Measurements of multiplicity fluctuations of identified hadrons in inelastic proton-proton interactions at the CERN Super Proton Synchrotron
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, Y. Nagai, M. Naskręt, V. Ozvenchuk, V. Paolone, O. Petukhov, I. Pidhurskyi, 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)
CERN-EP-2020-142September 7, 2020
Measurements of multiplicity fluctuations ofidentified hadrons in inelastic proton-proton interactions at the CERN Super ProtonSynchrotron
The NA61 / SHINE Collaboration
Measurements of multiplicity fluctuations of identified hadrons produced in inelastic p + p interactions at 31, 40, 80, and 158 GeV / c beam momentum are presented. Four di ff erentmeasures of multiplicity fluctuations are used: the scaled variance ω and strongly inten-sive measures Σ , Φ and ∆ . These fluctuation measures involve second and first moments ofjoint multiplicity distributions. Data analysis is preformed using the Identity method whichcorrects for incomplete particle identification. Strongly intensive quantities are calculated inorder to allow for a direct comparison to corresponding results on nucleus-nucleus collisions.The results for di ff erent hadron types are shown as a function of collision energy. A compar-ison with predictions of string-resonance Monte-Carlo models: E pos , S mash and V enus , isalso presented. c (cid:13) / 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 ] S e p Introduction
This paper presents experimental results on event-by-event fluctuations of multiplicities of identified par-ticles produced in inelastic proton-proton ( p + p ) interactions at 31, 40, 80, and 158 GeV / c ( √ s NN = / SHINE [1] exper-iment at the CERN Super Proton Synchrotron (SPS) in 2009. They are part of the strong interactionsprogramme devoted to the study of the properties of the onset of deconfinement and search for the criticalpoint of strongly interacting matter. Within this program, a two dimensional scan in collision energy andsize of colliding nuclei was performed [2].An interpretation of the experimental results on nucleus-nucleus (A + A) collisions relies to a large ex-tent on a comparison with the corresponding data on p + p and p + A interactions. However, availableresults on fluctuations of identified hadrons in these reactions are sparse. Moreover, fluctuation mea-surements cannot be corrected in a model independent manner for partial phase-space acceptance. Thusall measurements of the scan should be performed in the same phase space region. This motivated theNA61 / SHINE Collaboration to analyse data on p + p interactions with respect to fluctuations using thesame experimental methods, acceptance and measures as used to study nucleus-nucleus collisions.Fluctuations in A + A collisions are susceptible to two trivial sources: the finite and fluctuating numberof produced particles and event-by-event fluctuations of the collision geometry. Suitable statistical toolshave to be chosen to extract the fluctuations of interest. In this publication four di ff erent event-by-eventfluctuation measures are used: the scaled variance ω , the Φ quantity [3], and the ∆ and Σ measuresintroduced in Refs. [4, 5]. They were already successfully utilized by the NA49 experiment at the CERNSPS, see e.g. Refs. [6, 7, 8, 9, 10, 11, 12] and NA61 / SHINE, see e.g. Ref. [13].Experimental measurements of multiplicity distributions of identified hadrons are challenging because itis often impossible to identify a particle with su ffi cient precision. In this paper the Identity method [14,15, 16, 17, 18, 19] is employed to circumvent this problem. The Identity method has already beensuccessfully used in the past by collaborations NA49 [9], NA61 / SHINE [20], and ALICE [21, 22, 23].The paper is organized as follows. In Sec. 2 intensive and strongly intensive measures of fluctuationsused in this analysis are introduced and briefly discussed. The Identity method which allows to take intoaccount the incomplete particle identification is presented in Sec. 3. The NA61 / SHINE set-up and thedata reconstruction method are presented in Secs. 4 and 5, respectively. The data analysis procedure isintroduced in Secs. 6, 7 and 8. Applied corrections and remaining uncertainties are presented in Sec. 9.Results on the collision energy dependence of multiplicity fluctuations of identified hadrons in inelastic p + p collisions at 31, 40, 80, and 158 GeV / c beam momentum are presented, discussed and comparedwith model predictions in Sec. 10. A summary closes the paper.Throughout this paper the rapidity is calculated in the collision center of mass system: y = atanh( β L ),where β L = p L / E is the longitudinal ( z ) component of the velocity, p L and E are particle longitudinal2omentum and energy given in the collision center of mass system. The transverse component of themomentum is denoted as p T and the azimuthal angle φ is the angle between the transverse momentumvector and the horizontal ( x ) axis. Total momentum in the laboratory system is denoted as p lab . Thecollision energy per nucleon pair in the center of mass system is denoted as √ s NN , respectively. Measures