Spectra and mean multiplicities of π^{-} in central {}^{40}Ar+{}^{45}Sc collisions at 13A, 19A, 30A, 40A, 75A and 150A GeV/c beam momenta measured by the NA61/SHINE spectrometer at the CERN SPS
NA61/SHINE collaboration, A. Acharya, H. Adhikary, K.K. Allison, E.V. Andronov, T. Anti?i?, V. Babkin, M. Baszczyk, S. Bhosale, A. Blondel, M. Bogomilov, A. Brandin, A. Bravar, W. Bryli?ski, J. Brzychczyk, M. Buryakov, O. Busygina, A. Bzdak, H. Cherif, M. ?irkovi?, 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. Kie?bowicz, V.A. Kireyeu, V. Klochkov, V.I. Kolesnikov, D. Kolev, A. Korzenev, V.N. Kovalenko, S. Kowalski, M. Koziel, B. Koz?owski, A. Krasnoperov, W. Kucewicz, M. Kuich, A. Kurepin, D. Larsen, A. László, T.V. Lazareva, M. Lewicki, K. ?ojek, V.V. Lyubushkin, M. Ma?kowiak-Paw?owska, 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, ?. Mik, S. Morozov, Y. Nagai, M. Naskr?t, V. Ozvenchuk, V. Paolone, O. Petukhov, I. Pidhurskyi, R. P?aneta, P. Podlaski, B.A. Popov, B. Porfy, M. Posiada?a-Zezula, D.S. Prokhorova, D. Pszczel, S. Pu?awski, J. Puzovi?, et al. (42 additional authors not shown)
EEUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)
Submitted to: Eur. Phys. J. C CERN-EP-2021-010January 26, 2021
Spectra and mean multiplicities of π − in central Ar+ Sc collisions at 13 A , 19 A ,30 A , 40 A , 75 A and 150 A GeV /c beammomenta measured by the NA61/SHINEspectrometer at the CERN SPS The NA61/SHINE Collaboration
The physics goal of the strong interaction program of the NA61/SHINE experiment atthe CERN Super Proton Synchrotron (SPS) is to study the phase diagram of hadronicmatter by a scan of particle production in collisions of nuclei with various sizes ata set of energies covering the SPS energy range. This paper presents differentialinclusive spectra of transverse momentum, transverse mass and rapidity of π − mesonsproduced in central Ar+ Sc collisions at beam momenta of 13 A , 19 A , 30 A , 40 A ,75 A and 150 A GeV /c . Energy and system size dependence of parameters of thesedistributions – mean transverse mass, the inverse slope parameter of transverse massspectra, width of the rapidity distribution and mean multiplicity – are presented anddiscussed. Furthermore, the dependence of the ratio of the mean number of producedpions to the mean number of wounded nucleons on the collision energy was derived.The results are compared to predictions of several models. © 2021 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 : . [ h e p - e x ] J a n he NA61/SHINE Collaboration A. Acharya , H. Adhikary , 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 , B. Kozłowski , 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 ,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 , , K. Wójcik ,O. Wyszyński , A. Zaitsev , 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 the NA61/SHINE experiment on spectra and mean multi-plicities of π − mesons produced in central Ar+ Sc collisions at beam momenta of 13 A , 19 A ,30 A , 40 A , 75 A and 150 A GeV /c . These studies form part of the strong interactions program ofNA61/SHINE [1, 2] investigating the properties of the onset of deconfinement and searching forthe possible existence of a critical point in the phase diagram of strongly interacting matter. Theprogram is mainly 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 [3, 4], namely a sharppeak in the Kaon to pion ratio ("horn"), the start of a plateau in the inverse slope parameterfor Kaons ("step"), and a steepening of the increase of pion production per wounded nucleonwith increasing collision energy ("kink"). These findings were predicted as signals of the onset ofdeconfinement [5]. They were recently confirmed by the RHIC beam energy program [6] and theinterpretation is supported by the LHC results (see Ref. [7] and references therein).The goals of the NA61/SHINE strong interaction program are pursued experimentally by a twodimensional scan in collision energy and nuclear mass number of colliding nuclei. This allows toexplore systematically the phase diagram of strongly interacting matter [2]. 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 program 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 2022 [11]. Results on π − spectra and multiplicities have already been publishedfrom p + p interactions [12, 13] and Be+ Be collisions [14, 15]. The latter provide the basicreference of a light isospin zero system for the study of dense matter effects in collisions of heaviernuclei.In 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 reliably subtracted.The paper is organized as follows: after this introduction the experiment is briefly described inSec. 2. The analysis procedure is discussed in Sec. 3. Section 4 presents the results of the analysis.In Sec. 5 the new measurements are compared to model calculations. The relevance of the newresults for the study of the onset of deconfinement is discussed in Sec. 6. A summary and outlookin Sec. 7 closes the paper. 3he following variables and definitions are used in this paper. The particle rapidity y is calculatedin the nucleon-nucleon collision center of mass system (cms), y = 0 . E + cp L ) / ( E − cp L )],where E and p L are the particle energy and longitudinal momentum, respectively. The transversecomponent of the 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 in GeV. The momentum in the laboratoryframe is denoted p lab and the collision energy per nucleon pair in the center of mass by √ s NN .The Ar+Sc collisions are selected by requiring a low value of the forward energy - the energyemitted into the region populated by projectile spectators. These collisions are referred to as central collisions and a selection of collisions based on the forward energy is called a centrality selection. Although for Ar+Sc collisions the forward energy is not tightly correlated with theimpact parameter of the collision, the terms central and centrality are adopted following theconvention widely used in heavy-ion physics. 4 NA61/SHINE detector ~13 m ToF-LToF-R PSDMTPC-RMTPC-LVTPC-2VTPC-1 Vertex magnetsTargetBeam S5
S2S1BPD-1 BPD-2 BPD-3V1 zxy
Figure 1: The schematic layout of the NA61/SHINE experiment at the CERN SPS [1] showing thecomponents used for the Ar+Sc energy scan (horizontal cut, not to scale). The trigger detector configurationupstream of the target is shown in the inset. Alignment of the chosen coordinate system is shown on theplot; its origin lies in the middle of VTPC-2, on the beam axis. The nominal beam direction is alongthe z -axis. The magnetic field bends charged particle trajectories in the x – z (horizontal) plane. The driftdirection in the TPCs is along the (vertical) y -axis. The NA61/SHINE detector (see Fig. 1) is a large-acceptance hadron spectrometer situated inthe North Area H2 beam-line of the CERN SPS [1]. The main components of the detectionsystem used in the analysis are four large volume Time Projection Chambers (TPC). Two ofthem, called Vertex TPCs (VTPC), are located downstream of the target inside superconductingmagnets with maximum combined bending power of 9 Tm. The magnetic field was scaled downin proportion to the beam momentum in order to obtain similar phase space acceptance at allenergies. The main TPCs (MTPC) and two walls of pixel Time-of-Flight (ToF-L/R) detectorsare placed symmetrically on either side of the beamline downstream of the magnets. The TPCsare filled with Ar:CO gas mixtures in proportions 90:10 for the VTPCs and 95:5 for the MTPCs.The Projectile Spectator Detector (PSD) is positioned 20.5 m (16.7 m) downstream of theMTPCs at beam momenta of 75 A and 150 A GeV /c (13 A , 19 A , 30 A , 40 A GeV /c ), centered in thetransverse plane on the deflected position of the beam. Moreover a brass cylinder of 10 cm (30 A –150 A GeV /c ) or 5 cm (19 A GeV/c) length and 5 cm diameter (degrader) was placed in front ofthe center of the PSD in order to reduce electronic saturation effects and shower leakage from thedownstream side.Primary beams of fully ionized Ar nuclei were extracted from the SPS accelerator at beammomenta of 13 A , 19 A , 30 A , 40 A , 75 A and 150 A GeV /c . Two scintillation counters, S1 and S2,provide beam definition, together with a veto counter V1 with a 1 cm diameter hole, which definesthe beam before the target. The S1 counter provides also the timing reference (start time for5ll counters). Beam particles are selected by the trigger system requiring the coincidence T1 =S1 ∧ S2 ∧ V1. Individual beam particle trajectories are precisely measured by the three beamposition detectors (BPDs) placed upstream of the target [1]. Collimators in the beam line wereadjusted to obtain beam rates of ≈ /s during the ≈
