@ CPOD2011 Wuhan November 2011 Department of Physics, Osaka University Masayuki Asakawa Baryon Number Cumulants and Proton Number Cumulants in Relativistic.

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@ CPOD2011 Wuhan November 2011 Department of Physics, Osaka University Masayuki Asakawa Baryon Number Cumulants and Proton Number Cumulants in Relativistic Heavy Ion Collisions Baryon Number Cumulants and Proton Number Cumulants in Relativistic Heavy Ion Collisions S. Ejiri, M. Kitazawa, and M. A., PRL 103 (2009) M. Kitazawa and M.A., (2011) to be published

M. Asakawa (Osaka University) Two Meanings of Fluctuation Observables Asakawa, Heinz, Müller, Jeon, Koch, Ejiri, Kitazawa, … Distinction of Phases (conserved charge fluctuation) Detection of Increase of Fluctuation (or Correlation Length) at 2nd order Phase Transition Critical End Point = 2nd order phase transition point Phase structure of QCD Long History of Fluctuation Observations (including intermittency) in HI Collisions

M. Asakawa (Osaka University) QCD Phase Diagram CSC (color superconductivity) QGP (quark-gluon plasma) Hadron Phase T BB chiral symmetry breaking confinement order ? 1st order crossover CEP(critical end point) MeV 5-10  0 RHIC LHC

M. Asakawa (Osaka University) Higher Moments Recently higher moments have attracted quite a lot of attention  (Roughly) Two Reasons Larger critical exponents around CEP (=A  z ) Sign change across the phase transition (crossover) line Stephanov (2008) Next Slide Asakawa, Ejiri, Kitazawa (2009)

M. Asakawa (Osaka University) Odd Power Fluctuation Moments Fluctuation of Conserved Charges: not subject to final state interactions Usual Fluctuations such as : positive definite Absolute values carry information of states (D-measure) Odd power fluctuations : Asakawa, Heinz, Müller, Jeon, Koch On the other hand, In general, do not vanish (exception, ) Sign also carry information of states NOT positive definite Usually fluctuations such as have been considered even power

M. Asakawa (Osaka University) Physical Meaning of 3rd Fluc. Moment BB : Baryon number susceptibility in general, has a peak along phase transition changes the sign at QCD phase boundary ! In the Language of fluctuation moments: more information than usual fluctuation

M. Asakawa (Osaka University) (Hopefully) More Easily Measured Moments Third Moment of Electric Charge Fluctuation iso-vector susceptibility nonsingular when Isospin-symm. Hatta and Stephanov 2002 BI/9BI/9

M. Asakawa (Osaka University) Recent Progress: Proton Cumulants Hatta and Stephanov, 2003 Comparisons of experimental results and lattice predictions have been done （ e.g. Gupta et al., Science 2011) STAR, QM2011 Experiment: Net Proton Theory: Net Baryon Proton Fluctuation has been attracting a lot of interest because it can be observed experimentally Proton Fluctuation diverges at CEP Is this harmless?

M. Asakawa (Osaka University) Protons and Baryons In free nucleon gas in equilibrium, Otherwise, in general, The question here is how these are related to each other:

M. Asakawa (Osaka University) Freezeouts Net proton may be considered as an alternative of net baryon Chemical freezeout is close to the crossover, and (anti)proton number is expected to be fixed early (?) Thremalization ExpansionHadronizationKinetic Freezeout Collision © C.Nonaka  But Not all particle numbers and fluctuations are fixed at chemical freezeout

M. Asakawa (Osaka University) Exception If there are low mass resonances, exception happens In our case at hand,  resonances cross section 200mb=20fm 2

M. Asakawa (Osaka University) Effect of  :1 1:2 branching ratio of  ratio of cross sections

M. Asakawa (Osaka University) Effect of  :1 1:2 branching ratio of  ratio of cross sections

M. Asakawa (Osaka University) How long is the mean free time? :1 1:2 Meantime to create  + or  0 BW for  & thermal pion branching ratio of  ratio of cross sections

