BeamEnergy Scan T Hadrons Color SC 0 m

Beam-Energy Scan T Hadrons Color SC 0 m

Beam-Energy Scan STAR 2012 high bea T me ner gy low Hadrons Color SC 0 m

Fluctuations Observables in equilibrium are fluctuating. P(N) N V N

Fluctuations Observables in equilibrium are fluctuating. P(N) N Ø Variance: Ø Skewness: Ø Kurtosis: V N

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

Event-by-Event Analysis @ HIC Fluctuations can be measured by e-by-e analysis in experiments. STAR, PRL 105 (2010) Detector

Conserved Charges : Theoretical Advantage p Definite definition for operators - as a Noether current - calculable on any theory ex: on the lattice

Conserved Charges : Theoretical Advantage p Definite definition for operators - as a Noether current - calculable on any theory ex: on the lattice p Simple thermodynamic relations - Intuitive interpretation for the behaviors of cumulants ex:

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

Fluctuations Free Boltzmann Poisson

Fluctuations Free Boltzmann Poisson RBC-Bielefeld ’ 09

Proton # Fluctuations @ STAR-BES STAR, PRL 2010

Proton # Fluctuations @ STAR-BES STAR, PRL 2010 STAR, 2011 high m low m

Proton # Fluctuations @ STAR-BES STAR, 2012 (Quark Matter) STAR, 2011 high m low m

Proton # Cumulants @ STAR-BES STAR, QM 2012 No characteristic signals on phase transition to QGP nor QCD CP

Proton # Cumulants @ STAR-BES STAR, QM 2012 Athanasiou, Rajagopal, Stephanov, 2010 No characteristic signals on phase transition to QGP nor QCD CP

Charge Fluctuations @ STAR-BES STAR, QM 2012 Suppression? ? Similar result @ PHENIX Ur. QMD

Charge Fluctuation @ LHC ALICE, PRL 110, 152301(2013) D-measure • D ~ 3 -4 Hadronic • D ~ 1 Quark LHC: significant suppression from hadronic value ＬＨＣ終状態の電荷ゆらぎは、ハドロン化以前に生成されたものを強く反映している！

Dh Dependence @ ALICE PRL 2013 t Dh z rapidity window

Dissipation of a Conserved Charge

Time Evolution in HIC Quark-Gluon Plasma Hadronization Freezeout

<d. NB 2> and < d. Np 2 > @ LHC ? should have different Dh dependence.

<d. NQ 4> @ LHC ? How does behave as a function of Dh? Left (suppression) or Right (hadronic)

Baryon vs Proton Number Fluctuations MK, Asakawa, PRC 85, 021901 C(2012); PRC 86, 024904(2012) p p are experimentally observable

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

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

Slot Machine Analogy = + P (N) N

Extreme Examples Fixed # of coins Constant probabilities N N

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

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

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

D(1232) cross sections of p 2 1: 2 1 2: 1 3 decay rates of D Lifetime to create D+ or D 0 BW for s & thermal pion

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

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

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

Secondary Protons detector MK+, in preparation Secondary (knockout) protons 20% of observed protons @ STAR dca [cm] Measurement STAR, PRC 79, 034909(2009)

MK+, in preparation Secondary Protons detector Secondary (knockout) protons 20% of observed protons @ STAR dca [cm] Measurement Their contribution can be eliminated! STAR, PRC 79, 034909(2009)

Time Evolution of Higher Order Cumulants MK, Asakawa, Ono, ar. Xiv: 1307. xxxx

Time Evolution in HIC Quark-Gluon Plasma Hadronization Freezeout

Hydrodynamic Fluctuations Landau, Lifshitz, Statistical Mechaniqs II Kapusta, Muller, Stephanov, 2012 Diffusion equation Stochastic diffusion equation

Dh Dependence Shuryak, Stephanov, 2001 p Initial condition: p Translational invariance initial equilibrium

Diffusion Master Equation Divide spatial coordinate into discrete cells probability

Diffusion Master Equation Divide spatial coordinate into discrete cells probability Master Equation for P(n) x-hat: lattice-QCD notation Solve the DME exactly, and take a 0 limit No approx. , ex. van Kampen’s system size expansion

Solution of DME 1 st initial Deterministic part diffusion equation at long wave length (1/a<<k) Appropriate continuum limit with ga 2=D

Solution of DME 1 st initial Deterministic part diffusion equation at long wave length (1/a<<k) Appropriate continuum limit with ga 2=D 2 nd Consistent with stochastic diffusion eq. (for sufficiently smooth initial condition)

Net Charge Number Prepare 2 species of (non-interacting) particles Let us investigate at freezeout time t

Initial Condition at Hadronization p Boost invariance / infinitely long system p Local equilibration / local correlation p Initial fluctuations suppression owing to local charge conservation strongly dependent on hadronization mechanism

Dh Dependence at Freezeout Initial fluctuations: 2 nd 4 th

<d. NQ 4> @ LHC Assumptions • boost invariant system • small fluctuations of CC at hadronization • short correlation in hadronic stage Suppression of 4 th-order cumulant is anticipated at LHC energy!

Dh Dependence at STAR, QM 2012 decreases as Dh becomes larger at RHIC.

Dh Dependence at Freezeout Initial fluctuations: 2 nd 4 th

Fluctuation in initial state Time evolution in the QGP approach to HRG by diffusion volume fluctuation experimental effects particle miss. ID, etc. Evolution of Fluctuations

Time Evolution in HIC Quark-Gluon Plasma Hadronization Freezeout

Time Evolution in HIC Pre-Equilibrium Quark-Gluon Plasma Hadronization Freezeout