Centrality determination in MPD at NICA: Glauber model application - PowerPoint PPT Presentation

Centrality determination in MPD at NICA: Glauber model application Petr Parfenov 1,2 , Dim Idrisov 1 , Ilya Segal 1 , Vinh Luong 1 , Ilya Selyuzhenkov 1,3 , Arkadiy Taranenko 1 , Aleksandr Ivashkin 2 1 NRNU MEPhI, 2 INR RAS, 3 GSI for MPD Collaboration Workshop on analysis techniques for centrality determination and flow measurements at FAIR and NICA, 24-28 August 2020 This work is supported by: the RFBR according to the research project No. 18-02-40086 and No. 18-02-40065 the European Union‘s Horizon 2020 research and innovation program under grant agreement No. 871072

Outline ● Introduction ● Centrality framework implementation in MPD – Fitting procedure using MC Glauber – Comparison of the initial geometry parameters between colliding systems, energies and models (UrQMD, SMASH, PHSD and MC Glauber) ● Direct impact parameter reconstruction method ● Initial state of HIC: comparison of eccentricities ● Summary and outlook 2

Motivation Evolution of matter produced in heavy-ion collisions depend on its initial geometry Centrality procedure maps initial geometry parameters with measurable quantities This allows comparison of the future MPD results with the data from other experiments (RHIC BES, NA49/NA61 scans) and theoretical models ● Collision geometry: impact parameter, number of participating nucleons, number of binary NN collisions, etc. ● Measurable quantities: multiplicity of the produced charged particles, energy of the spectators 3

BES programs STAR BES-II program Beam energy √s NN (GeV) Run Time Species Number Events (GeV/nucleon) 9.8 19.6 4.5 weeks Au+Au 400M MB 7.3 14.5 5.5 weeks Au+Au 300M MB 5.75 11.5 5 weeks Au+Au 230M MB 4.6 9.1 4 weeks Au+Au 160M MB 31.2 7.7 (FXT) 2 days Au+Au 100M MB 19.5 6.2 (FXT) 2 days Au+Au 100M MB 13.5 5.2 (FXT) 2 days Au+Au 100M MB 9.8 4.5 (FXT) 2 days Au+Au 100M MB 7.3 3.9 (FXT) 2 days Au+Au 100M MB 5.75 3.5 (FXT) 2 days Au+Au 100M MB Many new experimental results at NICA energy range (√s NN =4-11 GeV) will be done during STAR (RHIC) and NA61/SHINE (SPS) BES 4 This will require comparison of the future MPD measurements with the RHIC/SPS

Centrality in STAR experiment Phys. Rev. C 86 (2012) 54908 Uncorrected charged particle ● multiplicity distribution in TPC (|η|<0.5) Comparison with ● MC Glauber simulations Fitted using ● two-component model: dN ch d η | = n pp [ ( 1 − x ) N part / 2 + xN coll ] η = 0 See talk by S. Esumi Similar centrality estimator is needed in MPD (NICA) for comparisons with experimental results from STAR (RHIC) 5

Centrality determination in MPD (NICA) Multiplicity of produced charged ● particles in Time Projection Chamber (TPC) |η|<1.5 ● Energy of the spectators deposited in Forward Hadron Calorimeter (FHCal) 2<|η|<5 6

Charged particle multiplicity in MPD Simulated data sets: ● UrQMD 3.4, SMASH 1.7, PHSD 4.0 – Au+Au, N ev =500k, √s NN =5, 7.7, 11.5 GeV – Bi+Bi, N ev =500k, √s NN =5, 7.7, 11.5 GeV ● Full realistic reconstruction of UrQMD generated events in MPDROOT framework with GEANT4 Hadron selection: ● |η|<0.5 ● p T >0.15 GeV/c 7

Integrating the CBM Centrality framework Evaluate N a : Call Evaluate χ 2 MC Glauber data NBD(μ,k) x N a N a = fN part +(1-f)N coll Build multiplicity fitting function Input multiplicity Minimize χ 2 to find distribution f, μ, k ● PHOBOS MC-Glauber v3.2: https://tglaubermc.hepforge.org/downloads/ ● This centrality framework was developed in CBM (tested on existed experimental data from NA49, NA61/SHINE and HADES experiments): Klochkov, Selyuzhenkov, EPJ Web Conf. 182 (2018) 02132 ● CBM centrality framework: git.cbm.gsi.de/pwg-c2f/analysis/centrality 8 ● Implemantation for MPD: https://github.com/IlyaSegal/NICA

MC Glauber fit: h ± multiplicity f=0.24, k=2, μ=0.71, χ 2 =1.24±0.06, M=(15,380) MC Glauber fit is in the good agreement with simulated input for the wide multiplicity range 9

b vs N ch & N ch centrality classes √s NN =5 GeV √s NN =7.7 GeV √s NN =11.5 GeV 30-40% 20-30% 10-20% 0-10% 30-40% 20-30% 10-20% 0-10% 30-40% 20-30% 10-20% 0-10% 10 Events in multiplicities M ± ΔM have impact parameter in range b ± σ b

b distribution in centrality classes √s NN =5 GeV √s NN =7.7 GeV √s NN =11.5 GeV 11

N part distribution in centrality classes √s NN =5 GeV √s NN =7.7 GeV √s NN =11.5 GeV 12