10 s spill and a cycle time of 32.4 s.The target was a stack of 2.5 x 2.5 cm area and 1 mm thick Sc plates of 6 mm total thicknessplaced ≈
80 cm upstream of VTPC-1. Impurities due to other isotopes and elements weremeasured to be 0.3 %. Their influence on the pion multiplicity was estimated to be an increaseby less than 0.2 % caused by the admixture of heavier elements [16]. No correction was appliedfor this negligible contamination. Data were taken with target inserted (denoted I) and targetremoved (denoted R).Interactions in the target are selected with the trigger system by requiring an incoming Ar ionand a signal below that of beam ions from S5, a small 2 cm diameter scintillation counter placedon the beam trajectory behind the MTPCs. This minimum bias trigger is based on the breakup ofthe beam ion due to interactions in and downstream of the target. In addition, central collisionswere selected by requiring an energy signal below a set threshold from the 16 central modules ofthe PSD which measure mainly the energy carried by projectile spectators. The cut was set toretain only the events with the ≈
30% smallest energies in the PSD. The event trigger conditionthus was T2 = T1 ∧ S5 ∧ PSD. The statistics of recorded events are summarized in Table 1.
Table 1: Basic beam properties and number of events recorded and used in the analysis of Ar+ Scinteractions at incident momenta of 13 A , 19 A , 30 A , 40 A , 75 A and 150 A GeV /c . p beam (GeV /c ) √ s NN (GeV) Recordedeventtriggers Number ofselectedevents Fraction ofbackground eventsafter selection cuts13 5.1 3 . · . · −
19 6.1 3 . · . · −
30 7.6 4 . · . · −
40 8.8 8 . · . · −
75 11.9 4 . · . · −
150 16.8 0 . · . · − Analysis procedure
This section starts with a brief overview of the data analysis procedure and the applied corrections.It also defines to which class of particles the final results correspond. A description of thecalibration and 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 its parameters,(v) calculation of statistical and systematic uncertainties.Corrections for the following biases were evaluated and applied when significant:(i) contribution from off-target interactions,(ii) procedure of selecting central collisions,(iii) geometrical acceptance,(iv) contribution of particles other than primary (see below) negatively charged pions producedin Ar+Sc interactions,(v) losses of produced negatively charged pions due to their decays and secondary interactions.Correction (i) was found to be negligible and was therefore not applied. Corrections (ii)-(v) areestimated by simulations. Events were generated with the
Epos1.99 model (version CRMC1.5.3) [17, 18, 19], passed through detector simulation employing the
Geant3 package [20]and then reconstructed by the standard NA61/SHINE program chain. Event selection in thesimulation was based on the number of projectile spectator nucleons which is available from the
Epos1.99 model.The final results refer to π − produced in central Ar+Sc interactions by strong interaction processesand in electromagnetic decays of produced hadrons. Such hadrons are referred to as primary hadrons. The definition of central collisions is given in Sec. 3.1.
Central collisions
A short description of the procedure defining central collisions is given below. For more detailssee Ref. [21].Final results presented in this paper refer to the 5% of Ar+Sc collisions with the lowest value ofthe forward energy E F ( central collisions). The quantity E F is defined as the total energy in thelaboratory system of all particles produced in Ar+Sc collisions via strong and electromagneticprocesses in the forward momentum region defined by the acceptance map in Ref. [22]. Final resultson central collisions, derived using this procedure, allow a precise comparison with predictions ofmodels without any additional information about the NA61/SHINE setup and used magnetic7eld. Using this definition the mean number of wounded nucleons h W i was calculated within theWounded Nucleon Model (WNM) [23] as implemented in Epos .
29 30 31 3244 17 18 19 20 3343 28 1 2 3 45 6 7 8 21 3442 27 9 10 11 1213 14 15 16 22 3541 26 25 24 23 3640 39 38 37
T2 trigger
29 30 31 3244 17 18 19 20 3343 28 1 2 3 45 6 7 8 21 3442 27 9 10 11 1213 14 15 16 22 3541 26 25 24 23 3640 39 38 37 A GeV /c
29 30 31 3244 17 18 19 20 3343 28 1 2 3 45 6 7 8 21 3442 27 9 10 11 1213 14 15 16 22 3541 26 25 24 23 3640 39 38 37 A , 40 A , 30 A GeV /c
29 30 31 3244 17 18 19 20 3343 28 1 2 3 45 6 7 8 21 3442 27 9 10 11 1213 14 15 16 22 3541 26 25 24 23 3640 39 38 37 A , 13 A GeV /c Figure 2: Schematic diagrams indicating by shading the PSD modules used in the online and offlineevent selection. The trigger is derived from the energy in the central 16 modules (1-16) in blue color.Determination of the PSD energy E PSD uses the green (150 A GeV /c ), orange (75 A , 40 A , 30 A GeV /c ) or allmodules (19 A , 13 A GeV /c ) at the respective beam momenta. For analysis of the data the event selection was based on the ≈
5% of collisions with the lowestvalue of the energy E PSD measured by a subset of PSD modules (see Fig. 2) in order to optimizethe sensitivity to projectile spectators. The acceptance resulting from the definition of the forwardenergy E F corresponds closely to the acceptance of this subset of PSD modules.Online event selection by the hardware trigger (T2) used a threshold on the sum of electronicsignals from the 16 central modules of the PSD set to accept ≈
30% of the inelastic interactions.Measured distributions of E PSD for minimum-bias and T2 trigger selected events, calculated in theoffline analysis, are shown in Fig. 3 at beam momenta of 19 A GeV /c and 150 A GeV /c , respectively.The accepted region corresponding to the 5% most central collisions is indicated by shading. Theminimum-bias distribution was obtained using the data from the beam trigger T1 with offlineselection of events by requiring an event vertex in the target region. A properly normalizedspectrum for target removed events was subtracted.The forward energy E F cannot be measured directly. However, both E F and E PSD can beobtained from simulations using the
Epos1.99 (version CRMC 1.5.3) [17, 18, 19] model. Aglobal factor c cent (listed in Table 2) was then calculated as the ratio of mean negatively chargedpion multiplicities obtained with the two selection procedures in the 5% most central events.8
200 400 600 800 E PSD (GeV) a r b i t r a r y un i t s A GeV/ c E PSD (GeV) a r b i t r a r y un i t s A GeV/ c T1 trigger T2 trigger (scaled) (cid:103)
5% centrality Normalization region
Figure 3: Event centrality selection using the energy E PSD measured by the PSD calorimeter. Distributionsare shown of measured E PSD for minimum-bias selected (blue histograms) and T2 selected (red histograms)events for 19 A (left plot) and 150 A GeV /c (right plot) beam momenta. Histograms are normalized to agreein the overlap region (from the beginning of the distribution to the black dashed line). The T2 trigger wasset to accept ≈
30% of the inelastic cross section. The accepted region corresponding to the 5% collisionswith the smallest E PSD is indicated by shading.