of multiplicities and fluctuations are called intensive when they are independent of the vol-ume ( V ) of systems modelled by the ideal Boltzmann grand canonical ensemble (IB-GCE). In contrast,extensive quantities (for example mean multiplicity or variance of the multiplicity distribution) are pro-portional to the system volume within IB-GCE. One can also extend the notion of intensive and extensivequantities to the Wounded Nucleon Model (WNM) [24], where the intensive quantities are those whichare independent of the number of wounded nucleons ( W ), and extensive those which are proportionalto the number of wounded nucleons. Here it is assumed that the number of wounded nucleons is thesame for all collisions. The ratio of two extensive quantities is an intensive quantity [4]. Therefore,the ratio of mean multiplicities N a and N b , as well as the scaled variance of the multiplicity distribution ω [ a ] ≡ ( (cid:104) N a (cid:105) − (cid:104) N a (cid:105) ) / (cid:104) N a (cid:105) , are intensive measures. As a matter of fact, due to its intensity property, thescaled variance of the multiplicity distribution ω [ a ] is widely used to quantify multiplicity fluctuationsin high-energy heavy-ion experiments.The scaled variance takes the value ω [ a ] = N a = const . and ω [ a ] = N a . In nucleus-nucleus collisions the volume of the produced matter (or number of wounded nucleons) cannotbe fixed – it changes from one event to another. The quantities, which within the IB-GCE (or WNM)model are independent of V (or W ) fluctuations are called strongly intensive quantities [3, 4]. The ratioof mean multiplicities is both an intensive and a strongly intensive quantity, whereas the scaled varianceis an intensive but not strongly intensive quantity.Strongly intensive quantities ∆ and Σ used in this paper are defined as [5]: ∆ [ a , b ] ≡ (cid:104) N b (cid:105) − (cid:104) N a (cid:105) · (cid:16) (cid:104) N b (cid:105) ω [ a ] − (cid:104) N a (cid:105) ω [ b ] (cid:17) (1)3nd Σ [ a , b ] ≡ (cid:104) N b (cid:105) + (cid:104) N a (cid:105) · (cid:20) (cid:104) N b (cid:105) ω [ a ] + (cid:104) N a (cid:105) ω [ b ] − (cid:16) (cid:104) N a N b (cid:105) − (cid:104) N a (cid:105)(cid:104) N b (cid:105) (cid:17)(cid:21) , (2)where N a and N b stand for multiplicities of particles of type a and b , respectively. First and second puremoments, (cid:104) N a (cid:105) , (cid:104) N b (cid:105) , and (cid:104) N a (cid:105) , (cid:104) N b (cid:105) define ∆ [ a , b ]. In addition, the second mixed moment, (cid:104) N a N b (cid:105) , isneeded to calculate Σ [ a , b ].The first strongly intensive quantity Φ was introduced in 1992 [3] and can be expressed via Σ : Φ [ a , b ] = √(cid:104) N a (cid:105)(cid:104) N b (cid:105)(cid:104) N a + N b (cid:105) · (cid:16) (cid:112) Σ [ a , b ] − (cid:17) . (3)With the normalization of ∆ and Σ used here [5], the quantities ∆ [ a , b ] and Σ [ a , b ] are dimensionlessand have a common scale required for a quantitative comparison of fluctuations of di ff erent, in generaldimensional, extensive quantities. More precisely, the values of ∆ and Σ are equal to zero in the absenceof event-by-event fluctuations ( N a = const ., N b = const .) and equal to one for fluctuations given by themodel of independent particle production (Independent Particle Model) [5]. Experimental measurement of a joint multiplicity distribution of identified hadrons is challenging. Typi-cal tracking detectors, like time projection chambers used by NA61 / SHINE, allow for a precise measure-ment of momenta of charged particles and sign of their electric charges. In order to be able to distinguishbetween di ff erent particle types (e.g. a particle type a being e + , π + , K + or p ) a determination of particlemass is necessary. This is done indirectly by measuring for each particle a value of the specific energyloss d E / d x in the tracking detectors, the distribution of which depends on mass, momentum and charge.The resolution of d E / d x measurements is usually poor. Probabilities to register particles of di ff erent typeswith the same value of d E / d x are often comparable. Consequently, it is impossible to identify particlesindividually with reasonable confidence. The Identity method [14, 15, 16, 17, 18, 19] is a tool to measuremoments of multiplicity distribution of identified particles, which circumvents the experimental issue ofincomplete particle identification.The method employs the fitted inclusive d E / d x distribution functions of particles of type a , ρ a (d E / d x ) inmomentum bins. Each event has a set of measured d E / d x values corresponding to each track in the event.For each track in an event the probability w a of being a particle of type a is calculated: w a = ρ a (d E / d x ) / ρ (d E / d x ) , (4)where ρ (d E / d x ) = (cid:88) a ρ a (d E / d x ) . (5)4
13 m ToF-LToF-R PSDToF-FMTPC-RMTPC-LVTPC-2VTPC-1 Vertex magnetsTarget GAPTPCBeam S4 S5
S2S1BPD-1 BPD-2 BPD-3V1V1V0THCCEDAR zxy p Figure 1: (Color online) The schematic layout of the NA61 / SHINE experiment at the CERN SPS (horizontal cut,not to scale), see text and Ref. [1] for details.