N coll distribution in centrality classes √s NN =5 GeV √s NN =7.7 GeV √s NN =11.5 GeV 13

<b> vs centrality: MC Glauber vs UrQMD Reasonable agreement between MC Glauber and UrQMD 14

b vs centrality: different models Centrality, % Centrality, % Similar behavior for different models 15

Centrality framework: Bi+Bi vs Au+Au UrQMD 3.4 UrQMD 3.4 UrQMD 3.4 Similar behavior between Au+Au and Bi+Bi 16

Gausian & gamma function mapping of multiplicity to impact parameter Phys.Rev. C97 (2018) no.1, 014905 Probability of N ch for fixed b : -Gaussian approach (Phys.Rev. C97 (2018) no.1, 014905): 2 2 ) −( N ch − N ch ) 1 σ ( c b ) exp ( P ( N ch | c b )= 2 σ ( c b ) -Approach using gamma distribution (Phys.Rev. C98 (2018) no.2, 024902): Phys.Rev. C98 (2018) no.2, 024902 − n 1 k ( c b )− 1 e P ( N ch | c b )= k N ch θ Γ( k ( c b )) θ where c b – centrality defined from impact parameter: b 2 c b = 1 P inel ( b' ) 2 π b' db' ≃ π b σ inel ∫ σ inel 0 17

Fit function Probability function for multiplicity distribution: UrQMD 3.4 1 P ( N ch )= ∫ P ( N ch | c b ) d c b 0 Parameters for Gaussian approach: 3 N ch ( c b ) i ) , σ ( c b )= σ ( 0 ) √ N ch ( c b )= N knee ⋅ exp ( − ∑ a i c b N ch ( 0 ) i = 1 Free parameters: N knee , σ ( 0 ) ,a i . Parameters for gamma-function approach: 4 k ( c b )= k max ⋅ exp ( − ∑ i ) , θ = const ( k ( c b ) θ ≡ N ch ( c b ) , √ k ( 0 ) θ ≡ σ ( 0 ) ) a i c b i = 1 Free parameters: k max , θ ,a i . Probability function fit reproduces N ch distribution from the model 18

Reconstruction of b Find probability of b for fixed N ch using Bayes’ theorem: ● UrQMD, Au+Au P ( N ch | c b ) 2 π b σ inel P inel ( b ) P ( b | N ch )= P ( N ch | b ) P ( b ) √s NN =7.7 GeV 2 π b σ inel P ( n ) P ( N ch | b ) , = = P ( n ) P ( n ) where P inel ( b )≃ 1 , σ inel = 685 fm 2 , c b ≃ π b 2 σ inel Experimental centrality: ∞ c ( N ch )= ∫ P ( N ' ch ) d N ' ch N ch Main steps to reconstruct b from N ch : Fit normalized multiplicity distribution with P(N ch ) – Define centrality c(N ch ) – Construct P( b |N ch ) using Bayes’ theorem using – parameters from the fit 19

b vs centrality: comparison with MC Glauber UrQMD, Au+Au, √s NN =7.7 GeV UrQMD, Au+Au, √s NN =11.5 GeV Reasonable agreement with MC Glauber 20

N part : MC Glauber vs. UrQMD 21 Larger differences for N part between MC Glauber and UrQMD at lower energies

Eccentricity ε n ● Eccentricity characterizes initial-state spatial anisotropy ● In MC Glauber, ε n defined as a ε part in the center‑of-mass system of the participant nuclei at passing time t pass (Phys.Rev. C81 (2010) 054905) : 2 sin ( n φ ) ⟩ 2 + ⟨ r 2 ε n = √ ⟨ r 2 cos ( n φ ) ⟩ 2 ⟩ ⟨ r ● ε 2 is system dependent ● ε 3 is system independent 22 MC-Glauber predicts weak energy dependence

Eccentricity comparison: Glauber vs. UrQMD 23 Large difference for ε 2 between MC Glauber and UrQMD at lower energies

Summary and next steps ● MC Glauber based procedure for centrality determination is established – UrQMD at two energies (√s NN =5, 7.7, 11.5 GeV) are under study – Fit reproduces charged particle multiplicity with chosen parameters ● Extracted relation between model parameters (b, N part , N coll ) and multiplicity centrality classes – Impact parameter from MC Glauber and UrQMD (SMASH, PHSD) in given centrality classes are in reasonable agreement for different models and colliding systems ● First comparison with the new method proposed by J. Ollitrault shows reasonable agreement with standard method based on MC Glauber – Comparison with the new improved method based on Gamma function is in progress ● Comparison of the ε n between MC Glauber and UrQMD shows notable difference 24

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Backup 26

Glauber Model configuration C. Loizides, J. Nagle and P. Steinberg, SoftwareX 1-2 (2015) 13-18 Used TGlauberMC-3.2 version from tglaubermc.hepforge.org Input to the model Output from the model ● TNtuple with model parameters: Inelastic NN cross section ● – Impact parameter b σ NN =29.3 mb for √s NN =5.0 GeV – – Number of participating in the σ NN =29.7 mb for √s NN =7.7 GeV collision nucleons N part – – Number of NN collisions N coll σ NN =31.2 mb for √s NN =11.5 GeV – – Participant eccentricity ε n Colliding nuclei ● – etc. “Au(197,79)”+”Au(197,79)” – In progress: comparison MC Glauber with GLISSANDO arXiv:1901.04484 [nucl-th] 27