The resulting factors c cent range from 1.002 to 1.005 and correspond to only a small correctioncompared to the systematic uncertainties of the measured particle multiplicities. A possibledependence of the scaling factor on rapidity and transverse momentum was neglected. Thecorrections ( c cent ) are negligibly small compared to the systematic uncertainties of the measuredparticle multiplicities and are therefore not applied in the calculation of π − yields and neglectedin the quoted systematic uncertainties.Finally, events generated with the Epos code with its implementation of the Wounded NucleonModel [19] were used to estimate the average number of wounded nucleons h W i for the 5% ofevents with the smallest number of spectator nucleons and with the smallest value of E F . Forthe latter selection the average impact parameter h b i was obtained as well. Results are listed inTable 2. Example distributions of events in the W − E F plane for 19 A and 150 A GeV /c beammomenta are shown in Fig. 4. These distributions are quite broad and emphasize the importanceof proper simulation of the centrality selection when comparing model calculations with theexperimental results. For comparison h W i was also calculated from the GLISSANDO modelwhich uses a different implementation of the Wounded Nucleon Model [24]. The resulting pionmultiplicities, also listed in Table 2, differ by about 5%. This uncertainty is not shown in theplots of the results. 9
200 400 600 800 E F (GeV) W A GeV/ c E F (GeV) W A GeV/ c Figure 4: Distributions of W versus E F for all inelastic collisions at 19 A ( left ) and 150 A GeV /c ( right )beam momenta calculated from the Epos1.99 model. The vertical red lines show the value of the cut on E F for selecting the 5% most central collisions.Table 2: Average number of wounded nucleons h W i in the 5% most central Ar+Sc collisions estimatedfrom simulations using the
Epos [17, 18, 19] and GLISSANDO [24] models. In the
Epos
WNM case theaverage impact parameter h b i is presented as well. The values of σ denote the widths of the distributions of W and b . Results from Epos
WNM and Glissando are for centrality selection using the smallest number ofspectators, whereas the
Epos E F results are obtained using the forward energy E F within the acceptancemap in Ref. [22]. The last line presents numerical values of the c cent factor. Momentum ( A GeV /c ) 13 19 30 40 75 150 Epos
WNM h W i . . . . . . σ . . . . . . h W i . . . . . . σ . . . . . . Epos E F h W i . . . . . . σ . . . . . . h b i .
82 1 .
95 2 .
00 2 .
09 2 .
23 2 . σ .
79 0 .
84 0 .
86 0 .
89 0 .
94 0 . c cent .
005 1 .
005 1 .
002 1 .
003 1 .
005 1 . .2 Event and track selection Central Ar+Sc events were selected using the following criteria:(i) no offtime 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-2and in both planes of BPD-3,(iii) a well reconstructed interaction vertex with z position (fitted using the beam trajectory andTPC tracks) not farther away than 10 cm from the center of the Sc target (see Fig. 5),(iv) an upper cut on the energy E PSD in order to select the 5 % collisions with the lowest E PSD . -650 -600 -550 -500 z fitted vertex (cm) e v e n t s A GeV/ c Target inserted (cid:103)
Target removed × . Figure 5: Distribution of fitted vertex z coordinate for T1 triggered events of Ar+Sc interactions at150 A GeV /c with target inserted and target removed (shaded histogram). The distribution for the datarecorded with the Sc target removed was divided by a factor of N I /N R , where N I and N R are the numbersof events with Sc target inserted and removed, respectively. Vertical dashed lines show the acceptanceregion. · − and was therefore neglected.The event statistics after applying the selection criteria are summarized in Table 1. In order to select tracks of primary charged hadrons and to reduce the contamination of tracksfrom secondary interactions and weak decays, the following track selection criteria were applied:(i) track momentum fit at the interaction vertex should have converged,(ii) fitted x component of track momentum is negative. This selection minimizes the anglebetween the track trajectory and the TPC pad direction for the chosen magnetic fielddirection, reducing uncertainties of the reconstructed cluster position, energy depositionand track parameters,(iii) total number of reconstructed points on the track should be greater than 30,(iv) sum of the number of reconstructed points in VTPC-1 and VTPC-2 should be greaterthan 15,(v) the distance between the track extrapolated to the interaction plane and the interactionpoint (impact parameter) should be smaller than 4 cm in the horizontal (bending) planeand 2 cm in the vertical (drift) plane,(vi) electron tracks were excluded by a cut on the particle energy loss d E /dx in the TPCs (seeFig. 6).The analysis was performed in ( y, p T ) and ( y, m T − m π ) 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. Uncorrected yields of negatively charged hadrons per event after all event and track cuts n [ h − ] raw divided by bin dimensions are shown in Fig. 7. In order to determine the mean multiplicityof primary π − mesons produced in central Ar+Sc collisions a set of corrections was appliedto the extracted raw yields. The main biasing effects are detector acceptance, loss of eventsdue to the cut on reconstructed vertex position, track selection cuts, reconstruction efficiency,contributions of particles from weak decays (feed-down), and contribution of primary hadronsother than negatively charged pions (mostly K − mesons). Contamination from events occurringoutside the target was negligible.A simulation of the NA61/SHINE detector is used to correct the data for acceptance, reconstructionefficiency, feed-down and contamination from re-interactions of produced particles. Only Ar+Sc12 log [ p/ (1 GeV/ c )] d E / d x -1 0 1 2 3 log [ p/ (1 GeV/ c )] d E / d x e − π − Figure 6: 2D histograms of specific energy loss d E /dx versus momentum in Ar+Sc interactions at 150 A GeV /c before ( left ) and after ( right ) electron exclusion. The Bethe-Bloch functions for electrons and negativelycharged pions are plotted by dashed and solid lines, respectively. interactions in the target material were simulated and reconstructed. The Epos model [17, 18, 19]was selected to generate the primary interactions. 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 standard NA61/SHINE reconstruction chain and reconstructed tracks were matched tothe simulated particles based on the cluster positions. Hadrons which were not produced in theprimary interaction can amount to a significant fraction of the selected track sample. Thus acareful effort was undertaken to evaluate and subtract this contribution.Since
Epos provides only an approximate description of the measurements of particle productionin Ar+Sc collisions, a data-based effort was made to improve the estimate of contamination from π − wrongly accepted as coming from the primary interaction. Yields of misidentified Kaonswere estimated from preliminary results of NA61/SHINE (see Ref. [25]) on K − production andthe contribution of π − from decays of hyperons was estimated from published results of otherexperiments (see Ref. [26]). The relative effect of such tuning of the yields of negatively chargedhadrons was below 5% for majority of the bins and did not exceed 7% for all the beam momenta.Backward rapidity bins with relative statistical uncertainties exceeding 20% in case of the higherbeam momenta (150 A and 75 A GeV /c ) and 30% in case of the lower beam momenta (40 A , 30 A ,19 A and 13 A GeV /c ) were not used since they suffer from limited backward rapidity acceptance ofthe detector.The correction factor c yp T , based on the event and detector simulation was calculated for each y and p T bin as: c yp T = n [ π − ] MCgen / n [ h − ] MCsel , (1)13 y p T ( G e V / c ) n [ h − ] d a t a (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) n [ h − ] d a t a (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) n [ h − ] d a t a (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) n [ h − ] d a t a (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) n [ h − ] d a t a (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) n [ h − ] d a t a (cid:2) ( G e V / c ) − (cid:3) A GeV/ c Figure 7: Uncorrected double-differential spectra n [ h − ] raw / ∆ y/ ∆ p T of negatively charged hadrons producedin the 5% Ar+Sc collisions with the smallest E P SD energy at beam momenta of 13 A , 19 A , 30 A , 40 A , 75 A and 150 A GeV /c . 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 centrality selected Ar+Sc collisions generated by the
