Baryon Number Fluctuations in Energy Scan Program at RHIC

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1 Baryon Number Fluctuations in Energy Scan Program at RHIC Masakiyo Kitazawa (Osaka U.) MK, Asakawa, arxiv: (to appear in PRC) HIRSCHEGG2012, 18, Jan, 2012, Hirschegg

2 Energy Scan RHIC T high low Phase Structure Dynamics for m~0 Hadrons Color SC 0 m

3 Fluctuations Observables in equilibrium is fluctuating. P(N) N V N

4 Fluctuations Observables in equilibrium is fluctuating. P(N) N V N Variance: Skewness: Kurtosis:

5 Event-by-Event HIC Fluctuations can be measured by e-by-e analysis in experiments. V Detector

6 Event-by-Event HIC Fluctuations can be measured by e-by-e analysis in experiments. STAR, PRL105 (2010) Detector

7 Fluctuations 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)

8 Fluctuations 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) 2 nd order phase transition at the CP. divergences in fluctuations of p T distribution freezeout T baryon number, proton, chage,

9 Ratios of Cumulants Boltzmann gas (=Poisson distribution) Asakawa, Heinz, Muller, 00 Jeon, Koch, 00 Ejiri, Karsch, Redlich, 06 Hadrons: Quark-gluon: p p s d u u n n p n s d d u

10 Take a Derivative of c B Asakawa, Ejiri, MK, 2009 c B has an edge along the phase boundary c B c B m B V 2 1 B m 2 B ( N ) VT ( NB) V m VT 3 2 B 2 m 3 (BB B) c B m B changes the sign at QCD phase boundary!

11 Impact of Negative Third Moments Once negative m 3 (BBB) is established, it is evidences that (1) c B has a peak structure in the QCD phase diagram. (2) Hot matter beyond the peak is created in the collisions. No dependence on any specific models. Just the sign! No normalization (such as by N ch ).

12 Fluctuations of Conserved Charges When is experimentally measured D formed? t Dy N Q Dy z Conserved charges can remember fluctuations at early stage, if diffusions are sufficiently slow. Asakawa,Heintz,Muller ( 00); Jeon,Koch ( 00); Shuryak, Stephanov ( 02)

13 Proton # STAR 2011 (Quark Matter) HRG: Hadron Resonance Gas = Free gas composed of all hadrons & resonances high m low m

14 Proton # STAR 2011 (Quark Matter) No negative S No suppression of ks 2 Do fireballs forget all information in the early stage? high m low m

15 ? In equilibrated free nucleon gas, If the medium is not equilibrated,

16 Nucleon Isospin as Two Sides of a Coin N p n Nucleons have two isospin states.

17 Nucleon Isospin as Two Sides of a Coin N a coin p n Nucleons have two isospin states. Coins have two sides.

18 Slot Machine Analogy P (N) = + P (N) N N

19 Extreme Examples Fixed # of coins Constant probabilities N N N N

20 Baryon Number Fluctuations are Better Since it is a conserved charge Expectation values are well defined possible slow diffusion in hadronic stage Asakawa,Heintz,Muller ( 00); Jeon, Koch ( 00) Clearest observable for enhancement near CP Same critical exponents for baryon, charge, proton # Hatta, Stephanov ( 02) - But singular contribution is largest in baryon # Ratio of cumulants behaves most drastically

21 Reconstructing Total Coin Number P (N )= P (N )B 1/2 (N ;N ) :binomial distr. func.

22 Nucleon Isospin in Hadronic Medium cross section Isospin of baryons can vary after chemical freezeout via charge exchange reactions mediated by D(1232): 200mb=20fm 2

23 1:2 2:1 D(1232) cross sections of p decay rates of D

24 1:2 2:1 D(1232) cross sections of p decay rates of D

25 1:2 2:1 D(1232) cross sections of p decay rates of D BW for s & thermal pion Lifetime to create D + or D 0 c.f.) Nonaka, Bass, 2007

26 hadronize chem. f.o. kinetic f.o. Nucleons in Hadronic Phase time 10~20fm mesons baryons rare NN collisions no quantum corr. many pions

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

28 Nucleon & Proton Number Fluctuations for isospin symmetric medium effect of isospin density <10% Similar formulas up to any order! For free gas

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

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

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

32 Proton # STAR 2011 (Quark Matter) No negative S No suppression of ks 2 Do fireballs forget all information in the early stage? high m low m

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

34 Summary Baryon and proton number fluctuations are different. To see non-thermal effects in heavy ion collisions, baryon number s 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 Distribution function itself Incorporating effects of efficiency and acceptance in exp. / correlation between isospin fluctuations of pions Discussion on dynamical evolution of fluctuations

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

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

37 3 rd & 4 th Order Fluctuations

38 Isospin Distributions Large pion density Small nucleon density because M N /T<<1 For top RHIC energy, N p ~20N N Nucleons exclusively interact with pions Rare NN collisions Huge pp reactions Nonaka, Bass, 07 All formations and decays of D take place independently

39 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 (Poissonian) ones.