Critical Fluctuations in HeavyIon Collisions Masakiyo Kitazawa Osaka

Critical Fluctuations in Heavy-Ion Collisions Masakiyo Kitazawa (Osaka U. ) Workshop on QCD in the Nonperturbative Regime TIFR, Mumbai, India, 18/Nov. /2019

Beam-Energy Scan Program in Heavy-Ion Collisions T 150 Me. V high bea. Quark-Gluon Plasma me ner gy ＱＣＤ Critical Point low Hadron Phase (confined) Our Universe Color SC ~1015 g/cm 3 m

Event-by-Event Fluctuations Review: Asakawa, MK, PPNP 90 (2016) STAR, PRL 105 (2010) Detector Structure of distribution reflects microscopic properties Cumulants:

A Coin Game ①Bet 25 Euro ②You get head coins of A. 50 x 1 Euro B. 25 x 2 Euro Same expectation value.

A Coin Game ①Bet 25 Euro ②You get head coins of A. 50 x 1 Euro B. 25 x 2 Euro C. 1 x 50 Euro Same expectation value. But, different fluctuation.

Fluctuations in HIC: 2 nd Order Search for QCD CP Onset of QGP Fluctuation increases Fluctuation decreases Stephanov, Rajagopal, Shuryak, 1998; 1999 Asakawa, Heinz, Muller, 2000; Jeon, Koch, 2000

Higher-order Cumulants A. 50 x 1 Euro B. 25 x 2 Euro d€ 2 d€ 3 € 4 Asakawa, MK, PPNP 90, 299 (2016)

Non-Gaussian Fluctuations Onset of QGP Search for QCD CP Fluctuation decreases Fluctuation increases Ejiri, Karsch, Redlich, 2006 Stephanov, 2009

Sign of Higher-order Cumulants Higher order cumulants can change sign near CP. Asakawa, Ejiri, MK, 2009 Stephanov, 2011; Friman, Karsch, Redlich, Skokov, 2011; …

Higher-Order Cumulants STAR 2010~ Enhancement Supression Non-zero non-Gaussian cumulants have been established! General Review: Asakawa, MK, PPNP (2016)

2 nd Order @ ALICE Net charge fluctuation D-measure ALICE, PRL 2013

2 nd Order @ ALICE Net charge fluctuation Net proton fluctuation ALICE, PRL 2013 Rustamov, 2017 p Net-charge fluctuation has a suppression, p but net-proton fluctuation does not. Why? ?

<d N B 2> and < d N p 2 > @ LHC ? should have different Dh dependence. MK, presentations GSI, Jan. 2013 Berkeley, Sep. 2014 FIAS, Jul. 2015 GSI, Jan. 2016 … Baryon # cumulants are experimentally observable! MK, Asakawa, 2012

Message Understand 2 nd-order fluctuations @ LHC & top-RHIC 1. Problems in experimental analysis • proper correction of detector’s property 1. Dynamics of non-Gaussian fluctuations 2. A suggestion: chi. B/chi. Q

Detector-Response Correction True distribution Observed distr. Efficiency loss Particle miss. ID p Correction assuming a binomial response Bialas, Peschanski (1986); MK, Asakawa (2012); Bzdak, Koch (2012); …. But, the response of the detector is not binomial…

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.

Proton vs Baryon Cumulants MK, Asakawa, 2012; 2012 Experiments Many theories proton number cumulants baryon number cumulants measurement with 50% efficiency loss p Clear difference b/w these cumulants. p Isospin randomization justifies the reconstruction of <NBn>c via the binomial model. p Similar problem on the momentum cut…

Fragile Higher Orders Ex. : Relation b/w baryon & proton # cumulants (with approximations) MK, Asakawa, 2012 genuine info. Poisson noise Higher orders are more seriously affected by efficiency loss.

Non-Binomial Correction p Response matrix Nonaka, MK, Esumi (2018) Reconstruction for any R(n; N) with moments of R(n; N) p Caveats: p R(n; N) describes the property of the detector. p Detailed properties of the detector have to be known. p Multi-distribution function can be handled. p Huge numerical cost would be required. p Truncation is required in general: another systematics?

Result in a Toy-Model Binomial w/ multiplicity-dependent efficiency Holtzman, Bzdak, Koch (16) Input P(N): Poisson(l=40) Red: true cumulant True cumulants are reproduced within statistics! Nonaka, MK, Esumi (2018) Reconstructed cumulants

Message Understand 2 nd-order fluctuations @ LHC & top-RHIC 1. Problems in experimental analysis • proper correction of detector’s property 1. Dynamics of non-Gaussian fluctuations 2. A suggestion: chi. B/chi. Q

Why Conserved Charges? p Direct comparison with theory / lattice p Strong constraint from lattice p Ignorance on spatial volume of medium p Slow time evolution

Why Conserved Charges? p Direct comparison with theory / lattice p Strong constraint from lattice p Ignorance on spatial volume of medium p Slow time evolution AHM-JK (2000) Ejiri-Karsch-Redlich D-measure Ratio of cumulants S is model dependent Experimentally difficult

Time Evolution of Fluctuations Detector ic n o dr Ha P G Q Distributions in DY and Dy are different due to “thermal blurring”. Ohnishi, MK, Asakawa, PRC(2016) Fluctuations in DY continue to change until kinetic f. o.