Epos model.The corrected multiplicities were then calculated as: n [ π − ] corr = c yp T · n [ h − ] raw . (2)Double differential distributions d n d y d p T of per event multiplicities are then given by:d n d y d p T = 1∆ y · ∆ p T n [ π − ] corr , (3)where n [ π − ] corr are the corrected per event multiplicities for π − in the ( y , p T ) bins with size ∆ y and ∆ p T . The distributions d n d y d m T were calculated with an analogous formula. Statistical uncertainties of the yields receive contributions from the finite statistics of both thedata and the correction factors derived from the simulations. The contribution from the statisticaluncertainty of the data is much larger than that from the correction factors c yp T which wastherefore neglected. The statistical uncertainty of the data was calculated assuming a Poissonprobability distribution for the number of entries in each y , p T bin. Systematic uncertainties presented in this paper were calculated taking into account contributionsfrom the following effects:(i) Possible biases which were not corrected for. These are:a) a possible bias due to the d E/ d x cut applied to reject electron tracks,b) a possible bias due to the removal of events with off-time beam particles close in timeto the trigger particle.Their magnitude was estimated by varying the values of the corresponding cut. The values ofthe selected d E/ d x band around the Bethe-Bloch function was changed by ± .
01 d E/ d x units(where 1 corresponds to a minimum ionizing particle, and 0.04 is a typical width of thed E/ d x distribution for π − ), and the rejection time window was changed to ± µ s and ± µ s. The systematic uncertainty was estimated as half of the maximum absolute differencebetween h − multiplicities when varying the cut values.(ii) Uncertainty of the correction for the track selection cuts used for data and Monte Carlo dataselection were estimated by removing the impact parameter cut and varying the minimumnumber of required points by ±
3. The observed changes suggest the potential bias is around1%. 15iii) Uncertainty of the correction for contamination of the primary π − mesons by daughtersof decays and re-interactions. It was estimated from simulations using the Epos modelwhere the production rates of parents were adjusted to extrapolations of published data(see Ref. [26]). The systematic uncertainty was estimated as 15% of the correction value.(iv) Uncertainty of correction for the contamination of particles other than π − in negativelycharged hadrons h − spectrum. The value of the uncertainty was assumed as 15% of thesimulated contribution of K − , Σ − and p to the total number of negatively charged hadrons.Values of σ sys are listed in the table 4. The total systematic uncertainty was calculated by addingin quadrature the individual contributions. Note that systematic biases in different bins arecorrelated, whereas statistical fluctuations are independent.Statistical and systematic uncertainties for all six beam momenta are shown as a function ofrapidity y in Fig. 8. This section presents results on negatively charged pion spectra at 13 A , 19 A , 30 A , 40 A , 75 A and150 A GeV /c beam momentum in the 5% most central Ar+ Sc collisions with statistical andsystematic uncertainties. The spectra refer to pions produced by strong interaction processesand in electromagnetic decays of produced hadrons. Comparisons of the new measurements ofspectra, their parameters and mean multiplicities of π − mesons in central Ar+Sc collisions withpredictions of the
Epos1.99 [17, 18, 19], U r qmd [27, 28] and Hijing [29] models are presented.In the model calculations connected with spectra the selection of the 5% most central collisionswas based on the number of projectile spectator nucleons. y , p T ) and ( y , m T − m π ) yields Figure 9 shows fully corrected double-differential ( y, p T ) distributions d n d y d p T of π − measured in central Ar+Sc collisions and illustrates the wide phase space acceptance of the detector. Thedistributions d n d y d m T were calculated using an analogous procedure. From these results spectra oftransverse momentum p T , transverse mass m T − m π , rapidity y , as well as total multiplicities h π − i were derived. Figure 10 shows measured transverse momentum p T spectra at mid-rapidity for all six beammomenta. The results are compared with Epos , U r qmd and Hijing model calculations. Thespectra differ significantly from the models’ predictions, especially for lower beam momenta, wherenone of the models can describe the data well. For higher beam momenta
Epos and U r qmd describe data with reasonable accuracy. 16 y − − R e l a t i v e σ ( % ) A GeV/ c y − R e l a t i v e σ ( % ) A GeV/ c y − − R e l a t i v e σ ( % ) A GeV/ c y − R e l a t i v e σ ( % ) A GeV/ c y − R e l a t i v e σ ( % ) A GeV/ c y − − R e l a t i v e σ ( % ) A GeV/ c (cid:103) σ stat σ sys σ i σ ii σ iii σ iv Figure 8: Statistical and systematic uncertainties for all six beam momenta as a function of rapidity y .Statistical uncertainties are shown by gray shaded area, systematic uncertainties by curves referring toelectron rejection and off-time events (i), track selection cuts (ii), contamination by decay daughters (iii),and contamination by primary mesons other than π − (iv), see text for details. y p T ( G e V / c ) d n d y d p T (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) d n d y d p T (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) d n d y d p T (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) d n d y d p T (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) d n d y d p T (cid:2) ( G e V / c ) − (cid:3) A GeV/ c -2 0 2 4 y p T ( G e V / c ) d n d y d p T (cid:2) ( G e V / c ) − (cid:3) A GeV/ c Figure 9: Corrected double-differential spectra d n d y d p T of negatively charged pions produced in the 5% most central Ar+Sc collisions at beam momenta of 13 A , 19 A , 30 A , 40 A , 75 A and 150 A GeV /c . .0 0.5 1.0 1.5 2.0 p T (GeV /c ) d n / d p T (cid:2) ( G e V / c ) − (cid:3) A GeV /c < y < p T (GeV /c ) d n / d p T (cid:2) ( G e V / c ) − (cid:3) A GeV /c < y < p T (GeV /c ) d n / d p T (cid:2) ( G e V / c ) − (cid:3) A GeV /c < y < p T (GeV /c ) d n / d p T (cid:2) ( G e V / c ) − (cid:3) A GeV /c < y < p T (GeV /c ) d n / d p T (cid:2) ( G e V / c ) − (cid:3) A GeV /c < y < p T (GeV /c ) d n / d p T (cid:2) ( G e V / c ) − (cid:3) A GeV /c < y < Epos [17, 18, 19] U r qmd [27, 28] Hijing [29]
Figure 10: Transverse momentum distributions d n/ d p T at mid-rapidity for all six beam momenta. Pre-dictions of Epos , U r qmd and Hijing models are shown by curves of different line styles. Statisticaluncertainties are smaller than the marker size and systematic uncertainties are indicated by shaded bands. .3 Transverse mass distributions Spectra of transverse mass m T − m π at mid-rapidity (0 < y < .