Next, an event variable W a (a smeared multiplicity of particle a in the event) is defined as: W a = N (cid:88) n = w a , n , (6)where N is the number of measured particles in the event.The Identity method unfolds moments of the true multiplicity distributions from moments of the smearedmultiplicity distribution P ( W a ) using a response matrix calculated from the measured ρ a (d E / d x ) distribu-tions [15]. The NA61 / SHINE experimental facility [1] consists of a large acceptance hadron spectrometer locatedin the H2 beam line of the CERN North Area. The schematic layout of the NA61 / SHINE detector isshown in Fig. 1.The results presented in this paper were obtained using measurement from the Time Projection Chambers(TPC), the Beam Position Detectors and the beam and trigger counters. These detector components aswell as the proton beam and the liquid hydrogen target are briefly described below. Further informationcan be found in Refs. [1, 25, 26].For data taking on p + p interactions a liquid hydrogen target of 20.29 cm length (2.8% interaction length)and 3 cm diameter was placed 88.4 cm upstream of VTPC-1.5econdary beams of positively charged hadrons at 31, 40, 80, and 158 GeV / c were produced from400 GeV / c protons extracted from the SPS onto a beryllium target. A selection based on signals froma set of detectors along the H2 beam-line (scintillation counters S, Cerenkov detectors CEDAR, THCand beam position detectors BPD (see inset in Fig. 1)) allowed to identify beam protons with a purity ofabout 99%. A coincidence of these signals provided the beam trigger T beam .The interaction trigger T int was provided by the anti-coincidence of the incoming proton beam and ascintillation counter S4 ( T int = T beam ∧ S4). The S4 counter with 2 cm diameter, was placed between theVTPC-1 and VTPC-2 detectors along the beam trajectory at about 3.7 m from the target, see Fig. 1.The main tracking devices of the spectrometer are four large volume TPCs. Two of them, the vertexTPCs (VTPC-1 and VTPC-2), are located in the magnetic fields of two super-conducting dipole magnetswith a maximum combined bending power of 9 Tm which corresponds to about 1.5 T and 1.1 T fields inthe upstream and downstream magnets, respectively. In order to optimize the acceptance of the detector,the fields in both magnets were adjusted proportionally to the beam momentum.Two large main TPCs (MTPC-L and MTPC-R) are positioned downstream of the magnets symmetricallyto the beam line. The fifth small TPC (GAP TPC) is placed between VTPC-1 and VTPC-2 directly onthe beam line. It closes the gap between the beam axis and the sensitive volumes of the other TPCs.Simultaneous measurements of d E / d x and p lab allow to extract information on particle mass, which isused to identify charged particles. Behind the MTPCs there were three Time-of-Flight (ToF) detectors. The event vertex and the produced particle tracks were reconstructed using the standard NA61 / SHINEsoftware. Details on the reconstruction procedure of proton-proton interactions in NA61 / SHINE can befound in Ref. [25].Detector parameters were optimized by a data-based calibration procedure which also took into accounttheir time dependence, for details see Refs. [25, 27].A simulation of the NA61 / SHINE detector response was used to correct the reconstructed data. SeveralMonte Carlo models were compared with the NA61 / SHINE results on p + p , p + C and π + C interactions:F luka qmd enus pos heisha et II-04 and S ibyll pos ff erences dueto the di ff erent identification procedures followed in the MC simulations and the real data are addressedin Ref. [26] and Sec. 9.3. 6t should be underlined that only inelastic p + p interactions in the hydrogen of the target cell were simu-lated and reconstructed. Thus the MC based corrections (see Sec. 9.1) can be applied only for inelasticevents. The contribution of elastic events is removed by the event selection cuts (see Sec. 7). This section starts with a brief overview of the data analysis procedure and the applied corrections. Italso defines which class of particles the final results correspond to.The analysis procedure consists of the following steps:(i) application of event and track selection criteria,(ii) determination of inclusive d E / d x spectra,(iii) determination of moments of identified hadron multiplicity distributions with the Identity method,(iv) evaluation of corrections to the moments based on experimental data and simulations,(v) calculation of the corrected moments and fluctuation quantities,(vi) calculation of statistical and systematic uncertainties.Corrections for the following biases were evaluated and applied:(i) contribution of particles other than primary (see below) hadrons produced in inelastic p + p interac-tions,(ii) losses of primary hadrons due to measurement ine ffi ciencies,(iii) losses of inelastic p + p interactions due to the trigger and the event and track selection criteriaemployed in the analysisThe final results refer to identified hadrons produced in inelastic p + p interactions by strong interactionprocesses and in electromagnetic decays of produced hadrons. Such hadrons are referred to as primary hadrons.The analysis was performed in the kinematic acceptance limited by the detector geometry and the statis-tics of inclusive d E / d x spectra. The acceptance is given in the form of two sets of tables:(i) three-dimensional tables representing the high e ffi ciency region of the detector,(ii) two-dimensional tables defining the d E / d x fit range.The acceptance tables can be found in Ref. [32]. 7 Event and track selection
