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

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

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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

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Centrality determination in MPD at NICA: Glauber model application

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

Petr Parfenov1,2, Dim Idrisov1, Ilya Segal1, Vinh Luong1, Ilya Selyuzhenkov1,3, Arkadiy Taranenko1, Aleksandr Ivashkin2

1 NRNU MEPhI, 2 INR RAS, 3 GSI

for MPD Collaboration

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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
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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

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BES programs

Many new experimental results at NICA energy range (√sNN=4-11 GeV) will be done during STAR (RHIC) and NA61/SHINE (SPS) BES This will require comparison of the future MPD measurements with the RHIC/SPS

STAR BES-II program

Beam energy (GeV/nucleon) √sNN (GeV) Run Time Species Number Events 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

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Centrality in STAR experiment

  • Uncorrected charged particle

multiplicity distribution in TPC (|η|<0.5)

  • Comparison with

MC Glauber simulations

  • Fitted using

two-component model:

  • Phys. Rev. C 86 (2012) 54908

dN ch d η |

η=0

=n pp[(1−x)N part/2+xN coll]

Similar centrality estimator is needed in MPD (NICA) for comparisons with experimental results from STAR (RHIC) See talk by S. Esumi

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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

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Charged particle multiplicity in MPD

Simulated data sets:

  • UrQMD 3.4, SMASH 1.7, PHSD 4.0

– Au+Au, Nev=500k, √sNN=5, 7.7, 11.5 GeV – Bi+Bi, Nev=500k, √sNN=5, 7.7, 11.5 GeV

  • Full realistic reconstruction of UrQMD

generated events in MPDROOT framework with GEANT4 Hadron selection:

  • |η|<0.5
  • pT>0.15 GeV/c
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Integrating the CBM Centrality framework

Input multiplicity distribution MC Glauber data Evaluate Na: Na = fNpart+(1-f)Ncoll Evaluate χ2 Minimize χ2 to find 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
  • Implemantation for MPD: https://github.com/IlyaSegal/NICA

Call NBD(μ,k) x Na Build multiplicity fitting function

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MC Glauber fit: h± multiplicity

MC Glauber fit is in the good agreement with simulated input for the wide multiplicity range

f=0.24, k=2, μ=0.71, χ2=1.24±0.06, M=(15,380)

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√sNN=5 GeV 10-20% 0-10% 20-30% 30-40% √sNN=7.7 GeV 10-20% 0-10% 20-30% 30-40% √sNN=11.5 GeV 10-20% 0-10% 20-30% 30-40% Events in multiplicities M ± ΔM have impact parameter in range b ± σb

b vs Nch & Nch centrality classes

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√sNN=5 GeV √sNN=7.7 GeV

b distribution in centrality classes

√sNN=11.5 GeV

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√sNN=5 GeV √sNN=7.7 GeV

Npart distribution in centrality classes

√sNN=11.5 GeV

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√sNN=5 GeV √sNN=7.7 GeV

Ncoll distribution in centrality classes

√sNN=11.5 GeV

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<b> vs centrality: MC Glauber vs UrQMD

Reasonable agreement between MC Glauber and UrQMD

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b vs centrality: different models

Similar behavior for different models

Centrality, % Centrality, %

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Centrality framework: Bi+Bi vs Au+Au

Similar behavior between Au+Au and Bi+Bi UrQMD 3.4 UrQMD 3.4 UrQMD 3.4

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Gausian & gamma function mapping of multiplicity to impact parameter

Probability of N ch for fixed b:

  • Gaussian approach

(Phys.Rev. C97 (2018) no.1, 014905): P( Nch|cb)= 1 σ (cb) exp( −(Nch−N ch)

2

2σ(cb)

2 )

  • Approach using gamma distribution

(Phys.Rev. C98 (2018) no.2, 024902): P( Nch|cb)= 1 Γ(k(cb))θ

k Nch k (cb)−1e −n θ

where cb – centrality defined from impact parameter: cb= 1 σinel∫

b

Pinel(b')2π b' db'≃ πb

2

σinel

Phys.Rev. C97 (2018) no.1, 014905 Phys.Rev. C98 (2018) no.2, 024902

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Fit function

Probability function for multiplicity distribution: P(N ch)=∫

1

P( N ch|cb)d cb Parameters for Gaussian approach: N ch(cb)=N knee⋅exp(−∑

i=1 3

aicb

i), σ(cb)=σ (0)√

N ch(cb) Nch(0) Free parameters: N knee,σ (0),ai. Parameters for gamma-function approach: k(cb)=kmax⋅exp(−∑

i=1 4

aicb

i), θ=const (k(cb)θ≡Nch(cb), √k(0)θ≡σ (0))

Free parameters: k max,θ,ai. UrQMD 3.4 Probability function fit reproduces Nch distribution from the model

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Reconstruction of b

  • Find probability of b for fixed Nch using Bayes’ theorem:

P(b|Nch)= P(N ch|b)P(b) P(n) = P(N ch|cb) 2π b σinel Pinel(b) P(n) = 2 π b σinel P(n) P( Nch|b), where Pinel(b)≃1, σinel=685fm2, cb≃ π b2 σinel Experimental centrality: c(Nch)=∫

N ch ∞

P(N 'ch)d N ' ch

Main steps to reconstruct b from Nch:

–

Fit normalized multiplicity distribution with P(Nch)

–

Define centrality c(Nch)

–

Construct P(b|Nch) using Bayes’ theorem using parameters from the fit

UrQMD, Au+Au √sNN=7.7 GeV

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b vs centrality: comparison with MC Glauber