2) are shown in Fig. 11. Forfurther comparisons a function d n d m T = A · m T · exp (cid:18) − m T T (cid:19) (4)was fitted in the range 0 . < m T − m π < .
72 GeV where no strong contributions from resonancedecays and radial flow are expected. The fitted parameters were the normalization A and theinverse slope parameter T . The results of the fits are indicated by lines in Fig. 11. The deviationof the measurements from the exponential shape for larger values of m T − m π is indicative ofcollective transverse flow [9] whereas the excess below the fit range can be explained by thecontribution of resonance decay products to the π − spectrum. m T − m π (GeV) − − − − − − m T d n d y d m T ( G e V − ) (cid:103) A GeV /c (cid:110) A GeV /c × − (cid:39) A GeV /c × − (cid:53) A GeV /c × − (cid:111) A GeV /c × − (cid:97) A GeV /c × − Figure 11: Transverse mass spectra at mid-rapidity (0 < y < . . < m T − m π < .
72 GeV and dashed lines outside the fit range.The data points for different beam momenta were scaled for better readability. Statistical uncertainties aresmaller than the marker size. Systematic uncertainties are not plotted.
Figure 12 presents the dependence of the inverse slope parameter T on the rapidity for the differentbeam energies. One finds the well known decrease towards larger rapidities. Moreover, an increaseof the values of T by about 20 MeV is seen from 13 A to 150 A GeV /c beam momentum.Inverse slope parameters fitted at mid-rapidity (0 < y < .
2) in the range 0 . < m T − m π < .
72 GeV are plotted versus √ s NN for inelastic p + p , 5% most central Ar+Sc, central
Be+Be andcentral Pb+Pb collisions in Fig. 13 ( left ). As seen from the plot, the values increase significantly20 .0 0.2 0.4 0.6 0.8 1.0 y/y beam T ( M e V ) (cid:103) A GeV /c (cid:110) A GeV /c (cid:39) A GeV /c (cid:53) A GeV /c (cid:111) A GeV /c (cid:97) A GeV /c Figure 12: The inverse slope parameter T of the transverse mass spectra as a function of rapidity dividedby the beam rapidity. The fit range is 0 . < m T − m π < .
72 GeV. Statistical uncertainties are usuallysmaller than the marker size and systematic uncertainties are indicated by shaded bands. (10 - 15 MeV) for all three reactions. The new Ar+Sc results are close to those for Pb+Pbreactions but about 15 MeV higher than for p + p and Be+Be reactions. Furthermore, Fig. 13( right ) shows that Epos model predictions for Ar+Sc collisions are lower than the NA61/SHINEmeasurements and stay even below the measurements in inelastic p + p interactions. Predictionsof U r qmd exhibit a non-monotonic behavior. They lie lower than measurements at low beammomenta and higher at high beam momenta. Hijing shows a concave behavior and unsatisfactoryagreement with measurements.Figure 14 presents the inverse slope parameter T plotted versus the number of wounded nucleons h W i which are a measure of the initial volume of the collision system. Although the uncertaintiesare large, the measurements show a modest monotonic rise with increasing system size for all thebeam momenta.As the distributions are not strictly exponential it may be better to characterize them by theiraverage values h m T i − m π . These were calculated by summing the m T − m π -weighted distributionsand adding an extrapolation for the region m T − m π > . p + p and central Be+Be, Ar+Sc and central Pb+Pb reactions are compatible withintheir uncertainties. Ar+Sc, Be+Be and p + p measurements show a rise with increasing collisionenergy which is more pronounced for Ar+Sc. Due to the large uncertainties for the Pb+Pb dataa significant discrimination between rise and constancy is not possible for this reaction. Epos and21 √ s NN (GeV) T ( M e V ) √ s NN (GeV) T ( M e V ) (cid:111) Ar+Sc (cid:112)
Be+Be [14] (cid:97) p + p [12] (cid:103) Pb+Pb (NA49 [3, 4]) (cid:111)
Ar+ScAr+Sc (
Hijing [29])Ar+Sc ( U r qmd [27, 28])Ar+Sc ( Epos [17, 18, 19])
Figure 13:
Left: inverse slope parameter T at mid-rapidity (0 < y < .
