 e + Be at A GeV/c, Spectators x (cm)40 − − y ( c m ) − − − Be + Be at 19
Be + Be at 150A GeV/c, Spectators x (cm)40 − − y ( c m ) − − − Be + Be at 150A GeV/c, Spectators
Figure 6:
Upper row:
Simulated impact points of particles on the front face of the PSD for beam momentumof 19 A GeV /c ( left ) and 150 A GeV /c ( right ). Lower row:
PSD modules included in the calculation of theprojectile spectator energy E P SD used for event selection for beam momenta of 19 A , and 30 A GeV /c ( left )and for 40 A , 75 A and 150 A GeV /c ( right ) Comparisons of particle yields in collisions of different size nuclei usually employs the averagenumber of wounded nucleons h W i in the respective reactions. For estimating the average numberof wounded nucleons corresponding to the selected central collisions Epos
Crmc
Epos was modified [24] to provide the values of W of its internal Glaubermodel calculation. The results on h W i for the 5% most central collisions from the Epos modelare listed in Table 2. Fluctuations of the listed values are due to the integer nature of W . As Epos simulates all particles of the final state a more realistic estimate of h W i is obtained byselecting central collisions based on the energy E F . The resulting mean number of woundednucleons and the mean impact parameter are also listed in Table 2. Values of h W i for the twoselection procedures differ by about two units. Examples of the distributions of W and b for the5% most central collisions are shown in Fig. 8. As the nucleon density is low in the Be nucleusthese distributions are quite broad. This emphasises that for model comparisons it is importantto use equivalent centrality selection procedures to obtain a meaningful result.11 (GeV) PSD
E0 100 200 N o r m a li ze d E n t r i e s A Be+Be at 19
Minimum bias selectionCentral trigger (GeV)
PSD
E0 500 1000 N o r m a li ze d E n t r i e s A Be+Be at 150
Minimum bias selectionCentral trigger
Figure 7: Two examples of the measured E P SD distribution for minimum-bias selected (blue data points)and T2 selected (red data points) events at 19 A GeV /c ( left ) and 150 A GeV /c ( right ) beam momentum.Histograms are normalized to agree in the overlap region. The limits used to select events are shown byblack lines and they correspond to ≈
5% and ≈
20% of inelastic collisions.
Momentum ( A GeV /c ) 19 30 40 75 150 Epos
WNM h W i . . . . . σ . . . . . Epos E F h W i .
54 9 .
44 9 .
67 9 .
61 9 . σ . . . . . h b i .
44 1 .
54 1 .
32 1 .
26 1 . σ . . . . . c cent .
019 1 .
029 1 .
001 1 .
005 1 . Table 2: Average number of wounded nucleons h W i and average impact parameter h b i in the 5% most central Be+Be collisions estimated from simulations using the
Epos [25] model. The values of σ denote thewidths of the distributions of W and b . Results Epos
WNM are for centrality selection using the smallestnumber of spectators,
Epos E F using the forward energy E F within the acceptance map in Ref. [21] For the analysis Be+Be events were selected using the following criteria:(i) four units of charge measured in S1, S2, and Z counters as well as BPD3 (this requirementalso rejects most interactions upstream of the Be target),(ii) no off-time beam particle detected within a time window of ± µ s around the triggerparticle,(iii) no other event trigger detected within a time window of ± µ s around the trigger particle,(iv) beam particle trajectory measured in at least three planes out of four of BPD-1 and BPD-2and in both planes of BPD-3, 12 W · nu m b e r o f e v e n t s F
5% E GeV A
150 0 2 4 6 b (fm) · nu m b e r o f e v e n t s F
5% E GeV A (GeV) F E W (GeV) F E b (f m ) Figure 8: Examples of the distribution of the number of wounded nucleons W ( top,left ) and impactparameter b ( top, right ) for events with the 5% smallest forward energies E F and E F versus W ( bottom,left ) and E F versus b ( bottom, right ) at beam momentum of 150 A GeV /c simulated with Epos using theacceptance map provided in Ref. [21]. (v) charge measured in the GTPC smaller than that of Be (applied at 40 A , 75 A and 150 A GeV /c ),(vi) a well reconstructed interaction vertex with z position (fitted using the beam trajectory andTPC tracks) not farther away than 15 cm from the center of the Be target (see Fig 9; thecut removes less than 0.4% of central interactions),(vii) the energy E P SD measured in the subset of the PSD modules smaller than an upper limit(55, 73, 104, 165, 442 GeV for collisions at 19 A , 20 A , 30 A , 40 A , 75 A and 150 A GeV /c ,respectively) in order to select the 5% most central collisions (see discussion in Sec. 3.1).The event statistics after applying the selection criteria are summarized in Table 1.13
915 cm 15 cm - . c m
