1. are experimentally observable     Baryon vs Proton Number Fluctuations MK, Asakawa, PRC85,021901C(2012); PRC86, 024904(2012)

2. Proton # Cumulants @ STAR-BES Proton # Cumulants @ STAR-BES STAR,QM2012 Something interesting?? CAUTION! proton numberbaryon number MK, Asakawa, 2011;2012

3. Nucleon Isospin as Two Sides of a Coin Nucleon Isospin as Two Sides of a Coin N p n Nucleons have two isospin states. MK, Asakawa,2012

4. Nucleon Isospin as Two Sides of a Coin Nucleon Isospin as Two Sides of a Coin N p n Nucleons have two isospin states. Coins have two sides. a coin MK, Asakawa,2012

5. Slot Machine Analogy Slot Machine Analogy N P (N) N = +

6. Extreme Examples Extreme Examples N Fixed # of coins N Constant probabilities NN

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

8. Nucleon Isospin in Hadronic Medium Nucleon Isospin in Hadronic Medium  Isospin of baryons can vary 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 cross sections of p decay rates of 

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

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

14. Difference btw Baryon and Proton Numbers Difference btw Baryon and Proton Numbers deviates from the equilibrium value.(1) (2) Boltzmann (Poisson) distribution for For free gas genuine info.noise

15. 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