2) fitted in the range 0 . 72 GeV plotted against the collision energy per nucleon together with measurements forinelastic p + p , central Be+Be and central Pb+Pb collisions. Statistical uncertainties are shown as verticalbars (often smaller than the marker size) and systematic uncertainties are indicated by shaded bands (orcaps for Pb+Pb collisions). Right: comparison of the results for Ar+Sc collisions as presented in the leftplot with Epos , U r qmd and Hijing model calculations (black curves). U r qmd model predictions show a slope that is more similar to p + p interactions and less steepthan for Ar+Sc with U r qmd covering two highest collision energies. Hijing shows a concavebehavior with extreme points matching the measurements.In order to compare the detailed features of the spectra, the ratios of the scaled differentialyields from p + p , Ar+Sc and Pb+Pb reactions to isospin symmetric Be+Be reference are plottedin Fig. 16. From the three panels of the figure one may conclude that compared to inelastic p + p collisions nucleus+nucleus interactions show a slightly concave behavior and a significantenhancement at small values of m T − m π . One clearly observes a hardening of the spectra at highvalues of m T − m π and an increased peak at low m T − m π for Ar+Sc and Pb+Pb collisions, mostlikely due to radial expansion flow and decays of strongly decaying resonance states, respectively.22 10 10 h W i T + a ( M e V ) (cid:103) A GeV /c , a = 120 MeV (cid:110) A GeV /c , a = 90 MeV (cid:39) A GeV /c , a = 60 MeV (cid:111) A GeV /c , a = 30 MeV (cid:97) A GeV /c , a = 0 MeV Figure 14: The inverse slope parameter T versus the mean number of wounded nucleons h W i in central Ar+Sc collisions at beam momenta from 19 A to 150 A GeV /c . Statistical uncertainties are smaller than themarker size. Systematic uncertainties are shown by shaded bands. For better visibility different energiesare offset vertically. √ s NN (GeV) h m T i − m π ( G e V ) √ s NN (GeV) h m T i − m π ( G e V ) (cid:111) Ar+Sc (cid:112) Be+Be [14] (cid:97) p + p [12] (cid:103) Pb+Pb (NA49 [3, 4]) (cid:111) Ar+ScAr+Sc ( Hijing [29])Ar+Sc ( U r qmd [27, 28])Ar+Sc ( Epos [17, 18, 19]) Figure 15: Left: average transverse mass h m T i − m π at mid-rapidity (0 < y < . 2) versus the collisionenergy. The results are compared with the corresponding data on inelastic p + p , central Be+Be andcentral Pb+Pb collisions. Statistical uncertainties are shown as vertical bars (occasionally smaller thanthe marker size and with caps for Pb+Pb) and systematic uncertainties are indicated by shaded bands. Right: comparison of the results for Ar+Sc collisions as presented in the left plot with Epos , U r qmd and Hijing model calculations (black curves). .0 0.2 0.4 0.6 0.8 1.0 m T − m π (GeV) ( A r + S c ) / ( B e + B e ) m T − m π (GeV) ( p + p ) / ( B e + B e ) m T − m π (GeV) ( P b + P b ) / ( B e + B e ) (cid:103) A GeV /c (cid:110) A GeV /c (cid:39) A GeV /c (cid:111) A GeV /c (cid:97) A GeV /c Figure 16: The ratio of transverse mass spectra of π − mesons at mid-rapidity: central Ar+Sc to cen-tral Be+Be, central Pb+Pb to central Be+Be and inelastic p + p to central Be+Be collisions. Statisticaluncertainties are shown as vertical bars and systematic uncertainties are indicated by shaded bands. Dataon Pb+Pb, p + p and Be+Be were taken from Refs. [3, 4], [12] and [14], respectively. .4 Rapidity distributions and mean multiplicities The NA61/SHINE experimental apparatus is characterized by large, but limited acceptance. Inorder to compute the rapidity distribution d n/ d y and mean multiplicity, one needs to extrapolatethe measured data to unmeasured regions.First, the p T distributions in each rapidity bin were extrapolated from the edge of acceptance to p T = 2 GeV /c , using the exponential form f ( p T ) = C · p T · exp − p ( cp T ) + m π T ! , (5)where C and T are fit parameters. To obtain d n/ d y , the measured p T data bins are summed andthe integral of the extrapolated curve is added:d n d y = p maxT X d p T d n d y d p T ! measured + Z p maxT f ( p T )d p T . (6)The results are shown by the solid data points in Fig. 17 together with Epos , U r qmd and Hijing model predictions. Figure 18 shows the results for all beam momenta combined into one plot.In a second step the rapidity spectra are extrapolated to the missing rapidity acceptance. Theevent trigger requires small energy emitted into the projectile spectator region but puts noconstraints on the target spectators. This together with the different number of nucleons in theAr and Sc nucleus might cause some forward-backward asymmetry of the rapidity distribution.Therefore, the sum of two symmetrically displaced Gaussians – related to projectile and targetcontributions – was fitted to the distributions: g ( y ) = A A rel σ √ π exp − ( y − y ) σ ! + A σ √ π exp − ( y + y ) σ ! , (7)where A and A rel are absolute and relative amplitudes, y is the displacement from center-of-massrapidity and σ is the common width. The fitted two Gaussians are plotted as dashed coloredcurves in Fig. 17. The figure shows that the asymmetry between the amplitudes of the twoGaussians increases with decreasing beam momentum from 0.97 to 0.84 between 150 A and19 A GeV /c beam momentum. This contrasts with the behavior observed for Be+Be collisions [14].At 13 A GeV /c there is no acceptance for y < σ d n/ d y differ by less than 5%from the widths approximated by a single Gaussian function.The total mean π − multiplicity was calculated using the formula: h π − i = Z y min − . g ( y )d y + y max X y min d y (cid:18) d n d y (cid:19) + Z . y max g ( y )d y, (8)where y min to y max is the interval of measurements for d n/ d y . The results are presented in Table 4.Statistical uncertainties σ stat ( h π − i ) were obtained by propagating the statistical uncertainties ofthe d n d y d p T spectra. 26 y d n / d y A GeV /c -4 -2 0 2 4 y d n / d y A GeV /c -4 -2 0 2 4 y d n / d y A GeV /c -4 -2 0 2 4 y d n / d y A GeV /c -4 -2 0 2 4 y d n / d y A GeV /c -4 -2 0 2 4 y d n / d y A GeV /c Epos [17, 18, 19] U r qmd [27, 28] Hijing [29] Figure 17: Rapidity distributions d n/ d y for all six beam momenta obtained by p T integration. Pointsincluded in the fit of the distribution are shown by full markers. The solid coloured curve is the result of afit to the data points using two Gaussians which are indicated by the dashed coloured curves. Predictionsof Epos , U r qmd and Hijing models are shown by black curves. All uncertainties are smaller than thesymbol size. able 3: Parameters A rel , y of the double Gaussian fit and r.m.s. width σ d n/ d y of the rapidity distributiontogether with their statistical and systematic uncertainties. Momentum ( A GeV /c ) 13 19 30 40 75 150 A rel σ stat ( A rel ) 0.0024 0.0110 0.0046 0.0038 0.0022 0.0052 σ sys ( A rel ) 0.2062 0.2275 0.1632 0.1284 0.1575 0.1988 y σ stat ( y ) 0.0293 0.0079 0.0038 0.0030 0.0014 0.0020 σ sys ( y ) 0.3402 0.2587 0.2415 0.2201 0.2737 0.3356 σ dn/dy σ stat ( σ d n/ d y ) 0.0156 0.0061 0.0033 0.0028 0.0016 0.0024 σ sys ( σ d n/ d y ) 0.0891 0.0824 0.0868 0.0944 0.1026 0.1350 -4 -2 0 2 4 y d n / d y (cid:103) A GeV /c (cid:110) A GeV /c (cid:39) A GeV /c (cid:53) A GeV /c (cid:111) A GeV /c (cid:97) A GeV /c Figure 