15 cm 15 cm - . c m z (cm) z (cm) at at cc Figure 9: Distribution of fitted vertex z coordinate for the 20% most central Be+ Be interactions withtarget inserted (green histogram) and target removed (red histogram). (Left) : 19 A GeV /c . (Right) :150 A GeV /c . Target position and cut values are marked. Target is installed in the box filled with He gasto minimise background interactions. Smaller peak on the right hand side of the plots corresponds tointeractions with a target holder window. In order to select tracks of primary charged hadrons and to reduce the contamination of tracksfrom secondary interactions, weak decays and off-time interactions, the following track selectioncriteria were applied:(i) track momentum fit at the interaction vertex should have converged,(ii) fitted x component of particle rigidity at the vertex ( p lab , x /q ) is positive. This selectionminimizes the angle between the track trajectory and the TPC pad direction for the givenmagnetic field direction, reducing uncertainties of the reconstructed cluster position, energydeposition and track parameters,(iii) total number of reconstructed points on the track should be greater than 15,(iv) sum of the number of reconstructed points in VTPC-1 and VTPC-2 should be greater than15 or greater than 4 in the GTPC,(v) the distance between the track extrapolated to the interaction plane and the interactionpoint (track impact parameter) should be smaller than 4 cm in the horizontal (bending)plane and 2 cm in the vertical (drift) plane,(vi) electron tracks were excluded by a cut on the measured particle energy loss d E/ d x in theTPCs. In order to determine the mean multiplicity of primary π − mesons produced in central Be+Becollisions a set of corrections was applied to the extracted raw results. The main effects aredetector acceptance, loss of events due to the cut on reconstructed vertex position, reconstructionefficiency, contributions of particles from weak decays (feed-down), and contribution of primary K − mesons). The contamination of eventsoccurring outside the target was negligible.A simulation of the NA61/SHINE detector is used to correct the data for acceptance, reconstructionefficiency and contamination. Only Be+Be interactions in the target material were simulated andreconstructed. The Epos model [25, 24] was selected to generate the primary interactions as itbest describes the NA61/SHINE measurements. A
Geant3 based program chain was used totrack particles through the spectrometer, generate decays and secondary interactions and simulatethe detector response (for more detail see Ref. [12]). Simulated events were then reconstructedusing the NA61/SHINE reconstruction chain and reconstructed tracks were matched to thesimulated particles based on the cluster positions. The same event selection procedure was usedas for data (cut on the summed energy in the subset of PSD modules used to select the 5% most central collisions). Particles which were not produced in the primary interaction can amount to asignificant fraction of the selected track sample. Thus a careful effort was undertaken to evaluateand subtract this contribution.The correction factor c yp T for primary π − , based on the event and detector simulation wascalculated for each y and p T bin as: c yp T = n [ π − ] MCgen / n [ h − ] MCsel (1)where n [ h − ] MCsel is the mean multiplicity of reconstructed negatively charged particles after theevent and track selection criteria and n [ π − ] MCgen is the mean multiplicity of primary negativelycharged pions from the E P SD -selected Be+Be collisions generated by the
Epos model.The corrected multiplicities were then calculated as: n [ π − ] corr = c yp T · n [ π − ] raw (2)The final results in bins of y and p T are shown in Fig. 10. Statistical uncertainties of the yields receive contributions from the finite statistics of both thedata and the simulated events used to obtain the correction factors. The dominating contributionis the uncertainty of the data which were calculated assuming a Poisson probability distributionfor the number of entries in a bin. Compared to the statistics of the data the statistics of thesimulation were much higher and the statistical uncertainties of the latter were neglected.
Systematic uncertainties presented in this paper were calculated taking into account contributionsfrom the following effects.(i) Possible biases due to track cuts which are not corrected for. These are:(a) a possible bias due to the d E/ d x cut applied to remove electrons,15b) a possible bias related to the removal of events with off-time beam particles close intime to the trigger particle.Their magnitude was estimated by varying the values of the corresponding cut for dataselection. The possible bias due to the d E/ d x cut was changed by ± .
