Bedanga Mohanty NISER With STAR Collaborators and S Samanta Outline Chemical Freezeout Dynamics RHICBES VDWHRG model and Criticality VDWHRG Model and Fluctuations data 0128 Chemical Freezeout at RHIC BES ID: 1029236
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1. Hadron Resonance Gas Model : Freeze-out, Criticality and FluctuationsBedanga MohantyNISER(With STAR Collaborators and S. Samanta)OutlineChemical Freeze-out Dynamics – RHIC-BESVDWHRG model and CriticalityVDWHRG Model and Fluctuations data01/28
2. Chemical Freeze-out at RHIC - BESSTAR: arXiv: 1701.07065 02/28
3. Chemical Freeze-out DynamicsDefinition:Inelastic collisions ceasesChemical composition or Particle ratios get fixedStatistical Thermal ModelParticle Abundances: Grand Canonical EnsembleDynamics Characterized by:Temperature Tch and baryon chemical potential mBModel Features: Assumes non-interacting hadrons and resonancesAssumes thermodynamically equilibrium systemEnsembles : Grand Canonical - average conservation of B, S, and Q Strangeness Canonical - exact conservation of S Canonical - exact conservation of B, S, and Q03/28THERMUS
4. Chemical Freeze-out Model used : THERMUS V2.1 (S. Wheaton & Cleymans, Comput. Phys. Commun. 180: 84-106, 2009)Particles yields used : π+, π- K+, K-, p, pbar, Λ , Λbar, Ξ, Ξbar Ensemble used: Grand Canonical Free parameters: chemical freeze-out temperature, Tch, baryon and strangeness chemical potential, μB, μs, strangeness saturation factor, γS ,Radius R quark chemical potential μqParticle densityTHERMUS used particles list including baryons and mesons as listed in Particle Physics Booklet of July 2002 (mass up to 2.6 GeV)04/28
5. Chemical Freeze-out Conditions Usedμq is fixed to 0Resonance widths are not included Excluded volume correction condition has not been usedIn experimental data, pion and lambda yields are weak decay feed-down corrected whereas proton yields are inclusiveIn THERMUS, week decay feed-down correction has been done accordingly as given below Decay Information: 1 : stable (not allowed for decay) 0 unstable (allowed for decay)HadronsK0SLambdaSigma+Sigma-Xi0Xi-Omegapi+/-1111111K+/-1111111p/pbar1001001K0S1111111La/Labar1111111Xi/Xibar111111105/28
6. Feed-down fractions to (anti)proton The feed-down fractions obtained from THERMUS (200 GeV) – Contributions from Lambda and Sigma+ to (anti)proton Centrality Proton (%)Anti-proton (%)0-55-1010-2020-3030-4040-6060-8031.0431.9032.5331.3130.3829.0525.4432.7733.2333.4932.5932.1330.4927.1706/28
7. Particle Yields: Typical Data (200 GeV)Λ, Ξ : Phys. Rev. Lett. 98, 062301 (2007) (200 GeV)Errors are the quadratic sum of statistical and systematic uncertainties, Sources of systematic uncertaintiesUsing different fit functions for yields in the extrapolated regionUncertainties due to different topological cutsUncertainties due to efficiency calculationsDifference between the MC simulation and real data which make the reconstructed yields sensitive to the choice of topological cutsBackground subtraction methodMeasured differences in the yield dependent on the direction of the applied magnetic fieldRapidityΛ, Λbar (|y| < 1) Ξ, Ξbar (|y| < 0.75)Feed-down correctionLambdas are feed-down corrected from multi-strange baryonsMeasured pT rangesΛ, Λbar : 0.6 – 5 (GeV/c), Ξ, Ξbar : 0.8 – 5 (GeV/c)Integrated YieldsThe dN/dy obtained from measured spectra and Boltzmann fits to the spectra for extrapolated region. 07/28
8. CFO: Data vs. Model08/28STAR: arXiv: 1701.07065 THERMUSS. Wheaton & Cleymans, Comput. Phys. Commun. 180: 84-106, 2009
9. CFO Dynamics: Centrality Dependence09/28First studies related to centrality dependence of chemical freeze-out parameters at lower beam energiesSTAR: arXiv: 1701.07065
10. CFO Dynamics : Systematics - EnsembleSTAR: arXiv: 1701.07065 10/28
11. CFO Dynamics : Systematics - ConstraintsmQ = B/2QmQ = B/2Q & mS = 0STAR: arXiv: 1701.07065 11/28
12. CFO Dynamics : Systematics - SpeciesSTAR: arXiv: 1701.07065 12/28
13. pT spectra W or W/o feed-down correction (200 GeV)10/10/17Phys. Rev. Lett. 97, 152301 (2006)Centrality dN/dy(w feed-downcorrection)dN/dy(w/o feed-downcorrection)Difference(%)0-1210-2020-4040-6060-8016.29 +- 1.4812.84 +- 1.207.48 +- 0.713.34 +- 0.271.055 +- 0.09828.31 +-0.8920.49 +- 0.7111.95 +- 0.425.27 +-0.201.605 +- 0.079 42.4 37.3 37.4 36.6 34.3- Feed-down corrected spectra of proton from Lambda and Sigma+Errors are statistical The feed down corrected pT spectra for protons are discussed in above STAR paperUsing pT spectra of proton: 13/28
