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Revealing Baryon Number Fluctuations in Heavy Ion Collisions

Revealing Baryon Number Fluctuations in Heavy Ion Collisions. Masakiyo Kitazawa (Osaka U.). MK, M. Asakawa , arXiv:1107.2755[ nucl-th ]. Energy Scan Program @ RHIC. high. beam energy. T. low. Hadrons. Color SC. m. 0. Fluctuations . Observables in equilibrium is fluctuating. V.

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Revealing Baryon Number Fluctuations in Heavy Ion Collisions

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

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

  3. Fluctuations • Observables in equilibrium is fluctuating. 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)

  4. Proton # Fluctuations @ STAR STAR, Quark Matter 2011 • No clear enhancements - No critical point? • No negative c3 • No decrease in c4/c2 Hadron Resonance Gas

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

  6. 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 • 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 • than electric charge fluctuations • additional nonsingular contribution in Q Example: singular nonsingular

  8. Variation of Proton # in Hadronic Phase • Proton number varies even after chemical freezeout • via charge exchange reactions mediated by D(1232): 200mb=20fm2 cross section

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

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

  11. D(1232) cross sections of p 3 1 2:1 2 1:2 decay rates of D BW for s & thermal pion Lifetime to create D+ or D0 c.f.) Nonaka, Bass, 2007

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

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

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

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

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

  17. 3rd & 4th Order Fluctuations

  18. Free Nucleon Gas Poisson distribution Pl(N)

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

  20. Time Scales • Time scales of fireballs: : time scale to realize isospinbinomiality : time scale of baryon number diffusion : life-time of hadronic medium in HIC hadronize

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

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

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

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

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

  26. 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 • 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 Freeze-out time Mean time to create D+,0 Nonaka, Bass, 2007

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