01 d E/ d x units(where 1 corresponds to a minimum ionising particle, and 0.04 is a typical width of thed E/ d x distribution for π − ), and the off-time interactions cut was varied from a ± . µ s to a ± . µ s time window. The assigned systematic uncertainty was calculated as the maximumof the absolute differences between the results obtained for lower and upper values. Theestimated bias is on the level of 1-3%.This uncertainty is listed in the tables including numerical values and it is visualised by ashaded band around the data points in plots presenting the results. Systematic biases indifferent bins are correlated, whereas statistical fluctuations are almost independent.(ii) Uncertainty related to the track cuts which were corrected for. It was estimated by varyingthe track selection cuts used for data and Monte Carlo events: removing the impactparameter cut and decreasing the minimum number of required points to 12 (total) and 10(in VTPCs). The potential bias is below 2%.(iii) Uncertainty of the correction for contamination of the primary π − mesons. There was nodata available to adjust the simulated spectra. To estimate a possible bias the simulatedspectra were instead adjusted to preliminary NA61/SHINE data on the K − /π − ratio [26],and the difference between the results with adjusted and standard correction of order 2% wasassigned as relative potential systematic uncertainty. Since K − are the main contribution tothe h − correction and the absolute correction is small, this contribution was finally neglectedin the systematic uncertainty estimate.The total systematic uncertainty was calculated by adding in quadrature the contributions(i) - (iii): σ sys = q σ + σ + σ . (3)This uncertainty is listed in the tables including numerical values and it is visualised by a shadedband around the data points in plots presenting the results. Systematic biases in different binsare correlated, whereas statistical fluctuations fluctuations are almost independent. This section presents results on negatively charged pion spectra at 19 A , 30 A , 40 A , 75 A and150 A GeV /c beam momentum in the 5% most central Be+ Be collisions (see Sec. 3.1 for definitionof central collisions). The results refer to primary pions produced by strong interaction and decayprocesses and in electromagnetic decays of neutral hadrons.16 .1 Double-differential ( y , p T ) and ( y , m T − m π ) yields Figure 10 shows fully corrected double-differential ( y , p T ) distributions d ndydp T of π − measured inBe+Be interactions and illustrates the wide phase space acceptance of the detector. Rapidity binswith limited acceptance ( y < − . A GeV, y < − . A GeV, y < − . A GeV, y < − . A GeV and y < − . A GeV /c ) are not used in the subsequent analysis. y-4 -3 -2 -1 0 1 2 3 4 ( G e V / c ) T p + X - π → Be + Be A GeV/c 0 - 5% y-4 -3 -2 -1 0 1 2 3 4 ( G e V / c ) T p + X - π → Be + Be A GeV/c 0 - 5% y-4 -3 -2 -1 0 1 2 3 4 ( G e V / c ) T p + X - π → Be + Be A GeV/c 0 - 5% y-4 -3 -2 -1 0 1 2 3 4 ( G e V / c ) T p + X - π → Be + Be A GeV/c 0 - 5% y-4 -3 -2 -1 0 1 2 3 4 ( G e V / c ) T p + X - π → Be + Be A GeV/c 0 - 5%
Figure 10: Double-differential spectra d ndydp T of negatively charged pions produced in the 5% most central Be+Be collisions at beam momenta of 19 A , 30 A , 40 A , 75 A and 150 A GeV /c . Spectra of transverse momentum p T in slices of rapidity y are plotted in Fig. 11. Superimposedcurves show the results obtained from fitting the function f ( p T ) = C · p T · exp − p ( cp T ) + m T ! , (4)motivated by the thermal model, where the inverse slope parameter T and the normalisationconstant C are the fit parameters.A summary of the fitted values of the inverse slope parameter T are shown in Fig. 12 plottedversus rapidity divided by beam rapidity. The decrease of T towards larger rapidities and theobtained values are close to those found for inelastic p+p interactions [12]. Numerical values of T at y ≈ (GeV/c) T p0 0.5 1 1.5 2 ) - ( G e V / c T d y dpn d - - - - - - - - - -0.7 » y · -0.5 » y -1 · -0.3 » y -2 · -0.1 » y -3 · » y -4 · » y -5 · » y -6 · » y -7 · » y -8 · » y -9 · » y -10 · » y -11 · » y -12 · » y -13 · » y -14 · » y -15 · +X at 19A GeV/c - pfi Be+Be (GeV/c) T p0 0.5 1 1.5 2 ) - ( G e V / c T d y dpn d - - - - - - - - - -0.7 » y · -0.5 » y -1 · -0.3 » y -2 · -0.1 » y -3 · » y -4 · » y -5 · » y -6 · » y -7 · » y -8 · » y -9 · » y -10 · » y -11 · » y -12 · » y -13 · » y -14 · » y -15 · » y -16 · +X at 30A GeV/c - pfi Be+Be (GeV/c) T p0 0.5 1 1.5 2 ) - ( G e V / c T d y dpn d - - - - - - - - - -0.9 » y · -0.7 » y -1 · -0.5 » y -2 · -0.3 » y -3 · -0.1 » y -4 · » y -5 · » y -6 · » y -7 · » y -8 · » y -9 · » y -10 · » y -11 · » y -12 · » y -13 · » y -14 · » y -15 · » y -16 · » y -17 · » y -18 · +X at 40A GeV/c - pfi Be+Be (GeV/c) T p0 0.5 1 1.5 2 ) - ( G e V / c T d y dpn d - - - - - - - - - - -1.1 » y · -0.9 » y -1 · -0.7 » y -2 · -0.5 » y -3 · -0.3 » y -4 · -0.1 » y -5 · » y -6 · » y -7 · » y -8 · » y -9 · » y -10 · » y -11 · » y -12 · » y -13 · » y -14 · » y -15 · » y -16 · » y -17 · » y -18 · » y -19 · » y -20 · » y -21 · » y -22 · +X at 75A GeV/c - pfi Be+Be (GeV/c) T p0 0.5 1 1.5 2 ) - ( G e V / c T d y dpn d - - - - - - - - -
10 1 -1.1 » y · -0.9 » y -1 · -0.7 » y -2 · -0.5 » y -3 · -0.3 » y -4 · -0.1 » y -5 · » y -6 · » y -7 · » y -8 · » y -9 · » y -10 · » y -11 · » y -12 · » y -13 · » y -14 · » y -15 · » y -16 · » y -17 · » y -18 · » y -19 · » y -20 · » y -21 · » y -22 · +X at 150A GeV/c - pfi Be+Be
Figure 11: Transverse momentum spectra of π − in rapidity slices produced in the 5% most central Be+Becollisions. Rapidity values given in the legends correspond to the middle of the corresponding interval.Data points for consecutive rapidity slices are scaled down by factors of 10. Shaded bands show systematicuncertainties. Curves depict thermal model motivated fits with Eq. 4.
Spectra of transverse mass m T − m π at mid-rapidity (0 < y < .
2) are shown in Fig. 13 for the5% most central
Be+Be collisions and for inelastic p+p interactions [12] as well as central Pb+Pbcollisions [2, 3]. The p+p data follow exponential distributions as shown by the lines fitted inthe range 0 . < m T − m π − < .
72 using Eq. 4 expressed in m T . Interestingly, relative to theexponential fits the spectra from nucleus-nucleus interactions develop enhancements at low andhigh transverse mass which increase with the size of the collision system. To compare in moredetail the transverse mass spectra between systems, each spectrum was normalized to the integralof the spectrum in the range of 0 . < m T − m π − < .
72. The normalized Be+Be spectra werethen divided by the corresponding p+p and Pb+Pb spectra used as a reference. The resultingratios of the normalised spectra are presented in Fig. 14.18 eam y/y T ( M e V ) c GeV/ A c GeV/ A c GeV/ A c GeV/ A c GeV/ A Figure 12: The inverse slope parameter T of the transverse mass spectra of negatively charged pions in central Be+Be collisions at the SPS energies as a function of rapidity divided by the beam rapidity. Thefit range is 0 . < m T − m π < . T near mid-rapidity fitted in the interval 0 . < m T − m π < . dn/dy of π − mesons in the 5% most central Be+Be collisions. For comparison inverseslope parameter T p+p near mid-rapidity fitted in the same interval of π − mesons in the p+p interactionsat close beam momenta [12]. p beam ( A GeV /c ) T (MeV) dn/dy ( y =0) T p + p (MeV)19 150 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± m T spectra in central Be+Be collisions is significantly different from the one observedin inelastic p+p interactions (Fig. 14 left ). However, it is important to note that the Be+Besystem is isospin symmetric whereas p+p has I = 1. Comparing Be+Be to Pb+Pb (Fig. 14 right ) reveals that both shapes are similar with a relative inclination in favor of the pion yieldat low m T . Note that Pb+Pb is to a large extent isospin neutral. The quantitative comparisonbetween Be+Be and Pb+Pb data are limited by large statistical uncertainties of the latter. To extract one-dimensional rapidity spectra from the two-dimensional y - p T spectra the contributionfrom the missing high p T acceptance has to be accounted for. The transverse momentum spectrumfor each rapidity bin was parametrized with Eq. 4. An additional constraint was added to the fit toensure that the integral of the fitted function agrees with the integral (sum) of the measurements19 (GeV/c - π - m T m0 0.2 0.4 0.6 0.8 1 1.2 - ) ( G e V / c T d y d m n d T m -3 -2 -1 GeV/c A A ) (GeV/c - π - m T m0 0.2 0.4 0.6 0.8 1 1.2 - ) ( G e V / c T d y d m n d T m -3 -2 -1 GeV/c A A ) (GeV/c - π - m