M. Asakawa (Osaka University) Nucleon Isospin Randomization in Pion Gas hadronization chem. f.o. kinetic f.o. a few fm time mesons baryons

M. Asakawa (Osaka University) Production of Additional Fluctuation 1. Original 2. Additional (from  N→  →  N) In, general, fluctuations of N N and N p are different Additional N p fluctuations are created by (thermal) pions

M. Asakawa (Osaka University) Dilute Nucleon Approximation hadronization chem. f.o. kinetic f.o. rare NN collisions no Pauli blocking many pions Isospins of nucleons are random, and have no correlations with one another + Ignore NN collisions mesons baryons

M. Asakawa (Osaka University) Probability Distribution hadronization chem. f.o. kinetic f.o.

M. Asakawa (Osaka University) Probability Distribution In the dilute approximation, N N (net) and N N (tot) are conserved, i.e. are conserved separately When are fixed and hadron phase is long enough compared to the mean free time of (anti)nucleons, the final state (anti)proton distribution is given by the binomial distribution

M. Asakawa (Osaka University) Probability Distribution As a result, the final state distribution is factorized as follows: The two variable function “F” includes the initial information (correlation) This form of P f enables to relate proton moments and nucleon moments

M. Asakawa (Osaka University) Proton and Nucleon Moments 1. Original 2. Additional (from  N→  →  N) For free nucleon gas for isospin symmetric matter

M. Asakawa (Osaka University) Proton and Nucleon Moments N p → N B N B → N p Similarly,

M. Asakawa (Osaka University) Time Scales hadronization  I : time scale to realize isospin randomization  hadron : time scale of hadron phase duration  hadron result of state-of-art hydro + cascade calculation

M. Asakawa (Osaka University) Result of Hydro+Cascade Calculation Nonaka and Bass, PRC 2007 Freezeout time distribution without after-burner with after-burner  hadron : 10 ~ 20 fm isospin: randomized

M. Asakawa (Osaka University) N N or N B : Strange Baryon Contribution Decay modes: Branching Ratios: Considering hyperon contribution is small, regard these ratios even, and incorporate (anti)protons from these decays into the binomial distribution, then, N N  N B

M. Asakawa (Osaka University) Summary Conserved Charges and Higher Moments: Third Fluctuation Moments of Conserved Charges take negative values in regions on the FAR SIDE of Phase Transition (more information!) Proton Number Cumulants and Baryon Number Ones: Proton Number Cumulants are not frozen at chemical freezeout Mean Free Time of Protons in hadron phase is very short owing to  formation and isospin is randomized This makes it possible to relate the initial baryon number cumulants and final proton number cumulants, and vice versa Final p, p, n, n distributions are factorized (NOT an assumption!) Extension to isospin nonsymmetric case is straightforward, and in progress

M. Asakawa (Osaka University) Fluctuations in Heavy Ion Collisions V Detector Observables in equilibrium is fluctuating Momentum and Space correlation is essential Fluctuations reflect properties of matter. Enhancement near the critical end point Stephanov, Rajagopal, Shuryak (98); Hatta, Stephanov (02); Stephanov (09) Ratios between cumulants of conserved charges Asakawa, Heinz, Müller (00); Jeon, Koch (00); Ejiri, Karsch, Redlich(06) Signs of higher order cumulants Asakawa, Ejiri, Kitazawa (09); Friman et al. (11); Stephanov (11)

M. Asakawa (Osaka University) Comparison of Various Moments 2-flavor NJL with standard parameters Different moments have different regions with negative moments By comparing the signs of various moments, possible to pin down the origin of moments Negative m 3 (EEE) region extends to T-axis (in this particular model) Sign of m 3 (EEE) may be used to estimate heat conductivity G=5.5GeV -2 m q =5.5MeV  =631MeV Near Side Far Side

M. Asakawa (Osaka University) Free Nucleon Gas Case Poisson distribution P (N)  The factorization is satisfied in free nucleon gas.