14. FO parameters w or w/o feed-down correction (200 GeV)Au+Au : 10-20%Centrality FO parameters(w feed-downcorrection)FO parameters(w/o feed-downcorrection)TμBμsγSRChisq/ndf165.2 +- 3.322.6 +- 7.93.2 +- 5.41.05 +- 0.046.05 +- 0.334.45167.8 +-3.823.2 +- 10.23.0 +- 6.70.988 +-0.055.91 +- 0.353.9Same fraction of feed down contribution assumed for anti-protons as is usedfor protons in last slide. 14/28
15. CFO: QCD Phase Diagram15/28STAR: arXiv: 1701.07065
16. Part – IIVDWHRG16/28
17. Success of HRG ModelsComparison with various order moments of multiplicity distributions and LQCDA. Andronic, P. Braun-Munzinger, J. Stachel and M. Winn, Phys. Lett. B 718, 80 (2012)HotQCD: arXiv:1708.04897v2Paolo Alba, Wanda Alberico, Rene Bellwied, Marcus Bluhm, Valentina Mantovani Sarti, Marlene Nahrgang, Claudia Ratti,Phys.Lett. B738 (2014) 305-31017/28
18. Recent VDWHRG WorkIn, V. Vovchenko, D. V. Anchishkin and M. I. Gorenstein, Phys. Rev. C 91, 064314 (2015).V. Vovchenko, M. I. Gorenstein and H. Stoecker, Phys. Rev. Lett. 118, 182301 (2017).Van der Waal Model parameters fixed to explain ground state nuclear matter data (n0 = 0.16 fm3 & E/N = 16 MeV), looked at comparison to LQCD data18/28
19. Basic Idea The motivation of the present work is to carry out the reverse prescription, that is to find out van der Waals parameters a and b that gives the best description of LQCD data at zero chemical potential using VDWHRG model and then extend this work to the finite chemical potential and try to locate the existence of a critical point in the T vs. mB phase diagram.Assumptions:The same attractive and repulsive parameters are valid for non-zero mB Only baryons have interactions Does not include the missing resonances in hadron spectrum19/28
20. VDWHRG ModelNon-interacting HRGvan der Waals interactionGrand Canonical EnsembleInteractions only considered for baryonsin this work.arXiv: 1709.04446 20/28
21. VDWHRG vs. Lattice QCDThe best fit in terms of c2 is achieved for parameter values of a (attractive) = 1250± 150 MeV fm3 and r (repulsive) = 0. 7± 0. 05 fm.arXiv: 1709.04446 21/28
22. VDWHRG vs. Lattice QCD Ideal HRG model speed of sound decreases with increasing temperature, in VDWHRG model it shows a minimum near T = 150 MeV which is consistent with the LQCD data.Temperature dependence of second order fluctuations of conserved baryon charges at zero chemical potential22/28
23. VDWHRG Model: Criticality Temperature and chemical potential where there is discontinuity. arXiv: 1709.04446 23/28
24. VDWHRG Model : CriticalityLattice Points:Z. Fodor and S. D. Katz, JHEP 0404, 050 (2004)S. Datta, R. V. Gavai and S. Gupta, Phys. Rev. D 95, 054512(2017)Chemical Freeze-out points:A. Andronic, P. Braun-Munzinger and J. Stachel, Nucl. Phys. A 772, 167 (2006)J. Cleymans, H. Oeschler, K. Redlich and S. Wheaton, Phys. Rev. C 73, 034905 (2006).T = 62.1 MeV (+ 25.4, -19.1)mB = 708 MeV ( + 90, - 146)arXiv: 1709.04446 24/28
25. Attractive & Repulsive Interactions vs. √snnIdea:Use VDWHRG Model with a and b as parameters Fix T and mB to that extracted from particle yields Get the best fit values of a and b by comparing to experimental data on fluctuationsSTAR:Phys. Rev. Lett. 112 (2014) 032302Phys. Rev. Lett. 113, 092301 (2014)25/28
26. Results: Net-proton26/28
27. Attractive & Repulsive Interactions vs. √snn27/28
28. SummaryWe have used LQCD data of p/T4,e/T4, s/T3,CV /T3 and c2B at μ = 0 to extract the van der Waals parameters in the VDWHRG model. We get a = 1250± 150 MeV fm3 and r = 0. 7± 0. 05 fm in our present work which best describes the LQCD data at μ = 0 within the temperature range 130− 180 MeV. With these parameters which explains the QCD matter simulated by lattice, we observe a phase transition in VDWHRG model at large baryon chemical potential with a critical point in the (T,μB) phase diagram at T = 62. 1 MeV and μB = 708 MeV.We tried to explain the fluctuation data from RHIC BES program on net-protons using VWDHRG model.This will allow us to look at the variation of attractive and repulsive parameters in the model as a function of beam energy. A comprehensive study of chemical freeze-out parameters carried out at RHIC – Beam Energy Scan Program.28/28