T m0 0.2 0.4 0.6 0.8 1 1.2 - ) ( G e V / c T d y d m n d T m -3 -2 -1 GeV/c A A ) (GeV/c - π - m T m0 0.2 0.4 0.6 0.8 1 1.2 - ) ( G e V / c T d y d m n d T m -3 -2 -1 GeV/c A A ))) (GeV/c - π - m T m0 0.2 0.4 0.6 0.8 1 1.2 - ) ( G e V / c T d y d m n d T m -3 -2 -1 GeV/c A A Figure 13: Transverse mass spectra m T d ndydm T of negatively charged pions produced in central Be+Becollisions at the SPS energies. Statistical errors are smaller than the size of the points. Results frominelastic p+p interactions [12] and central Pb+Pb interactions [2, 3] are shown for comparison. Lines showexponential fits with Eq. 4. ) (GeV/c π - m T m0 0.2 0.4 0.6 0.8 100.20.40.60.811.21.41.61.82 GeV/c A
150 GeV/c A
75 GeV/c A
40 GeV/c A
30 GeV/c A - π→ Be+Be ( B e + B e ) / ( p + p ) ) (GeV/c p - m T m0 0.2 0.4 0.6 0.8 1 ( B e + B e ) / ( P b + P b ) GeV/c A
150 GeV/c A
75 GeV/c A
30 GeV/c A
40 GeV/c A Figure 14: Ratio of normalized transverse mass spectra: Be+Be/ p+p (left) and Be+Be/Pb+Pb (right) atthe SPS energies. over the interval where data are available. The p T extrapolation increases the value of the summedmeasurements by ≈ . y > omentum ( A GeV /c ) 19 30 40 75 150 A rel .
975 0 .
919 0 .
858 0 .
828 0 . δ ( A rel ) 0 . . . . . y .
659 0 .
667 0 .
720 0 .
778 0 . δ ( y ) 0 . . . . . σ y .
025 1 .
067 1 .
148 1 .
265 1 . δ ( σ y ) 0 .
048 0 .
052 0 .
061 0 .
059 0 . Table 4: Fitted parameters A rel , y of the double Gaussian fit and RMS width σ y of the rapidity distributioncalculated from Eq. 6. The rapidity spectra are plotted in Fig. 15. A closer look reveals an asymmetry of the spectra withrespect to mid-rapidity. To quantify the amount of asymmetry the spectra were parametrizedwith the sum of two Gaussian functions with the same width and mean value displaced frommid-rapidity by the same amount: g ( y ) = A · A rel σ √ π exp − ( y − y ) σ ! + A σ √ π exp − ( y + y ) σ ! , (5)where A is the normalization parameter, A rel is the relative amplitude of the Gaussian distributions, σ is the common width and y is the displacement from mid-rapidity. Results for the fittedfunctions are presented in Fig. 15. Numerical values of the fitted parameters A rel , y as well asthe RMS width σ y of the rapidity distribution calculated from σ y = q σ + y (6)are listed in Table 4.The relative amplitude of the Gaussian distributions decreases slowly with increasing beammomentum, i.e the asymmetry increases. This deviation of A rel from unity signals a forward-backward asymmetry of the rapidity distribution which may be explained by the asymmetry ofthe collision system and the event selection procedure:(i) Asymmetric collisions of a Be beam with a larger mass Be target may lead to enhancedparticle production at backward rapidity,(ii) a larger number of neutrons in the Be target nuclei might result in a difference in the ratioof π − to π + in the backward and forward rapidity regions,(iii) selection of central collisions by requiring the forward energy E F below a cut value.The asymmetry was studied using the Wounded Nucleon Model (WNM) [22], where productionof particles in the backward hemisphere is proportional to the number of wounded nucleons inthe target and production of particles in the forward hemisphere is proportional to the number ofwounded nucleons in the projectile. In the WNM the effect of the asymmetric system leads to asmall enhancement of of the particle yield below mid-rapidity, which is opposite to what is seenin the data. On the other hand, the effect of the centrality selection based only on the forwardenergy is enhancing particle production at forward rapidity. The data show that the latter effectdominates. 21 - - - - dn / d y GeV/c A +X at 19 - p fi Be+Be y - - - - dn / d y GeV/c A +X at 30 - p fi Be+Be y - - - - dn / d y GeV/c A +X at 40 - p fi Be+Be y - - - - dn / d y GeV/c A +X at 75 - p fi Be+Be y - - - - dn / d y GeV/c A +X at 150 - p fi Be+Be
Figure 15: Rapidity distributions of negatively charged pions in central
Be+Be collisions at the SPSenergies. The parametrization of the spectra by Eq. 5 is shown. The solid line shows the fitted functionin the range of the fit, and the red dashed line depicts the extrapolation of the fitted function. The twoGaussian functions constituting the fitted function are represented by the black dashed lines.