Reasonable agreement with MC Glauber

UrQMD, Au+Au, √sNN=7.7 GeV UrQMD, Au+Au, √sNN=11.5 GeV

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Npart: MC Glauber vs. UrQMD

Larger differences for Npart between MC Glauber and UrQMD at lower energies

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Eccentricity εn

  • Eccentricity characterizes initial-state spatial

anisotropy

  • In MC Glauber, εn defined as a εpart in the

center‑of-mass system of the participant nuclei at passing time tpass (Phys.Rev. C81 (2010) 054905):

  • ε2 is system dependent
  • ε3 is system independent

εn=√⟨r

2cos(nφ)⟩ 2+⟨r 2 sin(nφ)⟩ 2

⟨r

2⟩

MC-Glauber predicts weak energy dependence

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Eccentricity comparison: Glauber vs. UrQMD

Large difference for ε2 between MC Glauber and UrQMD at lower energies

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Summary and next steps

  • MC Glauber based procedure for centrality determination is established

– UrQMD at two energies (√sNN=5, 7.7, 11.5 GeV) are under study – Fit reproduces charged particle multiplicity with chosen parameters

  • Extracted relation between model parameters (b, Npart, Ncoll) 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 εn between MC Glauber and UrQMD shows notable difference
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Thank you for your attention!

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Backup

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Glauber Model configuration

Input to the model

  • Inelastic NN cross section

–

σNN=29.3 mb for √sNN=5.0 GeV

–

σNN=29.7 mb for √sNN=7.7 GeV

–

σNN=31.2 mb for √sNN=11.5 GeV

  • Colliding nuclei

–

“Au(197,79)”+”Au(197,79)”

  • C. Loizides, J. Nagle and P. Steinberg, SoftwareX 1-2 (2015) 13-18

Used TGlauberMC-3.2 version from tglaubermc.hepforge.org

Output from the model

  • TNtuple with model parameters:

– Impact parameter b – Number of participating in the

collision nucleons Npart

– Number of NN collisions Ncoll – Participant eccentricity εn – etc.

In progress: comparison MC Glauber with GLISSANDO arXiv:1901.04484 [nucl-th]

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Centrality framework configuration

NBD Equation: Pμ , k(n)= Γ(n+k) Γ(n+1)Γ(k)⋅( μ k)

n

(

μ k+1)

n+k

Fitting region: N ch={ (10−235), √sNN=5.GeV (20−310), √sNN=7.7 GeV (15−380), √sNN=11.5GeV Normalization of the total number of events: N ev

reco

N ev

MC Glauber = 1

10 Parameter range: f =(0−1), f step=0.01 k=(0−50), k step=1 Fitting function for charged particle multiplicity: N ch(f ,μ,k)=Pμ,k(n)⋅

[f N part+(1−f )N coll]

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Fit parameters f,k vs χ2

f=0.24, k=2, μ=0.71, χ2=1.24±0.06, M=(15,380) f=0, k=14, μ=0.31, χ2=1.46±0.12, M=(20,310) f=0, k=8, μ=0.23, χ2=2.04±0.10, M=(10,235)

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MC Glauber fit: h± multiplicity

MC Glauber fit is in the good agreement with simulated input for the large multiplicity region

f=0, k=14, μ=0.31, χ2=1.46±0.12, M=(20,310)

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<b> vs centrality: Glauber vs SMASH

Reasonable agreement between MC Glauber and SMASH

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<b> vs centrality: Glauber vs PHSD

Reasonable agreement between MC Glauber and PHSD

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Comparison of the UrQMD, PHSD, SMASH and MC Glauber parameters

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Generated vs reconstructed UrQMD

Reasonable agreement between reconstructed data and pure model

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b vs centrality: MC Glauber vs UrQMD

Reasonable agreement between MC Glauber and UrQMD

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b vs centrality: Glauber vs PHSD

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b vs centrality: all models

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Reconstructing the impact parameter of nucleus-nucleus collisions

based on the work of R. Rogly and G. Giacalone

Phys.Rev. C97 (2018) no.1, 014905 Phys.Rev. C98 (2018) no.2, 024902

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Gaussian approach: b distribution

New method √sNN=7.7 GeV New method √sNN=11.5 GeV

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b vs centrality: method comparison

Reasonable agreement between two methods √sNN=7.7 GeV √sNN=11.5 GeV

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Gaussian approach: fitting procedure

Fit reproduces charge particle multiplicity from pure UrQMD

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Γ-function approach: fitting procedure

Fit reproduces charge particle multiplicity from reco UrQMD √sNN=7.7 GeV √sNN=11.5 GeV

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Γ-function approach: b distribution

Comparison with method based on MC Glauber is in progress √sNN=7.7 GeV √sNN=11.5 GeV b, fm b, fm

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Eccentricity comparison

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Eccentricity comparison

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Eccentricity comparison

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Eccentricity comparison

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Eccentricity comparison

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Eccentricity comparison

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Eccentricity comparison

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Energy comparison: ε2

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Energy comparison: ε3

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Energy comparison: ε2

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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Energy comparison: ε3

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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Eccentricity comparison

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Eccentricity comparison

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Eccentricity comparison

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Npart comparison

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Energy comparison: ε2

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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Energy comparison: ε3

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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MC-Glauber

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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MC-Glauber

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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MC-Glauber

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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UrQMD

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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UrQMD

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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UrQMD

Ratio: ecc(√sNN)/ecc(4.5 GeV)

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System comparison: MC-Glauber

Small difference between Au+Au and Bi+Bi

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System comparison: UrQMD

Small difference between Au+Au and Bi+Bi