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Revealing Baryon Number Fluctuations in Heavy Ion Collisions Masakiyo Kitazawa (Osaka U.) MK, M. Asakawa, arXiv:1107.2755[nucl-th]

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Presentation on theme: "Revealing Baryon Number Fluctuations in Heavy Ion Collisions Masakiyo Kitazawa (Osaka U.) MK, M. Asakawa, arXiv:1107.2755[nucl-th]"— Presentation transcript:

1 Revealing Baryon Number Fluctuations in Heavy Ion Collisions Masakiyo Kitazawa (Osaka U.) MK, M. Asakawa, arXiv:1107.2755[nucl-th]

2 Energy Scan Program @ RHIC Energy Scan Program @ RHIC T 0 Hadrons Color SC  high low beam energy

3 Fluctuations Fluctuations V Detector  Fluctuations reflect properties of matter.  Enhancement near the critical point Stephanov,Rajagopal,Shuryak(’98); Hatta,Stephanov(’02); Stephanov(’09);…  Ratios between cumulants of conserved charges Asakawa,Heintz,Muller(’00); Jeon, Koch(’00); Ejiri,Karsch,Redlich(’06)  Signs of higher order cumulants Asakawa,Ejiri,MK(’09); Friman,et al.(’11); Stephanov(’11)  Observables in equilibrium is fluctuating.

4 Proton # Fluctuations @ STAR Proton # Fluctuations @ STAR STAR, Quark Matter 2011 Hadron Resonance Gas  No clear enhancements  No negative  3  No decrease in  4 /  2 - No critical point?

5 ?  In free nucleon gas in equilibrium,  If the medium is not equilibrated,

6 Baryon Number Fluctuations are Better Baryon Number Fluctuations are Better  than proton’s since it is not a conserved charge  simple theoretical treatment for conserved charges  possible slow diffusion in hadronic stage Asakawa, Heintz, Muller, 2000; Jeon, Koch, 2000

7 Baryon Number Fluctuations are Better Baryon Number Fluctuations are Better  than proton’s since it is not a conserved charge  simple theoretical treatment for conserved charges  possible slow diffusion in hadronic stage  than electric charge fluctuations  additional nonsingular contribution in Q Asakawa, Heintz, Muller, 2000; Jeon, Koch, 2000 singular nonsingular Example:

8 Variation of Proton # in Hadronic Phase Variation of Proton # in Hadronic Phase  Proton number varies even after chemical freezeout via charge exchange reactions mediated by  (1232): 200mb=20fm 2 cross section

9  (1232)  (1232) 3 1 2 2:1 1:2 cross sections of p decay rates of 

10  (1232)  (1232) 3 1 2 2:1 1:2 cross sections of p decay rates of 

11  (1232)  (1232) 3 1 2 2:1 1:2 Lifetime to create  + or  0 BW for  & thermal pion c.f.) Nonaka, Bass, 2007 cross sections of p decay rates of 

12 Baryon & Proton Number Fluctuations Baryon & Proton Number Fluctuations  In, general, fluctuations of N N and N p are different.  Due to the isospin fluctuations, N p fluctuations tend to be close to equilibrium ones than N N fluctuations.

13 Nucleons in Hadronic Phase Nucleons in Hadronic Phase hadronize chem. f.o. kinetic f.o. ~20fm mesons baryons time rare NN collisions no quantum corr. many pions

14 Nucleons in Hadronic Phase Nucleons in Hadronic Phase hadronize chem. f.o. kinetic f.o. ~20fm mesons baryons time rare NN collisions no quantum corr. many pions Isospins of nucleons are random, and have no correlations with one another.

15 Probability Distribution Probability Distribution Detector binomial distribution func.    for any phase space in the final state.

16 Baryon & Proton Number Fluctuations Baryon & Proton Number Fluctuations For free gas for isospin symmetric medium Similar formulas up to any order! 

17 3 rd & 4 th Order Fluctuations 3 rd & 4 th Order Fluctuations

18 Free Nucleon Gas Free Nucleon Gas Poisson distribution P (N)

19 Free Nucleon Gas Free Nucleon Gas Poisson distribution P (N)  The factrization is satisfied in free nucleon gas.

20 Time Scales Time Scales : time scale to realize isospin binomiality : time scale of baryon number diffusion : life-time of hadronic medium in HIC  Time scales of fireballs: hadronize

21 Effect of Isospin Distribution Effect of Isospin Distribution deviates from the equilibrium value.(1) (2) Boltzmann (Poisson) distribution for

22 Effect of Isospin Distribution Effect of Isospin Distribution deviates from the equilibrium value.(1) (2) Boltzmann (Poisson) distribution for For free gas genuine info.noise

23 Example1 : 4 th /2 nd Example1 : 4 th /2 nd RBC-Bielefeld ’09 ~ 1 (hadron) ~ 1/9 (quark) Ejiri, Karsch, Redlich, 2006 Stephanov, 2011 No suppression Fireballs forget primordial flucs? No. Not necessarily. < 0 (near CP)

24 Example2 : 3 rd Moment Example2 : 3 rd Moment beyond the QCD phase boundary near the CP Fireballs forget scenery over the QCD mountains? No. Not necessarily. Note: Asakawa, Ejiri, MK, 2009

25 Strange Baryons Strange Baryons Decay modes: Decay Rates: Regarding these ratios even, protons from these decays is incorporated into the binomial distribution. Then, N N  N B

26 Summary Summary  Baryon and proton number fluctuations are different in nonequilibrium medium. To see non-thermal contribution, baryon number is better.  Formulas to reveal baryon # cumulants in experiments.  Experimental analysis of baryon # fluctuations may verify  signals of QCD phase transition  speed of baryon number diffusion in the hadronic stage. Future Work Future Work  Refinement of the formulas to incorporate nonzero isospin density / low beam energy region  Discussion on time evolution of fluctuations @STAR

27 Nucleon Time Scales in Fireballs Nucleon Time Scales in Fireballs Mean time to create  +,0 Nonaka, Bass, 2007 Freeze-out time

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