Inelastic p + p events were selected using the following criteria:(i) no o ff -time beam particle detected within a time window of ± µ s around the trigger particle,(ii) beam particle trajectory measured in at least three planes out of four of BPD-1 and BPD-2 and inboth planes of BPD-3,(iii) the primary interaction vertex fit converged,(iv) z position of the interaction vertex (fitted using the beam trajectory and TPC tracks) not furtheraway than 20 cm from the center of the liquid hydrogen target (LHT),(v) events with a single, positively charged track with absolute momentum close to the beam momen-tum (see Ref. [25]) are removed in order to eliminate elastic scattering reactions. In order to select tracks of primary charged hadrons and to reduce the contamination of tracks fromsecondary interactions, weak decays and o ff -time interactions, the following track selection criteria wereapplied:(i) track momentum fit at the interaction vertex should have converged,(ii) total number of reconstructed points on the track should be greater than 30,(iii) sum of the number of reconstructed points in VTPC-1 and VTPC-2 should be greater than 15 orthe number of reconstructed points in the GAP TPC should be greater than 4,(iv) the distance between the track extrapolated to the interaction plane and the interaction point (impactparameter) should be smaller than 4 cm in the horizontal (bending) plane and 2 cm in the vertical(drift) plane,(v) the total number of reconstructed d E / d x points on the track should be greater than 30,(vi) the track lies in the high e ffi ciency region of the detector and the d E / d x fit acceptance maps givenin Ref. [32].The event and track statistics after applying the selection criteria are summarized in Table 1.8 able 1: Statistics of accepted events as well as number of accepted positively and negatively charged tracks fordata sets analysed in the paper. Beam momentum / c ] charged tracks charged tracks31 819710 530971 13218740 2641412 2071490 67525880 1531849 2061069 1020267158 1587680 3243819 1980037 In order to calculate moments of multiplicity distributions of identified hadrons corrected for incompleteparticle identification the analysis was performed using the Identity method. The analysis consists ofthree steps:(i) parametrization of inclusive d E / d x spectra,(ii) calculation of smeared multiplicity distributions and their moments,(iii) correcting smeared moments for incomplete particle identification using the d E / d x response matrix.The Identity analysis steps are briefly described below. E / d x spectra For each particle its specific energy loss d E / d x is calculated as the truncated mean (smallest 50%) ofcluster charges measured along the track trajectory. As an example, d E / d x measured in p + p interactionsat 80 GeV / c , for positively and negatively charged particles, as a function of q × p lab is presented in Fig. 2.The expected mean values of d E / d x for di ff erent particle types are shown by the Bethe-Bloch curves.The parametrization of d E / d x spectra of e + , e − , π + , π − , K + , K − , p, and ¯p were obtained by fitting thed E / d x distributions separately for positively and negatively charged particles in bins of p lab and transversemomentum p T with a sum of four functions [26, 33, 34] each corresponding to the expected d E / d x distribution for a given particle type. The details of this fitting procedure can be found in Ref. [26]. Incontrast to spectra analysis [26] separate fits were performed in order to extend acceptance by addingparticles with negative p lab , x / q . Systematic uncertainties arising from the fitting procedure are estimatedin Sec. 9. 9 E / d x [ a r b . un i t s ] q x p [GeV/c] lab Figure 2: (Color online) Distribution of charged particles in the d E / d x - q × p lab ( q represents electric charge) plane.The energy loss in the TPCs for di ff erent charged particles for events and tracks selected for the analysis of p + p interactions at 80 GeV / c . Expectations for the dependence of the mean d E / d x on p lab for the considered particletypes are shown by the curves calculated based on the Bethe-Bloch function. In order to ensure similar particle numbers in each bin, 20 logarithmic bins were chosen in p lab in therange 1 −
100 GeV / c . Furthermore, the data were binned in 20 equal p T intervals in the range 0 − / c .The d E / d x spectrum for a given particle type was parametrized by the sum of asymmetric Gaussianswith widths σ a , l depending on the particle type a and the number of points l measured in the TPCs.Simplifying the notation in the fit formulae, the peak position of the d E / d x distribution for particle type a is denoted as x a . The contribution of a reconstructed particle track to the fit function reads: f ( x ) = (cid:88) a f a ( x ) = (cid:88) a = π, p , K , e Y a (cid:80) l n l (cid:88) l n l √ πσ l exp − (cid:32) x − x a (1 ± δ ) σ l (cid:33) , (7)where x is the d E / d x of the particle, n l is the number of tracks with number of points l in the sample and Y a is the amplitude of the contribution of particles of type a . The second sum is the weighted averageof the line-shapes from the di ff erent numbers of measured points (proportional to track-length) in thesample. The quantity σ l is written as: σ l = σ (cid:32) x i x π (cid:33) . (cid:46) √ l , (8)10here the width parameter σ is assumed to be common for all particle types and bins. A 1 / √ l depen-dence on number of points is assumed. The Gaussian peaks are allowed to be asymmetric to describe thetail of the Landau distribution which may still be present after truncation.Examples of fits for p + p interactions at 31 and 158 GeV / c are shown in Fig. 3.In order to ensure good fit quality, only bins with number of tracks greater than 500 were used for furtheranalysis. The Bethe-Bloch curves for di ff erent particle types cross each other at low values of the totalmomentum. Thus, the proposed technique is not su ffi cient for particle identification at low p lab and binswith p lab < / c were excluded from this analysis based solely on d E / d x .The requirement of at least 500 tracks with good quality d E / d x measurement in each p lab , p T bin reducesthe acceptance available for the analysis. Due to di ff erent multiplicities the acceptance is di ff erent forpositively and negatively charged particles. Moreover, it also changes with beam momentum. Thus, thelargest acceptance was found for positively charged hadrons at 158 GeV / c and the smallest at 31 GeV / c for negatively charged hadrons. The acceptance used in this analysis is given separately for negativelyand positively charged particles by a set of publicly available acceptance tables [32]. The correspondingrapidity and transverse momentum acceptances at 31 and 158 GeV / c are shown in Fig. 4. The parametrization of inclusive d E / d x spectra of identified particles is first used to calculate the particleidentities w a (see Sec. 3). Distributions of w a for p + p interactions at 31 and 158 GeV / c are shown inFigs. 