Rapidity spectra in central
Be+Be collisions are compared to results from inelastic p+p inter-22 omentum ( A GeV /c ) 19 30 40 75 150 h π − i .
33 7 .
61 8 .
75 11 .
98 14 . δ stat ( h π − i ) ± . ± . ± . ± . ± . δ sys ( h π − i ) ± . ± . ± . ± . ± . h π i / h W i Table 5: Mean π − multiplicities in the 5% most central Be+Be collisions with statistical and systematicuncertainties as well as ratios of mean π multiplicities to average number of wounded nucleons. actions [12] in Fig. 16. Mean negative pion multiplicities h π − i were obtained by summing themeasured data points and adding a contribution from the fitted function Eq. 5 for the unmeasuredregion. Half of the contribution added based on the fit is added to systematic uncertainty. Theresults are listed in Table 5.The widths of the rapidity distributions were calculated from Eq.6 and are listed in Table 4. Thebeam energy dependence of the width of the rapidity distribution divided by the beam rapidity σ y /y beam is presented in Fig. 17. For Be+Be and Pb+Pb interactions the ratio was calculated for π − mesons. Since the p+p collision system is not isospin symmetric the isospin average ( π − + π + )/2 was plotted for comparison. These results are referred to as results for nucleon-nucleon( N+N ) collisions [18]. For all system sizes the relative width decreases monotonically with beamenergy and system size.
Several features of π meson production were predicted to be sensitive to the onset of deconfinement,namely the energy dependence of the transverse mass distribution, the width of the rapiditydistribution - both due to the softening of the equation of state [27, 28, 29] - and the meanmultiplicity due to the increasing entropy during the transition from the hadronic to the partonicphase [30]. The data presented in this paper are discussed in the context of these predictions inthe following.In the collision energy range in which the mixed hadron and parton matter is created a stallingof the expansion of the system is expected [31]. This results in a slowing of the increase of radialflow of the produced particles and in a step-like structure in the energy dependence of the inverseslope parameter of the transverse mass spectra T [4]. This feature was clearly observed for K mesons in central Pb+Pb collisions and was interpreted as one of the indications of the onset ofdeconfinement [2, 3].Pion transverse mass spectra deviate significantly from the exponential function Eq. 4 usedto fit the inverse slope parameter. This is attributed to a large contribution of pions fromresonance decays and possible effect of transverse collective flow [31]. Thus in order to avoidmodel-dependence of results π transverse mass spectra are characterize by the mean transversemass h m T i − m . Figure 18 shows the "step" plot for π − in central Be+Be collisions comparedto central Pb+Pb interactions and inelastic p+p reactions. The values and energy dependencemeasured in Be+Be collisions are surprisingly similar to those in inelastic p+p interactions andthere is only a small increase towards central
Pb+Pb collisions. This suggests that the average23 -4 -3 -2 -1 0 1 2 3 4 d y dn GeV/c A GeV/c A Be+Be; 0 - 5% y-4 -3 -2 -1 0 1 2 3 4 d y dn GeV/c A GeV/c A y-4 -3 -2 -1 0 1 2 3 4 d y dn GeV/c A GeV/c A y-4 -3 -2 -1 0 1 2 3 4 d y dn GeV/c A GeV/c A y-4 -3 -2 -1 0 1 2 3 4 d y dn GeV/c A GeV/c A Figure 16: Rapidity spectra of π − produced in the 5% most central Be+Be collisions at the SPS energies.Results from inelastic p+p interactions [12] are shown for comparison. Statistical errors are smaller thanthe size of the markers. transverse mass of π − mesons is only weakly sensitive to the transverse flow and thus it is not adiscriminating observable for the onset of deconfinement.24 (GeV) NN s5 10 15 20 b ea m / y y s N+NBe+Be Pb+Pb
WORLDNA61/SHINE
Figure 17: Collision energy dependence of the ratio of the width σ y of the rapidity distribution to thebeam rapidity y beam for central Be+Be and Pb+Pb collisions and inelastic
N+N interactions. (GeV) NN s10 ) ( G e V / c p - m æ T m Æ NA61/SHINE WORLDPb+Pbp+pBe+Be Au+Au
AGS SPS RHIC
Figure 18: Energy dependence of the mean transverse mass of π − measured at mid-rapidity in central Be+Be, Pb+Pb [2, 3] and Au+Au [32, 33] collisions and inelastic p+p interactions [34].