Time Evolution of Fluctuations Quark-Gluon Plasma Hadronization Freezeout Variation of a conserved charge is achieved only through diffusion. The larger Dh, the slower diffusion

Thermal distribution in y space nucleon pion Blast wave squeezes the distribution in rapidity space Ohnishi, MK, Asakawa, PRC (2016) • pions • nucleons • assume Bjoroken picture • blast wave • flat freezeout surface

Dh Dependence Initial condition (before blurring) Ohnishi, MK, Asakawa, PRC (2016) Cumulants after blurring no e-v-e fluctuations Cumulants after blurring can take nonzero values At Dy=1, the effect is not well suppressed • pions • nucleons

Very Low Energy Collisions p Large contribution of global charge conservation p Violation of Bjorken scaling detector Careful treatment is required to interpret fluctuations at low beam energies! Many information should be encoded in Dh dep.

Evolution of Conserved-Charge Fluctuations Equations describing transport of n: p Diffusion Equation p Stochastic Diffusion Equation (SDE) p SDE with non-linear terms

Analysis of 2 nd-order Cumulant Sakaida+ (2017) Evolution of baryon number density Stochastic Diffusion Equation : parameters characterizing criticality p Analytic solution is obtained. p Study 2 nd order cumulant & correlation function.

Parametrizing D(t) and c(t) (critical point) p. Critical behavior • 3 D Ising (r, H) • model H Berdnikov, Rajagopal (2000) Stephanov (2011); Mukherjee+(2015) p. Temperature dep. critical slowing down critical enhancement

Crossover / Cumulant ALICE PRL 2013 pmonotonically decresing Analytic result monotonically increasing monotonically decreasing

Critical Point / Cumulant pnon-monotonic Dy dep. Analytic result non-monotonic See also, Wu, Song ar. Xiv: 1903. 06075

Criticap Point / Correlation Func. pnon-monotonic Dy dep. Analytic result non-monotonic See also, Wu, Song ar. Xiv: 1903. 06075

Away from the CP (critical point) p Signal of the critical enhancement can be clearer on a path away from the CP. Away from the CP Weaker critical slowing down

Extension to Higher-order Cumulants Analyses with 1. Stochastic diffusion equation 2. Diffusion master equation

10~20 fm mesons baryons time kinetic f. o. chem. f. o. hadronize Baryons in Hadronic Phase e k i l e v a h e b s n Baryo r e t a w n i s n e l l o p n a i n w o r B

(Non-Interacting) Brownian Particle Model Initial condition (uniform) cumulants: random walk diffusion master equation: MK+, PLB(2014) probabilistic argument: Ohnishi+, PRC(2016)

(Non-Interacting) Brownian Particle Model Initial condition (uniform) cumulants: diffusion distance random walk Study DY dependence Poisson distribution diffusion master equation: MK+, PLB(2014) probabilistic argument: Ohnishi+, PRC(2016)

4 th Order Cumulant Before the diffusion MK+ (2014) MK (2015)

MK+ (2014) MK (2015) 4 th Order Cumulant After the diffusion (rough estimate) p Cumulant at small Dh is modified toward a Poisson value. p Non-monotonic behavior can appear.

Time Evolution of Fluctuations ic n o dr Ha P G Q As a result of a simple random walk… Detector

Rapidity Window Dep. 4 th-order cumulant Initial Conditions MK+, 2014 MK, 2015 STAR Collab. (X. Luo, CPOD 2014) p Is non-monotonic Dh dependence already observed? p Different initial conditions give rise to different characteristic Dh dependence. Study initial condition Finite volume effects: Sakaida+, PRC 90 (2015)

SDE with Non-Linear Terms p Higher order cumulants Nahrgang, Bluhm, Schaefer, Bass, PRD (2019); Pihan, Touroux, Nahrgang, Bluhm, Sami, MK, in prep. Time evolution of 4 th cumulant can be described. p 1 st order transition Domain formation and peak structure in the correlation function are found.

Message Understand 2 nd-order fluctuations @ LHC & top-RHIC 1. Problems in experimental analysis • proper correction of detector’s property 1. Dynamics of non-Gaussian fluctuations 2. A suggestion: chi. B/chi. Q

2 nd Order @ ALICE Net charge fluctuation Net proton fluctuation ALICE, PRL 2013 Rustamov, 2017 p Net-charge fluctuation has a suppression, p but net-proton fluctuation does not. Why? ?

<d N B 2> and < d N p 2 > @ LHC ? should have different Dh dependence. MK, presentations GSI, Jan. 2013 Berkeley, Sep. 2014 FIAS, Jul. 2015 GSI, Jan. 2016 … Baryon # cumulants are experimentally observable! MK, Asakawa, 2012

A Suggestion Net charge fluctuation p Construct p Then, take ratio ALICE, PRL 2013 p Compare it with lattice Net proton fluctuation Hot. QCD preliminary Rustamov, 2017 ü linear T dependence near Tc !! ü only 2 nd order: reliable !!

Prediction LATTICE ALICE Primordial Fluctuation Hot. QCD preliminary before continuum limit Resonance decays 1. 6 Δη dependence for tracing back the history!

Summary p Large ambiguity in the experimental analysis of higherorder cumulants. p Fluctuations observed in HIC are not in equilibrium. p Plenty of information encoded in rapidity window dependences p 2 nd-order cumulant (correlation function) already contains interesting information. p Future p Evolution of higher-order cumulants around the critical point / 1 st transition p combination to momentum (model-H) p more realistic model (dimension, Y dependence, …)

Resonance Decay Neutral Particles Decay into charged particles

Resonance Decay Neutral Particles Decay into charged particles The larger Dh, the slower diffusion.