5 and 6 for positively and negatively charged particles, separately.In the second step smeared multiplicities of identified particles W a (see Sec. 3) are calculated for eachselected event and their distributions are obtained. Examples of smeared multiplicity distributions for p + p interactions at 31 and 158 GeV / c are shown in Figs. 7 and 8 for positively and negatively chargedparticles, separately.Finally, first and second moments of smeared multiplicity distributions are calculated: (cid:104) W p (cid:105) , (cid:104) W K (cid:105) , (cid:104) W π (cid:105) , (cid:104) W e (cid:105) , (cid:104) W p (cid:105) , (cid:104) W K (cid:105) , (cid:104) W π (cid:105) , (cid:104) W e (cid:105) , (cid:104) W p W K (cid:105) , (cid:104) W p W π (cid:105) , (cid:104) W p W e (cid:105) , (cid:104) W K W π (cid:105) , (cid:104) W K W e (cid:105) , (cid:104) W π W e (cid:105) for positivelyand negatively charged particles, separately. Following the Identity method [15, 16] one calculates the first and second moments of multiplicity dis-tributions corrected for incomplete particle identification as follows.11 .6 0.8 1 1.2 1.4 1.6 1.8 21000200030004000500060007000 en t r i e s [ a r b . un i t s ] + p + e + Kp - - r e s i dua l s en t r i e s [ a r b . un i t s ] - p - e - Kp - - r e s i dua l s en t r i e s [ a r b . un i t s ] + p + e + Kp - - r e s i dua l s en t r i e s [ a r b . un i t s ] - p - e - Kp - - r e s i dua l s Figure 3: (Color online) The d E / d x distributions for positively ( left ) and negatively ( right ) charged particles in thebin 5.46 < p lab ≤ / c and 0.1 < p T ≤ / c produced in p + p interactions at 158 GeV / c ( top ) and31 GeV / c ( bottom ). The fit by a sum of contributions from di ff erent particle types is shown by black lines. Thecorresponding residuals (the di ff erence between the data and fit divided by the statistical uncertainty of the data) isshown in the bottom plots. - - - - y [ G e V / c ] T p + p
31 GeV/c - - - - y [ G e V / c ] T p - p
31 GeV/c - - - - y [ G e V / c ] T p + p
158 GeV/c - - - - y [ G e V / c ] T p - p
158 GeV/c
Figure 4: (Color online) Distributions of particles rapidity (calculated in the collision center-of-mass referencesystem assuming pion mass) and p T of all particles selected for the analysis. The two upper plots are for 31 GeV / c and the two lower plots for 158 GeV / c . The irregular edges of the distributions reflect the boundaries of the p lab , p T bins used in the d E / d x analysis. The first moments of the multiplicity distributions for complete particle identification, (cid:104) N a (cid:105) are equal tothe corresponding first moments of the smeared multiplicity distributions: (cid:104) N a (cid:105) = (cid:104) W a (cid:105) . (9)Second moments of the multiplicity distributions of identified hadrons are obtained by solving sets oflinear equations which relate them to the corresponding smeared moments. The coe ffi cients of the equa-tions are calculated using the identified particle densities in d E / d x . The Identity method was quanti-tatively tested by numerous simulations, see for example Refs. [16, 18]. Here results of a qualitativedata-based test are presented.The energy dependence of the scaled variance ω of all charged pions ω [ π ] calculated using the Identitymethod was compared with the scaled variance calculated for charged particles. The results are very13 p w e n t r i es [ a r b . un i t s ] p w e n t r i es [ a r b . un i t s ] + K w e n t r i es [ a r b . un i t s ] - K w e n t r i es [ a r b . un i t s ] + p w e n t r i es [ a r b . un i t s ] - p w e n t r i es [ a r b . un i t s ] + e w e n t r i es [ a r b . un i t s ] - e w e n t r i es [ a r b . un i t s ] Figure 5: (Color online) Distributions of identities of positively ( left ) and negatively ( right ) charged particles (fromtop to bottom: p , K , π , e ) selected for the analysis in p + p interactions at 31 GeV / c . p w e n t r i es [ a r b . un i t s ] p w e n t r i es [ a r b . un i t s ] + K w e n t r i es [ a r b . un i t s ] - K w e n t r i es [ a r b . un i t s ] + p w e n t r i es [ a r b . un i t s ] - p w e n t r i es [ a r b . un i t s ] + e w e n t r i es [ a r b . un i t s ] - e w e n t r i es [ a r b . un i t s ] Figure 6: (Color online) Distributions of identities of positively ( left ) and negatively ( right ) charged particles (fromtop to bottom: p , K , π , e ) selected for the analysis in p + p interactions at 158 GeV / c . p W e n t r i es [ a r b . un i t s ] p W e n t r i es [ a r b . un i t s ] + K W e n t r i es [ a r b . un i t s ] - K W e n t r i es [ a r b . un i t s ] + p W e n t r i es [ a r b . un i t s ] - p W e n t r i es [ a r b . un i t s ] + e W e n t r i es [ a r b . un i t s ] - e W e n t r i es [ a r b . un i t s ] Figure 7: (Color online) Smeared multiplicity distributions of positively ( left ) and negatively ( right ) charged par-ticles (from top to bottom: p , K , π , e ) in p + p interactions at 31 GeV / c . p W e n t r i es [ a r b . un i t s ] p W e n t r i es [ a r b . un i t s ] + K W e n t r i es [ a r b . un i t s ] - K W e n t r i es [ a r b . un i t s ] + p W e n t r i es [ a r b . un i t s ] - p W e n t r i es [ a r b . un i t s ] + e W e n t r i es [ a r b . un i t s ] - e W e n t r i es [ a r b . un i t s ] Figure 8: (Color online) Smeared multiplicity distributions of positively ( left ) and negatively ( right ) charged par-ticles (from top to bottom : p , K , π , e ) in p + p interactions at 158 GeV / c . This section briefly describes the corrections for biases and presents methods to calculate statistical andsystematic uncertainties.
The first and second moments of multiplicity distributions corrected for incomplete particle identificationwere also corrected for(i) loss of inelastic events due to the on-line and o ff -line event selection,(ii) loss of particles due to the detector ine ffi ciency and track selection,(iii) contribution of particles from weak decays and secondary interactions (feed-down).A simulation of the NA61 / SHINE detector response was used to correct the data for the above mentionedbiases. Corrections were calculated for moments of identified hadron multiplicity distributions. Eventssimulated with the E pos / SHINE software as de-scribed in Sec. 5. The multiplicative correction factors C ( k ) a and C ab , where a and b denotes particle type( a , b = π + / − , K + / − , p , ¯ p , e + / − ; and a (cid:44) b ) are defined as: C ( k ) a = ( N ka ) MC g en ( N ka ) MCsel , C ab = ( N ab ) MC g en ( N ab ) MCsel , (10)where:(i) ( N ka ) MC g en – moment k = , a ( a = π + / − , K + / − , p , ¯ p , e + / − ) generated by the model,(ii) ( N ka ) MCsel – moment k = , a ( a = π + / − , K + / − , p , ¯ p , e + / − ) generated by the modelwith the detector response simulation, reconstruction and selection,(iii) ( N ab ) MC g en / sel – mixed second moment of particle types a and b generated by the model ( g en ) andwith the detector response simulation, reconstruction and selection ( sel ).This way of implementing correction was tested on E pos and V enus models. For details see Sec. 9.5.The correction factors for first, second and mixed moments of identified hadrons are shown in Figs. 9, 10and 11. 18 [GeV] NN s p ( ) C