The Landau hydrodynamical model of high energy collisions [35, 36] predicts rapidity distributionsof Gaussian shapes. In fact this prediction is approximately confirmed by the experimental data,see Ref. [37] and references therein. Moreover, the collision energy dependence of the width wasderived by Shuryak [38] from the same model under simplifying assumptions and reads: σ y ( π − ) = 83 c − c ln √ s NN m p ! , (7)25here c s denotes the speed of sound, and c = 1 / σ y of the rapiditydistributions of π − mesons produced in central nucleus-nucleus collisions and inelastic nucleon-nucleon interactions in Fig. 19 ( left ) . The model calculations are close to the measured dependenceon the beam rapidity y beam . However, linear increase with y beam provides a better fit to themeasurements as shown by the straight line fit. The deviations were attributed to the changesin the equation of state [39, 40], which can be effectively parametrised by allowing the speed ofsound to be dependent on collision energy. Clearly the measured values of σ y differ very littlebetween the studied reactions in the SPS energy range. beam y0 2 4 6 y s NA61/SHINE WORLDPb+PbN+NBe+Be Au+Au
AGS SPS RHIClinear fit =1/3 s2 Landau, c (GeV) NN s10 c NA61/SHINE WORLDPb+PbN+NBe+Be Au+Au
AGS SPS RHIC
Figure 19: Comparison of the Landau hydrodynamical model with rapidity distributions of charged pionsproduced in central nucleus-nucleus collisions and inelastic nucleon-nucleon interactions.
Left:
The width σ y of the rapidity distributions of negatively charged pions in central Be+Be, Pb+Pb [2, 3] (Au+Au [32, 33])reactions and the width σ y of the average of rapidity distributions of positively and negatively chargedpions in p+p [13, 34] (denoted as N+N ) as a function of the beam rapidity y beam . The dotted line indicatesthe Landau model prediction with c = 1 /
3, while the full line shows a linear fit through the data points.
Right:
The speed of sound as a function of beam energy as extracted from the data using Eq. 7.
By inverting Eq. 7 one can express c in the medium as a function of the measured width of therapidity distribution. The energy dependence of the sound velocities extracted from the data arepresented in Fig. 19 ( right ). The energy range for results from Be+Be collisions and inelastic p+p reactions is too limited and the fluctuations in the data too large to allow a significant conclusionabout a possible minimum. Data on central Pb+Pb collisions, in combination with results fromAGS and RHIC on central Au+Au collisions, cover a much wider energy range. Here the soundvelocity exhibits a clear minimum (usually called the softest point) at √ s NN ≈
10 GeV consistentwith the reported onset of deconfinement [2, 3].Pions are the most copiously produced hadrons ( ≈ S ∼ F , (8) For p+p interactions the figure shows isospin symmetrised values denoted as
N+N [12] F = h ( √ s NN − m N ) / √ s NN i / . (9)Since the number of degrees of freedom g is higher for the quark-gluon plasma than for confinedmatter, it is also expected that the entropy density of the produced final state at given energydensity should also be higher in the first case. The following simple relation describes the expecteddependence [30]: S/V ∼ g / F . (10)Therefore, the entropy and information regarding the state of matter formed in the early stageof a collision should be reflected in the number of produced pions normalized to the volumeof the system. This intuitive argument was quantified in the Statistical Model of the EarlyStage (SMES) [4]. The increase with collision energy of the mean number of produced pions h π i , normalized to the number of wounded nucleons h W i [22] is expected to be linear whenplotted against F . The rate of increase is related to the number of degrees of freedom as given byEq. 10. This simple prediction is modified at low collision energies when absorption of pions inthe hadronic matter is expected to significantly decrease the final pion yield [4]. ) (GeV s » F æ W Æ / æpÆ NA61/SHINE (cid:103)
Be+Be (cid:97)
N+N [13]WORLD (cid:100)
N+N [2] (cid:103)
Pb+Pb [2, 3] (cid:103)
Au+Au [42, 31]
Figure 20: The "kink" plot showing the ratio of pion multiplicity h π i to number of wounded nucleons h W i versus the Fermi energy variable F ≈ s / NN . Results from central Be+Be collisions are compared tomeasurements in for inelastic nucleon-nucleon reactions and central collisions of heavier nuclei. Results ofBe+Be collisions are shown with statistical (vertical lines) and systematic (shaded band) uncertainties.All other results are presented with total uncertainty.
