Fluctuations and QCD phase structure

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1 Fluctuations and QCD phase structure Guo-yun Shao ( 邵国运 ) Xi an Jiaotong University Outline: Motivation Methods to describe fluctuations of conserved charges in heavy-ion collisions Numerical results and discussions Summary Based on a work in preparation The 12 th workshop on QCD phase transitions and relativistic heavy ion collisions, Xi an

2 I. Motivation A high-energy HIC process can be modeled into several stages: Pre-equilibrium : early thermalization stage Equilibrium state : Quark-Gluon Plasma is created and starts expanding Hadronization: Quarks and Gluons are coalescenced into hadrons with the system cooling down Free streaming : hadrons stop interacting and emitting independently

3 QCD Phase Diagram? Two types of phase transition Deconfinement transition Chiral phase transition Rich phase structure Crossover phase transition at high T and small baryon chemical potential Confirmed by LQCD and net-proton multiplicity distributions (science,323(2011)1525) First-order phase transition at intermediate baryon chemical potential Possibly much more complex at low T and large μ B Existence of Critical endpoint? the location?

4 Location of CEP from Lattice and effective field theories Lattice: (μ B,T)=(360,162)MeV Fodor & Katz, JHEP 0404(2004)050 (μ B,T)=(285,155)MeV Datta&Gavai&Gupta, arxiv: DSE: (μ B,T)=(372,129)MeV X.Y. Xin, S.X.Qin&Y.X.Liu,PRD 90(2014) Critical point does not exist G.Endrödi, Z.Fodor et al,jhep 1104,001(2011)... Still an open question about the existence of the CEP and the location

5 Some observables from RHIC (a hint of critical behavior) The non-monotonic behavior of the fluctuations of conserved charges possibly hints that a first-order phase transition of QGP occurs X.F.Luo, N.Xu arxiv: The analysis of event by event fluctuations of conserved charges can server as a powerful observables to study the phase transition and search for the CEP

6 Future experiments BES II program is scheduled to run during the years of 2019 and 2020 in GeV (an precise measurement of fluctuations) NICA in Dubna FAIR in Darmstadt A very good opportunity to explore the structure of QCD Fixed target experiment STAR

7 2. Methods to describe fluctuations of conserved charges A system in thermal equilibrium for a grand-canonical ensemble P T 1 ln[ Z ( V, T, B, Q, S )] VT 4 3 The generalized susceptibility of conserved charges are defined as ( i j k ) P ( / T ) ( / T ) ( / T) T BQS ijk i j k B Q S Simple relation between susceptibility and cumulants related to observables 4 C Z V T VT ( i j k ) BQS 3 BQS ijk ln[ (,, B, Q, S )] i j k ijk ( B / T ) ( Q / T ) ( S / T ) Denoting the ensemble average of a conserved charge number N X (X=B, Q, S) with N X, N X = N X - N X

8 Higher order fluctuations of the conserved charges can be derived distributions The skewness The kurtosis 1 VT X VT X 1 4 VT X 2 2 <( N 3 X ) >, 3 < ( N 3 X )> 4 <( N X) -3<( Experimental observables are constructed as the ratio of cumulants of multiplicity N ( S ) ( S ) ( S ) B Q S B, Q, B Q S S ( ) ( ) ( ) B Q S B, Q, B Q S S X 2 ) >

9 Some results from hadron resonance gas model (arxiv: ) Some results from effective field theory W. J. Fu, PRD 82 (2010) , PRD94 (2016), Stephanov, PRL107(2011)052301;Schafer&wagner, PRD 85(2012) J.W.Chen, J. Deng et al., 93(2016)034037

10 The Poyakov--Nambu--Jona-Lasinio quark model Two types of parameters : quark condensate: describing chiral phase transition and quark dynamical mass Poyakov loop and its conjugate

11 3. Numerical results and discussions Quark condensate and chiral phase transition Crossover phase transition at small quark chemical potential First-order phase transition occurs when q is larger than 297MeV the discontinuity of quark condensate and quark number densities

12 Deconfinement-confinement phase transition Continuum phase transition at small quark chemical potential A small jump of when the chiral first-order phase transition occurs

13 Phase structure Chiral crossover phase transition line with chemical potential φ q T takes the largest value for a given Deconfinement-confinement line: with Φ T taking the largest value Entropy density does not show a critical feature at CEP Features of the first-order phase transition in temperature-baryon density plane

14 A new quantum s/t 3 to describe the phase transition s/t 3 =7 is taken as chemical freeze-out condition in the hadronic model A. Tawfik, J. Phys. G: Nucl. Part. Phys. 31 (2005) S1105; Cleymans, PRC 73 (2006) Not suitable for quark degree of freedom at high density/ large chemical potential

15 Baryon number fluctuations: kurtosis Intense fluctuations nearby the CEP (a wide region along chiral phase transition line) Present the trace of chiral and deconfinement phase transition Confinement-deconfinement phase transition contributes more at low density (small quark chemical potential) J.W.Chen, J. Deng et al., 93(2016)034037

16 Baryon number fluctuations: kurtosis

17 Baryon number fluctuations: skewness Increasing fluctuation near the critical point, but less intensive than kurtosis

18 Baryon number fluctuations: skewness

19 The connection with observables Quark model with a first-order chiral phase transition and a CEP can qualitatively explain the behavior of the skewness and kurtosis from experiments Some questions still not solved The fluctuations of conserved charges is measured at chemical freeze out Where is the chemical freeze-out line (the relation between collision energy and chemical potential and temperature at chemical freeze out)?

20 To fix the chemical freeze-out line different criteria are taken Most of these criteria are based on the statistical thermal fit of the HRG model successful to describe particle yields and their ratios at crossover region but it leads to a large deviation in describing fluctuation at high density with a lower collision energy Cleymans, PRC 73 (2006) and reference therein

21 To what degree can we believe the chemical-freeze out line derived from the HRG model at low T and large μ B Interacting nuclear model should be considered Fukushima, PRC(2015) How do the fluctuations created at the phase transition transport to the position of the chemical freeze out? The fluctuations will be weaken in the expansion. Correlation strength and the time evolution of fluctuations Further studies are needed to determine the relation between QCD phase transition and the observed fluctuations and, as well as the freeze-out thermodynamic conditions

22 Summary We discussed the relation between QCD phase structure and baryon number fluctuations in the PNJL quark model Intense fluctuations appear near the critical point, which can qualitatively explain the behavior of kurtosis and skewness in experiments Both the chiral phase transition and deconfinement-deconfinment transition possibly play important roles on the generation of fluctuations in the evolution of QGP with different collision energy, The relation between the two kinds of transitions is still not clear. The precise measurement of fluctuations possibly provide a good opportunity to study the phase structure

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25 T, GeV t critical point QGP H hadron gas freezeout curve nuclear matter 1 m B, GeV

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