10 15 [GeV] NN s K ( ) C
10 15 [GeV] NN s p ( ) C all charges
10 15 [GeV] NN s p ( ) C
10 15 [GeV] NN s K ( ) C
10 15 [GeV] NN s p ( ) C positively charged
10 15 [GeV] NN s p ( ) C
10 15 [GeV] NN s K ( ) C
10 15 [GeV] NN s p ( ) C negatively charged Figure 9: (Color online) Energy dependence of correction factor C (1) a for all charged, positively and negativelycharged pions, kaons and protons. The sub-sample method was used to calculate statistical uncertainties of final results. All selected eventswere grouped into M =
30 non-overlapping sub-samples of events. Then a given fluctuation measure Q (for example Σ [ π + , p ]) was calculated for each sub-sample separately, and the variance of its distri-bution, Var [ Q ], was obtained. The statistical uncertainty of Q for all selected events was estimated as √ Var [ Q ] / M . The d E / d x parametrization requires a minimum number of tracks in a p lab , p T bin, thus19 [GeV] NN s ( ) p C
10 15 [GeV] NN s ( ) K C
10 15 [GeV] NN s ( ) p C all charges
10 15 [GeV] NN s ( ) p C
10 15 [GeV] NN s ( ) K C
10 15 [GeV] NN s ( ) p C positively charged
10 15 [GeV] NN s ( ) p C
10 15 [GeV] NN s ( ) K C
10 15 [GeV] NN s ( ) p C negatively charged Figure 10: (Color online) Energy dependence of correction factor C (2) a for all charged, positively and negativelycharged pions, kaons and protons. the acceptance in which the d E / d x parametrization can be obtained is larger for all selected events thanfor sub-samples of events. In order to have the maximum acceptance the same d E / d x parametrizationobtained using all events was used in the sub-sample analysis. It was checked using the bootstrapmethod [35, 36] that the above approximation leads only to a small underestimation of statistical uncer-tainties. 20 [GeV] NN s p K C
10 15 [GeV] NN s K p C
10 15 [GeV] NN s p p C all charges
10 15 [GeV] NN s p K C
10 15 [GeV] NN s K p C
10 15 [GeV] NN s p p C positively charged
10 15 [GeV] NN s p K C
10 15 [GeV] NN s K p C
10 15 [GeV] NN s p p C negatively charged Figure 11: (Color online) Energy dependence of correction factor C ab for all charged, positively and negativelycharged combinations of π ( p + ¯ p ), π K and pK . .3 Systematic uncertainties Systematic uncertainties originate from uncertainties of the detector response simulation and modelsused for calculation of corrections. The total systematic uncertainties were calculated by adding detector-related and model-related contributions in quadrature. ff ects: event and track selection These uncertainties were studied by applying standard (see Sec. 7) and loose cuts (see below). For eachchoice the complete analysis was repeated including the d E / d x fitting. The uncertainties are related toimperfectness of the reconstruction procedure and to the acceptance of events with additional tracks fromo ff -time particles. This systematic uncertainty was estimated by reducing the width of the time windowin which no o ff -time beam particles are allowed from 1.5 µ s to 0.5 µ s, by relaxing the maximum alloweddistance between fitted z position of the vertex and the center of the LHT from ±
20 cm to ±
40 cm, therequirement on the number of measured points along the track from 30 to 20 (also d E / d x points neededfor the fitting) and loosening the constraint on the distance of the track extrapolated back to the targetplane and the main vertex from 4 to 8 cm and from 2 to 4 cm in the x and y directions, respectively.An additional possible source of uncertainty is imperfectness of the d E / d x parametrization. Here thelargest uncertainty comes from uncertainties of the parameters of the kaon d E / d x distribution. The kaondistribution significantly overlaps with the proton and pion distributions. In the most di ffi cult low mo-mentum range the d E / d x fits were cross-checked using the time-of-flight information and found to be inagreement at the level of single particle spectra (see Ref. [26]).In this analysis, as it considers second order moments, two additional tests were performed. First, fitsof d E / d x distributions with fixed asymmetry parameter and without any constraint on asymmetry wereused to estimate the possible biases of fluctuation measures. The change of the results is below 10% formost quantities. Larger relative di ff erences appear only for quantities close to 0. The second test wasperformed to validate fit stability. The value of d E / d x for each reconstructed track in the Monte-Carlosimulation was generated using the parametrization of d E / d x response fitted to the data. Next, d E / d x fitswere performed on reconstructed E pos E / d x simulation. The change of the results is below 10% for most quantities and, for almost all, it iswithin or comparable to systematic uncertainty. The only exceptions are the scaled variance of protonsat 158 GeV / c (10% which normally is 5%) and pions at 31 GeV / c (15% which normally is 8%) as well as ∆ of pions and protons at 158 GeV / c (17% compared to 11%).Uncertainty related to the selection for the event and track cuts is the main source (about 50%) of thetotal systematic uncertainty, σ s y s , for the majority of the presented results (86 out of 140 measuredquantities). 22eam momentum [GeV / c ] (cid:104) π (cid:105) acc (cid:104) π (cid:105) (cid:104) K (cid:105) acc (cid:104) K (cid:105) (cid:104) p + ¯ p (cid:105) acc (cid:104) p + ¯ p (cid:105)
31 0.397(1) 3.556(37) 0.0440(3) 0.202(11) 0.280(1) 0.982(3)40 0.6233(3) 4.101(36) 0.0680(3) 0.254(11) 0.331(1) 1.101(3)80 1.416(1) 4.701(38) 0.1563(3) 0.296(11) 0.369(1) 1.111(4)158 2.360(2) 5.514(45) 0.2597(4) 0.366(18) 0.399(1) 1.194(10)
Table 2: Comparison of mean multiplicity in the analysis acceptance to mean multiplicity of identified hadrons inthe full phase-space (only statistical uncertainty indicated) [26].