18: Rapidity distributions d n/ d y for all six beam momenta. Measured points are shown by fullmarkers, values extrapolated by the fit function (see text) are plotted by open markers. All uncertaintiesare smaller than the symbol size.Table 4: Mean π − multiplicities in the 5% most central Ar+Sc collisions with statistical and systematicuncertainties. Momentum ( A GeV /c ) 13 19 30 40 75 150 h π − i σ stat ( h π − i ) 0.041 0.222 0.121 0.100 0.084 0.216 σ sys ( h π − i ) 7.3 4.6 5.3 5.7 6.7 12.8 y , proj , y , targ and σ , proj , σ , targ were fitted. The uncertainty of each fitting parameter and the mean π − multiplicitywas calculated as a standard deviation from the value calculated for the standard values of allparameters. The definition of σ d n/ d y was generalized to take into account that the width and theshift of the projectile and target Gaussians can be different and is given by the formula: σ d n/ d y = s(cid:18) y , proj + y , targ (cid:19) + (cid:18) σ , proj + σ , targ (cid:19) . Experimental data on the width σ d n/ d y of the rapidity distributions of π − mesons produced incentral nucleus-nucleus collisions and inelastic nucleon-nucleon interactions as function of thecollision energy are presented in Fig. 19. Since the p + p collision system is not isospin symmetricthe isospin average ( π − + π + ) / N + N ) collisions [30]. One observes that the width normalized to thebeam rapidity decreases slowly with increasing collision energy. When correcting the p + p datafor the isospin asymmetry one finds a monotonic decrease of σ d n/ d y with decreasing number ofnucleons in the colliding nuclei. One also observes that the measured values differ little withinthe SPS energy range. Epos , U r qmd and Hijing model predictions fit into the measurements’systematic uncertainties band. Figure 20 shows the width σ d n/ d y of the rapidity distributionsplotted versus the mean number of wounded nucleons h W i . The results seem to be independentof h W i from N + N to Pb+Pb collisions for all studied collision energies.29 10 15 √ s NN (GeV) σ d n / d y / y b e a m √ s NN (GeV) σ d n / d y / y b e a m (cid:111) Ar+Sc (cid:112) Be+Be [14] (cid:97) N + N [12, 13] (cid:103) Pb+Pb (NA49 [3, 4]) (cid:111) Ar+ScAr+Sc ( U r qmd [27, 28])Ar+Sc ( Hijing [29])Ar+Sc ( Epos [17, 18, 19]) Figure 19: Left: the width σ d n/ d y of the rapidity distributions of negatively charged pions to the beamrapidity y beam in inelastic N + N interactions and in central Ar+Sc, Be+Be and central Pb+Pb collisionsas a function of the center of mass energy √ s NN . Ar+Sc, N + N and Be+Be measurements are presentedwith statistical (vertical bars, often smaller than marker size) and systematic (shaded band) uncertainty,whereas Pb+Pb with statistical uncertainty only. Right: Comparison of the results for Ar+Sc collisions asshown in the left plot with Epos , U r qmd and Hijing model calculations (black curves). 10 10 h W i σ d n / d y + a (cid:103) A GeV /c , a = 0 . (cid:110) A GeV /c , a = 0 . (cid:39) A GeV /c , a = 0 . (cid:111) A GeV /c , a = 0 . (cid:97) A GeV /c , a = 0 . Figure 20: The widths σ d n/ d y of the rapidity distributions of negatively charged pions versus the meannumber of wounded nucleons h W i for beam momenta from 19 A to 150 A GeV /c . The data points fordifferent beam momenta were shifted for better readability. Ar+Sc, N + N and Be+Be measurements arepresented with statistical uncertainty as vertical bars (often smaller than marker size) and systematicuncertainty as a shaded band. For Pb+Pb statistical uncertainty only was published. .5 Mean multiplicities The mean multiplicity of π − mesons is plotted versus the center-of-mass energy in Fig. 21 for p + p and central Be+Be, Ar+Sc and central Pb+Pb collisions. As shown by the curves, thepredictions of the Epos and U r qmd models are within the uncertainties of the measurements. Hijing predictions are systematically higher than the measurements. √ s NN (GeV) h π − i √ s NN (GeV) h π − i (cid:111) Ar+Sc (cid:112) Be+Be [14] (cid:97) p + p [12] (cid:103) Pb+Pb (NA49 [3, 4]) (cid:111) Ar+ScAr+Sc ( Hijing [29])Ar+Sc ( Epos [17, 18, 19])Ar+Sc ( U r qmd [27, 28]) Figure 21: Left: The mean multiplicity of negatively charged pions in inelastic p + p interactions andin central Ar+Sc, Be+Be and central Pb+Pb collisions as a function of center of mass collision energy.Statistical uncertainties of the data points are smaller than the marker size. The systematic uncertaintiesare indicated by shaded bands. Right: Comparison of the results for Ar+Sc collisions as shown in the leftplot with Epos , U r qmd and Hijing model calculations (black curves). The Ar+Sc system is approximately isospin symmetric. The h π − i / h π + i ratio calculated within Epos1.99 was found to change from 0.954 to 0.984 between 13 A and 150 A GeV /c beam momentum.Based on these results one calculates mean multiplicity of π = π + + π − + π , h π i , as: h π i Ar+Sc = 1 . · ( h π − i + h π + i ) = 1 . · (1 + c isospin ) · h π − i , (9)where c isospin = h π − i / h π + i .Figure 22 shows the ratios of h π i over the mean number of wounded nucleons h W i plottedversus the collision system size. In general the measurements are close to the expectations of the For p + p interactions the figure shows isospin symmetrized values [12] h W i can be seen at higher beam momenta of 75 A and 150 A GeV /c in Ar+Sc and Pb+Pb reactions.Such an increase is not evident for lower beam momenta. h W i h π i / h W i + a (cid:103) A GeV /c , a = 4 (cid:110) A GeV /c , a = 3, (cid:39) A GeV /c , a = 2 (cid:111) A GeV /c , a = 1 (cid:97) A GeV /c , a = 0 Figure 22: Ratio of the mean pion multiplicity h π i over the mean number of wounded nucleons h W i plottedversus the collision system size for beam momenta from 19 A to 150 A GeV /c . The data points for differentbeam momenta were shifted for better readability. Statistical uncertainties are marked with vertical barsand are smaller than marker size. Systematic uncertainties are marked with shaded bands. The speed of sound in the dense matter produced in the collisions was predicted to show aminimum around the collision energy of the onset of deconfinement. This paper studies thisenergy dependence for central Ar+Sc collisions.The Landau hydrodynamical model of high energy collisions [31, 32] predicts rapidity distributionsof Gaussian shapes. In fact this prediction is approximately confirmed by the experimental data,see Ref. [33] and references therein. Moreover, the collision energy dependence of the width wasderived by Shuryak [34] from the same model under simplifying assumptions and reads: σ = 83 · c s − c s · ln √ s NN m p ! , (10)where c s denotes the speed of sound, and c s = 1 / c in the medium as a function of the measured width of therapidity distribution. The sound velocities extracted from the data on central Pb+Pb collisions,in combination with results from AGS and RHIC on central Au+Au collisions, cover a wide33 10 10 √ s N N (GeV) c s (cid:111) Ar+Sc (cid:112) Be+Be [14] (cid:97) N + N [12] (cid:103) Pb+Pb [3, 4] (cid:102) Au+Au [35, 36] Figure 23: The speed of sound as a function of beam energy as extracted from the data using Eq. 10.Statistical uncertainties are marked with a vertical bar (usually smaller than the bin size) and the systematicuncertainties as a shaded area. Only statistical uncertainties were available for Pb+Pb and for Au+Aumeasurements systematic uncertainties were negligible. energy range. Here, the sound velocity exhibits a clear minimum [37, 38] (usually called thesoftest point) at √ s NN ≈ 10 GeV consistent with the reported onset of deconfinement [3, 4]. Theenergy dependence of the sound velocities extracted from the new measurement are presentedin Fig. 23. The energy range covered by NA61/SHINE for results from central Ar+Sc, Be+Becollisions and inelastic N + N reactions is too limited to allow a significant conclusion about apossible minimum.Pions are the most copiously produced hadrons ( ≈ h π i , normalized to the number of wounded nucleons h W i [23] isexpected to be linear when plotted against the Fermi energy measure F = h ( √ s NN − m N ) / √ s NN i / , (11)where √ s NN is center-of-mass collision energy. The rate of increase depends on the number ofdegrees of freedom in the system, g , as g / . 