Figure 20 displays the ratio of mean pion multiplicitys to the number of wounded nucleon as afunction of F . The mean number of produced pions h π i is calculated as h π i = 3 · h π − i for nucleus-nucleus collisions and h π i = 1 . · ( h π + i + h π − i ) for N+N interactions h π i / h W i ratio in central Be+Be collisions are compared to acompilation of results from central Pb+Pb (Au+Au) collisions and inelastic nucleon-nucleoninteractions. Above F ≈ / the slope of the Pb+Pb dependence is about a factor 1.3higher than for nucleon-nucleon interactions. The ratio in central Be+Be collisions follows theratio for central Pb+Pb collisions up to F ≈ / . Thus in this energy range the Be+Beslope is also by a factor 1.3 higher than in N+N collisions. However this behaviour seems tochange at the top SPS energy where the slope for the Be+Be ratio decreases to the one observedin
N+N interactions. Note, that h W i is not a measured quantity, but has to be derived frommodels. Here the Epos model was used (see Sec. 3.1.3). Therefore the ratio h π i / h W i is directlymodel dependent and this dependence increases with decreasing nuclear mass number of collidingnuclei. For Be+Be collisions using different models leads to variation of the ratio of up to 10%,which is comparable to the difference between results on Be+Be and Pb+Pb collisions.New results on Ar+Sc and Xe+La collisions from NA61/SHINE will be available soon and areexpected to clarify the energy and system size dependence of h π i / h W i which is a measure of theentropy of the produced fireball. The NA61/SHINE experiment at the CERN SPS measured spectra and multiplicities of π − mesons produced in the 5% most central Be+ Be collisions at beam energies of 19 A , 30 A , 40 A ,75 A and 150 A GeV /c using the so-called h − method. This is the first step in the systematic studyof the phase diagram of hadronic matter and the first such measurement in Be+Be collisions.The normalized width of the rapidity distribution σ y /y beam decreases with increasing collisionenergy and the values lie between the results for inelastic nucleon-nucleon and central Pb+Pbcollisions. The average transverse mass h m T i − m versus collision energy shows a plateau in theSPS energy range at a similar level like in inelastic nucleon-nucleon and central Pb+Pb collisions.The mean multiplicity of pions per wounded nucleon in central Be+ Be collisions rises linearlywith the Fermi energy variable F and is close to the one in central Pb+Pb collisions expect forthe top SPS energy, where it is closer to the
N+N ratio.The results are discussed in the context of predictions for the onset of deconfinement at the CERNSPS collision energies. 28 cknowledgments
We would like to thank the CERN EP, BE, HSE and EN Departments for the strong supportof NA61/SHINE. We thank A. Kubala-Kukuś and D. Banaś from the Institute of Physics, JanKochanowski University for the target purity measurements with the WDXRF technique.This work was supported by the Hungarian Scientific Research Fund (grant NKFIH 123842/123959), the Polish Ministry of Science and Higher Education (grants 667/N-CERN/2010/0,NN 202 48 4339, NN 202 23 1837 and DIR/WK/2016/2017/10-1), the National Science CentrePoland (grants 2014/14/E/ST2/00018, 2014/15/B/ST2 / 02537 and 2015/18/M/ST2/00125,2015/19/N/ST2 /01689, 2016/23/B/ST2/00692, 2017/ 25/N/ ST2/ 02575, 2018/30/A/ST2/00226,2018/31/G/ST2/03910), the Russian Science Foundation, grant 16-12-10176 and 17-72-20045, theRussian Academy of Science and the Russian Foundation for Basic Research (grants 08-02-00018,09-02-00664 and 12-02-91503-CERN), the Russian Foundation for Basic Research (RFBR) fundingwithin the research project no. 18-02-00086, the National Research Nuclear University MEPhIin the framework of the Russian Academic Excellence Project (contract No. 02.a03.21.0005,27.08.2013), the Ministry of Science and Higher Education of the Russian Federation, Project"Fundamental properties of elementary particles and cosmology" No 0723-2020-0041, the EuropeanUnion’s Horizon 2020 research and innovation programme under grant agreement No. 871072,the Ministry of Education, Culture, Sports, Science and Technology, Japan, Grant-in-Aid forScientific Research (grants 18071005, 19034011, 19740162, 20740160 and 20039012), the GermanResearch Foundation (grant GA 1480/8-1), the Bulgarian Nuclear Regulatory Agency and theJoint Institute for Nuclear Research, Dubna (bilateral contract No. 4799-1-18/20), BulgarianNational Science Fund (grant DN08/11), Ministry of Education and Science of the Republic ofSerbia (grant OI171002), Swiss Nationalfonds Foundation (grant 200020117913/1), ETH ResearchGrant TH-01 07-3 and the Fermi National Accelerator Laboratory (Fermilab), a U.S. Departmentof Energy, Office of Science, HEP User Facility managed by Fermi Research Alliance, LLC (FRA),acting under Contract No. DE-AC02-07CH11359 and the IN2P3-CNRS (France).29 eferences [1] N. Antoniou et al. , [NA61/SHINE Collab.], “Study of hadron production in hadron nucleus and nucleusnucleus collisions at the CERN SPS,” 2006. CERN-SPSC-2006-034.[2] S. Afanasiev et al. , [NA49 Collab.]
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