The procedure applied to correct data and the lack of precise knowledge of the production cross sectionof weakly decaying particles leads to systematic uncertainty. The uncertainty was estimated using simu-lations preformed within the E pos enus pos data were correctedusing corrections obtained based on the V enus model and compared to the unbiased E pos results. Thenthe same procedure was repeated swapping E pos and V enus . The di ff erences between the unbiased andsimulated-corrected results were added to the systematic uncertainty. They are in average about 20%(E pos data) and 25% (V enus data) of σ s y s . Note the models show similar agreement with results on p + p interactions at the CERN SPS energies.
10 Results, discussion and comparison with models
In this section final experimental results are presented and discuss as well as compared with predictionsof selected string-hadronic models.
The final results presented in this section refer to identified hadrons produced in inelastic p + p interactionsby strong interaction processes and in electromagnetic decays of produced hadrons. They were obtainedwithin the kinematic acceptances given in Ref. [32] and illustrated in Fig. 4. Note, that the kinematicacceptances for positively and negatively charged hadrons are di ff erent.Mean multiplicities of pions, kaons and anti-protons in the acceptance region of the fluctuation analysisare plotted in Fig. 12 and compared to corresponding mean multiplicities measured in the full phase-space in Table 2.Pions are the most abundantly produced particles and they are the majority of accepted charged hadronsin all analyzed reactions. With decreasing beam momentum the contribution of protons increases andsmall contributions of kaons and anti-protons decrease. Almost all negatively charged hadrons are pions,23 [GeV] NN s æ acc N Æ pp+ p K Figure 12: (Color online) Mean multiplicities of charged π , K and p + ¯ p in the analysis acceptance as a functionof collision energy. Only statistical uncertainties are shown. whereas protons are majority of positively charged hadrons at the lowest beam momentum, 31 GeV / c .The changes of particle type composition with charge of selected hadrons and beam momentum arerelated to di ff erent thresholds for production of pions, kaons and anti-protons. Mean proton multiplicityin the full phase-space is about one (0.3-0.4 in the acceptance) and it is approximately independent ofbeam momentum. This is because final state protons are strongly correlated with two initial state protonsvia the baryon number conservation.Figure 13 shows the collision energy dependence of the scaled variance of pion, kaon and proton mul-tiplicity distributions. Note, the intensive fluctuation measure ω is one for a Poisson distribution andzero in the case of a constant multiplicity for all collisions. The scaled variance quantifies the widthof the multiplicity distribution relatively to the width of the Poisson distribution with the same meanmultiplicity. The results for all charged, positively charged and negatively charged hadrons are presentedseparately. One observes:(i) ω for pions increases with the collision energy. The increase is the strongest for all charged pions.This is likely to be related to the well established KNO scaling of the charged hadron multiplicitydistributions in inelastic p + p interactions with the scaled variance being proportional to mean mul-tiplicity [37, 38, 39]. Global and local (resonance decays) electric charge conservation correlatesmultiplicities of positively and negatively charged pions and thus the e ff ect is the most pronouncedfor all charged hadrons.(ii) The dependence of ω on beam momentum and hadron charge for kaons is qualitatively similar tothe one for pions but weaker. This is probably related with a significantly smaller mean multiplicityof kaons than pions. One notes that scaled variance of a single maximum multiplicity distribution24 [GeV] NN s [ p ] w
10 15 [GeV] NN s [ K ] w
10 15 [GeV] NN s ] p [ w all charges EPOS1.99VENUS4.12SMASH1.5
10 15 [GeV] NN s [ p ] w
10 15 [GeV] NN s [ K ] w
10 15 [GeV] NN s ] p [ w positively charged
10 15 [GeV] NN s [ p ] w
10 15 [GeV] NN s [ K ] w
10 15 [GeV] NN s ] p [ w negatively charged Figure 13: (Color online) The collision energy dependence of scaled variance of pion, kaon and protons producedin inelastic p + p interactions. Results for all charged, positively and negatively charged hadrons are presentedseparately. The solid, dashed and dotted lines show predictions of E pos mash enus [GeV] NN s [ p , K ] S
10 15 [GeV] NN s , K ] p [ S
10 15 [GeV] NN s , p ] p [ S all charges EPOS1.99VENUS4.12SMASH1.5
10 15 [GeV] NN s [ p , K ] S
10 15 [GeV] NN s , K ] p [ S
10 15 [GeV] NN s , p ] p [ S positively charged
10 15 [GeV] NN s [ p , K ] S
10 15 [GeV] NN s , K ] p [ S
10 15 [GeV] NN s , p ] p [ S negatively charged Figure 14: (Color online) The collision energy dependence of Σ [ π, ( p + p )], Σ [ π, K ] and Σ [( p + p ) , K ] in inelastic p + p interactions. Results for all charged, positively and negatively charged hadrons are presented separately.The solid, dashed and dotted lines show predictions of E pos mash enus [GeV] NN s - - [ p , K ] F
10 15 [GeV] NN s - - , K ] p [ F
10 15 [GeV] NN s - - , p ] p [ F all charges EPOS1.99VENUS4.12SMASH1.5
10 15 [GeV] NN s - - [ p , K ] F
10 15 [GeV] NN s - - , K ] p [ F
10 15 [GeV] NN s - - , p ] p [ F positively charged
10 15 [GeV] NN s - - [ p , K ] F
10 15 [GeV] NN s - - , K ] p [ F
10 15 [GeV] NN s - - , p ] p [ F negatively charged Figure 15: (Color online) The collision energy dependence of Φ [ π, ( p + p )], Φ [ π, K ] and Φ [( p + p ) , K ] in inelastic p + p interactions. Results for all charged, positively and negatively charged hadrons are presented separately.The solid, dashed and dotted lines show predictions of E pos mash enus [GeV] NN s [ p , K ] D
10 15 [GeV] NN s , K ] p [ D
10 15 [GeV] NN s , p ] p [ D all charges EPOS1.99VENUS4.12SMASH1.5
10 15 [GeV] NN s [ p , K ] D
10 15 [GeV] NN s , K ] p [ D
10 15 [GeV] NN s , p ] p [ D positively charged