34 F (GeV / ) h π i / h W i NA61/SHINE (cid:111) Ar+Sc (cid:112) Be+Be [14] (cid:97) N + N [12]NA49 (cid:103) Pb+Pb [3, 4]AGS (cid:102) Au+Au [35]WORLD (cid:100) N + N [3] Figure 24: 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 . Published results for inelastic nucleon-nucleon reactions andcentral nucleus-nucleus collisions are compared. The new NA61/SHINE results are presented in Fig.4. These, together with available measurementsfrom other experiments are presented in Fig. 24 . The uncertainty connected with the calculationof the number of wounded nucleons h W i was studied using different MC models. This indicated avariation of h π i / h W i of up to 6%. This source of uncertainty was not included in the systematicuncertainties plotted in Fig. 24. The world data on N + N and central Pb+Pb (Au+Au) collisionsestablished a well-known picture – the ”kink” plot. The results on N + N interactions increaselinearly with F , whereas the slope of the Pb+Pb results increase by about 30% in the low SPSbeam energy range (at ≈ A GeV). The suppression of pion yield in Pb+Pb collisions at lowcollision energies was attributed to pion absorption in the evolving fireball [41, 42]. The increaseof the ratio h π i / h W i can be related to activation of additional quark-gluon degrees of freedom.The NA61/SHINE results on N + N interactions agree well with the world data. The results onBe+Be collisions are mostly between measurements from N + N and Pb+Pb collisions. The newdata on Ar+Sc collisions seem to be systematically higher than the results for N + N , Be+Beand Pb+Pb collisions at the lower energies. They are close to the Pb+Pb results at the highest For p + p interactions the figure shows isospin symmetrized values denoted as N + N [12] h π i / h W i for Ar+Sc reactions equals that for inelastic N + N reactions at low SPSenergies whereas it is closer to that for Pb+Pb reactions at high SPS energies. Moreover, asuppression of the pion yield per wounded nucleon was observed in central Pb+Pb collisionscompared to inelastic N + N reactions at low energies which was attributed to pion absorption inthe evolving fireball [41, 42]. This effect is not found for the intermediate size Ar+Sc system inwhich a smaller less dense fireball is created. Spectra and mean multiplicities of π − produced in the 5% most central Ar+Sc collisions weremeasured by the NA61/SHINE experiment at the CERN SPS for beam momenta of 13 A , 19 A ,30 A , 40 A , 75 A and 150 A GeV /c using the h − method. The results represent the first measurementson pion production in an intermediate size collision system at SPS energies.Energy and system size dependence of parameters of measured distributions – mean transversemass, the inverse slope parameter of transverse mass spectra, width of the rapidity distributionand mean multiplicity – were presented and discussed.The inverse slope parameter of the transverse mass distribution increases with increasing systemsize and collision energy. Width of the rapidity distribution is independent of the system sizeand increases with collision energy. The mean multiplicity at high energies increases faster withthe system size than expected from the Wounded Nucleon Model. The rate of the increase withcollision energy is faster in Ar+Sc and Pb+Pb collisions than in N + N interactions. The newmeasurements were compared to predictions of Epos1.99 [17, 18, 19], U r qmd1.3.1 [27, 28] and Hijing [29] models. None of them provides a consistent description of the new NA61/SHINEmeasurements in Ar+Sc collisions.The new results on central Ar+Sc collisions were discussed in the context of the signatures of theonset of deconfinement. The velocity of sound extracted form the width of rapidity distributionis consistent with results for central Pb+Pb collisions as well as Be+Be and N+N interactions.Measurements in a broader energy range are needed to conclude on a possible minimum of thesound velocity in Ar+Sc collisions. The ratio of mean pion multiplicity to the number of woundednucleons and its collision energy dependence at the highest SPS energies are close to the onesfor central Pb+Pb collisions and higher than the corresponding results for N+N and Be+Beinteractions. This behavior suggests an increase of the effective number of degrees of freedomalready in central Ar+Sc collisions at the top SPS energies.36 Acknowledgments We would like to thank the CERN EP, BE, HSE and EN Departments for the strong support ofNA61/SHINE.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 and NN 202 23 1837), the National Science Centre Poland(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, DIR/WK/ 2016/2017/ 10-1, 2017/ 25/N/ ST2/ 02575, 2018/30/A/ST2/00226,2018/31/G/ST2/03910, 2019/32/T/ST2/00432), the Russian Science Foundation, grant 16-12-10176 and 17-72-20045, the Russian Academy of Science and the Russian Foundation for BasicResearch (grants 08-02-00018, 09-02-00664 and 12-02-91503-CERN), the Russian Foundationfor Basic Research (RFBR) funding within the research project no. 18-02-40086, the NationalResearch Nuclear University MEPhI in 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 theRussian Federation, Project "Fundamental properties of elementary particles and cosmology" No0723-2020-0041, the European Union’s Horizon 2020 research and innovation programme undergrant agreement No. 871072, the Ministry of Education, Culture, Sports, Science and Technology,Japan, Grant-in-Aid for Scientific Research (grants 18071005, 19034011, 19740162, 20740160and 20039012), the German Research Foundation (grant GA 1480/8-1), the Bulgarian NuclearRegulatory Agency and the Joint Institute for Nuclear Research, Dubna (bilateral contract No.4799-1-18/20), Bulgarian National Science Fund (grant DN08/11), Ministry of Education andScience of the Republic of Serbia (grant OI171002), Swiss Nationalfonds Foundation (grant 200020-117913/1), ETH Research Grant TH-01 07-3 and the Fermi National Accelerator Laboratory(Fermilab), a U.S. Department of Energy, Office of Science, HEP User Facility managed byFermi Research Alliance, LLC (FRA), acting under Contract No. DE-AC02-07CH11359 and theIN2P3-CNRS (France). 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