Diffusion of non-Gaussian
fluctuations of conserved charges
Masakiyo Kitazawa(Osaka U.)
MK, Asakawa, Ono, Phys. Lett. B728 (2014) 386-392;
MK, Nucl. Phys. A942 (2015) 65-96;
Y. Ohnishi et al., in prep.
『熱場の量子論』, YITP, 2015/9/1

Beam-Energy Scan

THadrons
Color SC
0µ

Beam-Energy Scan

STAR 2012

LHC
T

J-PARC

Hadrons
Color SC
0µ

Non-Gaussian Cumulants @ BES
Enhancement?

suppression?

STAR, PRL (early 2014)
STAR, CPOD (Nov., 2014)∆η Dependence @ ALICE
hadronic

ALICE
PRL 2013

D-measuresuppression• D ~ 3-4 Hadronic• D ~ 1-1.5 Quarkt∆η

rapidity windowz

Time Evolution of Fluctuations
Particle # in ∆η
① continues tochange until kinetic
freezeout due todiffusion.
② changes due to aconversion y  ηat kinetic freezeout“Thermal Blurring”

Time Evolution of Fluctuations
Particle # in ∆η
① continues tochange until kinetic
freezeout due todiffusion.
② changes due to aconversion y  ηat kinetic freezeout“Thermal Blurring”

Thermal Blurring

Thermal Blurring
Under Bjorken picture,
coordinate-space rapidityof medium

momentum-space rapidity

coordinate-space rapidityof individual particles

Thermal distribution in η space
nucleon• pions• nucleonswidth (∆y)

pion

Y. Ohnishi+
in preparation• blast wave
• flat freezeout surface

Centrality Dependence

More centrallower T
larger βWeakerblurring

Is the centrality dependence understoodsolely by the thermal blurring at kinetic f.o.?

Centrality Dependence
Assumptions:• Centrality independent
cumulant at kinetic f.o.
• Thermal blurring atkinetic f.o.

 Centrality dep. of blast wave parameters canqualitatively describe the one ofDiffusion + Thermal Blurring,Non-Gaussian Cumulants

theseprocesses

<δNQ4> @ LHC ?
How does
suppression

behave as a function of ∆η?
orenhancement

<δNQ4> @ LHC ?
How does
suppression

behave as a function of ∆η?
orenhancement

How to Introduce Non-Gaussianity?
Stochastic diffusion equation

Fluctuation of n is Gaussian in equilibrium

How to Introduce Non-Gaussianity?
Stochastic diffusion equation

Fluctuation of n is Gaussian in equilibrium
Choices to introduce non-Gaussianity in equil.: n dependence of diffusion constant D(n) colored noise discretization of nour choice
Fluctuations measured in

REMARK: HIC are almost Poissonian.

A Brownian Particle’s Model

Freezeout

Initial distribution + motion of each particle
 cumulants of particle # in ∆η

Time evolution

Hadronization (specific initial condition)

A Brownian Particle’s Model

Freezeout

Initial distribution + motion of each particle
 cumulants of particle # in ∆η

Time evolution

Hadronization (specific initial condition)

10~20fm

mesonsbaryons

kinetic f.o.

chem. f.o.

hadronize

Baryons in Hadronic PhasetimeDiffusion + Thermal BlurringHadronization

diffusion
Kinetic f.o. (coordinate space)blurring
Kinetic f.o. (momentum space)

Total diffusion: Diffusion + thermal blurring = described by a single P(x) Both are consistent with Gaussian  Single Gaussian∆η Dependence: 4th order

MK, NPA (2015)

Initial Condition

Characteristic ∆η dependences!

∆η Dependence: 4th order

MK, NPA (2015)

Initial Condition

at ALICE at ALICE

baryon #∆η Dependence: 3rd order

MK, NPA (2015)

Initial Condition

at ALICE at ALICE

baryon #4th order : Large Initial Fluc.

MK, NPA (2015)

Initial Condition

at ALICE at ALICE

baryon #∆η Dependence @ STAR
from X. Luo, CPOD2014

MK, 2015

Non-monotonic dependence on ∆η ?

Summary

Plenty of information in ∆η and centrality
dependences of various cumulants
and those of non-conserved charges, mixed cumulants…

With ∆η dep. we can exploreprimordial thermodynamics
non-thermal and transport property
effect of thermal blurringFuture Studies
 Experimental side: rapidity window dependences
 baryon number cumulants
 consistency between RHIC and LHC

 Theoretical side: rapidity window dependences in dynamical models
 description of non-equilibrium non-Gaussianity
 accurate measurements on the latticeBoth sides:
 Compare theory and experiment carefully Do not use a fixed ∆η cumulant for comparison!!!

Very Low Energy Collisions
Large contribution of global charge conservation
Violation of Bjorken scaling

detector

Fluctuations at low √s should be interpreted carefully!
Comparison with statistical mechanics would not make sense…

Initial Condition @ Hadronization
Hadronization (initial condition)

 Boost invariance / infinitely long system
 Local equilibration / local correlation

suppression owing tostrongly dependent on
local charge conservation hadronization mechanism

Thermal distribution in η space
nucleonpion

Blast wave squeezes thedistribution in rapidity space

Y. Ohnishi+
in preparation• pions• nucleons• blast wave
• flat freezeout surface

Time Evolution of Fluctuations

Time Evolution of Fluctuations
detector

Particle # in ∆η
① continues tochange until kinetic
freezeout due todiffusion.
② changes due to aconversion y  ηat kinetic freezeout“Thermal Blurring”