10 15 [GeV] NN s [ p , K ] D
10 15 [GeV] NN s , K ] p [ D
10 15 [GeV] NN s , p ] p [ D negatively charged Figure 16: (Color online) The collision energy dependence of ∆ [ π, ( p + p )], ∆ [ π, K ] and ∆ [( p + p ) , K ] in inelastic p + p interactions. Results for all charged, positively and negatively charged hadrons are presented separately.The solid, dashed and dotted lines show predictions of E pos mash enus ff ect is likely responsible for ω [ K − ] and ω [ p ] being close to one, mean multiplicity of K − and p in the acceptance is below 0.1and 0.03, respectively.(iii) The scaled variance of protons is about 0.8 and it weakly depends on the beam momentum. The net-baryon (baryon - anti-baryon) multiplicity in the full phase-space is exactly two. This is becausethe initial baryon number is two and the baryon number conservation. Thus the scaled varianceof the net-baryon multiplicity distribution is zero. The anti-baryon production at the SPS energiesis small and thus the net-baryon multiplicity is close to the baryon multiplicity. The baryons arepredominately protons and neutrons. Thus the proton fluctuations are expected to be mostly dueto fluctuation of the proton to neutron ratio and fluctuations caused by the limited acceptance ofprotons.Figures 14 and 15 show the results on Σ and Φ for pion-proton, pion-kaon and proton-kaon multiplicitiesmeasured separately for all charged, positively charged, and negatively charged hadrons produced ininelastic p + p collisions at 31–158 GeV / c beam momentum. The strongly intensive measures Σ and Φ di ff er only by a selection of the reference value (one for Σ and zero for Φ ) and a normalization factorwhich involves mean multiplicities, see Eq. 3. They are both presented here due to historical reasons,but only results for Σ are discussed. The Σ measure assumes value one in the Independent ParticleProduction Model which postulates that particle types are attributed to particles independent of eachother. This implies that Σ unlike ω is insensitive to particle multiplicity distribution. One observes:(i) For all and positively charged pions-protons Σ is significantly below one (approximately 0.8) and itis weakly dependent on the beam momentum. This is likely due to a large fraction of pion-protonpairs coming from decays of baryonic resonances [40, 41].(ii) Σ for all charge pions-kaons increases significantly with the beam momentum and it is about 1.2 at158 GeV / c . The origin of this behaviour is unclear.(iii) For remaining cases Σ is somewhat below or close to one suggesting a small contribution of hadronsfrom resonance decays.Figure 16 shows the results for ∆ of identified hadrons calculated separately for all charged, positivelycharged, and negatively charged hadrons produced in inelastic p + p collisions at beam momenta from 31to 158 GeV / c . The general properties of ∆ are similar to the properties of Σ discussed above. Unlike Σ , ∆ does not include a correlation term between multiplicities of two hadron types, see Eqs. 1 and 2. Oneobserves:(i) ∆ for all and positively charged pions and protons is below one. It is qualitatively similar to Σ andthus likely to be caused by resonance decays.(ii) ∆ [( p + ¯ p ) , K ] increases with the collision energy from about one to two. The origin of this depen-dence is unclear. 29 The results shown in Figs. 13, 14, 15 and 16 are compared with predictions of three string-resonancemodels: E pos mash enus p + p interactions presented here. In p + p interactions at CERN SPS energies one expects none ofthe high matter density phenomena usually studied and searched for in nucleus-nucleus collisions. Anydeviations from independent particle production are considered to be caused by well established e ff ectsdiscussed in Sec. 10.1.
11 Summary and outlook
In this paper experimental results on multiplicity fluctuations of identified hadrons produced in inelastic p + p interactions at 31, 40, 80, and 158 GeV / c beam momentum are presented. Four di ff erent measuresof multiplicity fluctuations are used: the scaled variance ω and the strongly intensive measures Σ , Φ and ∆ . The fluctuation measures involve second and first moments of joint multiplicity distributions. Dataanalysis was preformed using the Identity method which corrects for incomplete particle identification.Strongly intensive quantities are calculated in order to allow for a direct comparison with correspondingresults on nucleus-nucleus collisions. The results for di ff erent hadron types are shown as a function ofcollision energy.The measurements of NA61 / SHINE were compared with string-resonance models S mash pos enus + p interactions presented in this paper. 30 cknowledgements We would like to thank the CERN EP, BE, HSE and EN Departments for the strong support of NA61 / SHINE.This work was supported by the Hungarian Scientific Research Fund (grant NKFIH 123842 / / N-CERN / /
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A. Acharya , H. Adhikary , A. Aduszkiewicz , E.V. Andronov , T. Anti´ci´c , V. Babkin ,M. Baszczyk , S. Bhosale , A. Blondel , M. Bogomilov , A. Brandin , A. Bravar , W. Bryli´nski ,J. Brzychczyk , M. Buryakov , O. Busygina , A. Bzdak , H. Cherif , M. ´Cirkovi´c ,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. Ga´zdzicki , , 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. Ma´ckowiak-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. Mrówczy´nski , Y. Nagai , M. Naskr ˛et , 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. Puzovi´c , 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. Veberiˇc , V.V. Vechernin , A. Wickremasinghe , , Z. Włodarczyk , K. Wojcik , O. Wyszy´nski ,E.D. Zimmerman , and R. Zwaska National Nuclear Research Center, Baku, Azerbaijan Faculty of Physics, University of Sofia, Sofia, Bulgaria Ru ¯der Boškovi´c 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, Poland34 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, Russia University of Belgrade, Belgrade, Serbia University of Geneva, Geneva, Switzerland Fermilab, Batavia, USA University of Colorado, Boulder, USA26