Fluctuations of conserved charges and freeze-out conditions in heavy ion collisions

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1 Fluctuations of conserved charges and freeze-out conditions in heavy ion collisions Claudia Ratti University of Houston, Texas (USA) S. Borsanyi, Z. Fodor, S. Katz, S. Krieg, C. R., K. Szabo, PRL 2014 P. Alba, W. Alberico, R. Bellwied, M. Bluhm, V. Mantovani Sarti, M. Nahrgang, C. R., PLB 2014 Claudia Ratti 1

2 Motivation Synergy between fundamental theory and experiment We can create the deconfined phase of QCD in the laboratory Lattice QCD simulations have reached unprecedented levels of accuracy physical quark masses several lattice spacings continuum limit Can we learn something about hadronization from the synergy between fundamental theory and experiment? Claudia Ratti 2

3 The observables: fluctuations of conserved charges They can be calculated on the lattice as combinations of quark number susceptibilities They can be compared to experimental measurements (with some caveats) The chemical potentials are related: µ u = 1 3 µ B µ Q; µ d = 1 3 µ B 1 3 µ Q; µ s = 1 3 µ B 1 3 µ Q µ S. susceptibilities are defined as follows: χ BSQ lmn = l+m+n p/t 4 (µ B /T) l (µ S /T) m (µ Q /T) n. Claudia Ratti 3

4 Relating susceptibilities to moments In a thermally equilibrated system we can define susceptibilities c as 2 nd derivative of pressure with respect to chemical potential (1 st derivative of r). Starting from a given partition function we define the fluctuations of a set of conserved charges as:

5 Relating lattice results to experimental measurement we can relate susceptibilities to moments of multiplicity distributions: mean : M = χ 1 variance : σ 2 = χ 2 skewness : S = χ 3 /χ 3/2 2 kurtosis : κ = χ 4 /χ 2 2 Sσ = χ 3 /χ 2 κσ 2 = χ 4 /χ 2 M/σ 2 = χ 1 /χ 2 Sσ 3 /M = χ 3 /χ 1 F. Karsch (2012) Claudia Ratti 4

6 Experimental measurement I Star Collaboration: arxiv Claudia Ratti 5

7 Experimental measurement II Star Collaboration: PRL 2014 Claudia Ratti 6

8 Caveats Effects due to volume variation because of finite centrality bin width V. Skokov, B. Friman, K. Redlich, PRC (2013) Experimentally corrected by centrality-bin-width correction method Finite reconstruction efficiency Experimentally corrected based on binomial distribution A. Bzdak, V. Koch, PRC (2012) Spallation protons Experimentally removed with proper cuts inp T Canonical vs Gran Canonical ensemble Experimental cuts in the kinematics and acceptance V. Koch, S. Jeon, PRL (2000) Proton multiplicity distributions vs baryon number fluctuations Numerically very similar once protons are properly treated M. Asakawa and M. Kitazawa, PRC (2012), M. Nahrgang et al., Final-state interactions in the hadronic phase J.Steinheimer et al., PRL (2013) Consistency between different charges = fundamental test Claudia Ratti 7

9 Thermometer and Baryometer R B 31 : thermometer R31 B (T,µ B) = χb 3 (T,µ B) χ B 1 (T,µ B) = χb 4 (T,0)+χ BQ 31 (T,0)q 1(T)+χ BS 31 (T,0)s 1(T) χ B 2 (T,0)+χBQ 11 (T,0)q 1(T)+χ BS 11 (T,0)s 1(T) +O(µ2 B ) Expand numerator and denominator aroundµ B = 0: ratio is independent ofµ B R B 12 : baryometer R12 B (T,µ B) = χb 1 (T,µ B) χ B 2 (T,µ B) = χb 2 (T,0)+χ BQ 11 (T,0)q 1(T)+χ BS 11 (T,0)s 1(T) µ B χ B 2 (T,0) T +O(µ3 B ) Expand numerator and denominator aroundµ B = 0: ratio is proportional toµ B Claudia Ratti 8

10 Extracting freeze-out parameters from baryon number R B 31 =S B σ 3 B / MB STAR N t =6 N t =8 N t =10 N t =12 WB continuum limit R B 12 =M B /σ 2 B STAR, 27 GeV STAR, 62.4 GeV STAR, 39 GeV T [MeV] STAR, 200 GeV T=140 MeV T=145 MeV T=150 MeV µ B [MeV] WB Collaboration: PRL (2014); STAR data from Upper limit: T f 151±4MeV s[gev] µ f B [MeV] ± ± ± Claudia Ratti 9

11 Extracting freeze-outµ B from electric charge R Q 12 =M Q /σ 2 Q T=140 MeV T=145 MeV T=150 MeV R B 12 =M B /σ 2 B STAR, 27 GeV STAR, 39 GeV 0.08 STAR, 27 GeV 0.4 STAR, 62.4 GeV STAR, 200 GeV STAR, 62.4 GeV STAR, 39 GeV µ B [MeV] STAR, 200 GeV T=140 MeV T=145 MeV T=150 MeV µ B [MeV] WB Collaboration: PRL (2014); STAR data from and It is of fundamental importance to test the consistency between the freeze-out parameters obtained with different conserved charges This consistency check validates the method and shows equilibration of the medium Claudia Ratti 10

12 s[gev] µ f B Consistency is found! [MeV] (fromb) µf B [MeV] (fromq) ± ± ± ± ±11 101± ± µ B [MeV] from B from Q SHM model 20 s [GeV] Lattice: WB Collaboration: PRL (2014); SHM: Andronic et al., NPA (2006) Claudia Ratti 11

13 Freeze-out temperature from yields Fit to yields of identified particles: Statistical Hadronization Model (SHM) Model-dependent. Parameters: freeze-out temperature and chemical potential R. Preghenella for ALICE, SQM 2012 M. Floris, QM Claudia Ratti 13

14 HRG model analysis Experimental cuts in acceptance and momentum Resonance decay and regeneration P. Alba et al., PLB 2014 P. Alba et al., arxiv: Claudia Ratti 12

15 Quark model strange states 2,5 2 Lattice PDG QM χ 4 S /χ2 S 1,5 1 0, T (MeV) A. Bazavov et al.: PRL (2014) R. Bellwied et al.: in preparation Not-yet discovered strange states improve the BS correlator butχ S 4/χ S 2 gets worse Claudia Ratti 14

16 Fluctuations from yields K. Redlich et al., 2014 Claudia Ratti 15

17 Fluctuations from yields K. Redlich et al., 2014 Claudia Ratti 16

18 Conclusions It is possible to extract freeze-out parameters from first principles Higher order fluctuations of baryon number: R B 31(T,µ B ) = χb 3 (T,µ B) χ B 1 (T,µ B) : Thermometer R B 12(T,µ B ) = χb 1 (T,µ B) χ B 2 (T,µ B) : Baryometer Higher order fluctuations of electric charge: independent measurement R Q 12 (T,µ B) = χq 1 (T,µ B) χ Q 2 (T,µ B) : Baryometer The freeze-out parameter sets obtained from B and Q are consistent with each other Looking forward to strangeness fluctuation data! Claudia Ratti 17