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Diffusion of Non- Gaussianity in Heavy Ion Collisions. Masakiyo Kitazawa ( Osaka U. ). MK, Asakawa , Ono, arXiv:1307.2978. SQM , Birmingham, 2 3, July 2013. Beam-Energy Scan. STAR 2012. high. beam energy. T. low. Hadrons. Color SC. m. 0. Fluctuations .

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diffusion of non gaussianity in heavy ion collisions

Diffusion of Non-Gaussianityin Heavy Ion Collisions

Masakiyo Kitazawa

(Osaka U.)

MK, Asakawa, Ono, arXiv:1307.2978

SQM, Birmingham, 23, July 2013

beam energy scan
Beam-Energy Scan

STAR 2012

high

beam energy

T

low

Hadrons

Color SC

m

0

fluctuations
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)
conserved charges theoretical advantage
Conserved Charges : Theoretical Advantage
  • Definite definition for operators
  • as a Noether current
  • calculable on any theory

ex: on the lattice

conserved charges theoretical advantage1
Conserved Charges : Theoretical Advantage
  • Definite definition for operators
  • as a Noether current
  • calculable on any theory

ex: on the lattice

  • Simple thermodynamic relations
  • Intuitive interpretation for the behaviors of cumulants

ex:

Asakawa, Ejiri, MK, 2009

conserved charge fluctuations
Conserved Charge Fluctuations

RBC-Bielefeld ’09

Cumulants of NB and NQ are suppressedat high T.

Asakawa, Heintz, Muller, 2000; Jeon, Koch, 2000;

Ejiri, Karsch, Redlich, 2006; Asakawa, Ejiri, MK, 2009;

Friman, et al., 2011; Stephanov, 2011

proton cumulants @ star bes
Proton # Cumulants @ STAR-BES

STAR,QM2012

CAUTION!

Something

interesting??

proton number

baryon number

MK, Asakawa, 2011;2012

charge fluctuation @ lhc
Charge Fluctuation @ LHC

ALICE, PRL110,152301(2013)

D-measure

  • D ~ 3-4 Hadronic
  • D ~ 1 Quark

significant suppression

from hadronic value

at LHC energy!

is not equilibrated at freeze-out at LHC energy!

dh dependence @ alice
Dh Dependence @ ALICE

ALICE

PRL 2013

t

Dh

z

rapidity window

time evolution of cc
Time Evolution of CC

t

Dy

NQ

z

Dy

  • Variation of a conserved charge in Dy is achieved only through diffusion.
  • The larger Dy, the slower diffusion
dh dependence @ alice1
Dh Dependence @ ALICE

ALICE

PRL 2013

t

Dh

z

Dh dependences of fluctuation observables

encode history of the hot medium!

Higher-order cumulants as

thermometer?

d n b 2 and d n p 2 @ lhc
<dNB2> and <dNp2 > @ LHC ?

should have different Dh dependence.

Baryon # cumulants are experimentally observable! MK, Asakawa, 2011;2012

d n b 2 and d n p 2 @ lhc1
<dNB2> and <dNp2 > @ LHC ?

should have different Dh dependence.

Baryon # cumulants are experimentally observable! MK, Asakawa, 2011;2012

d n b 2 and d n p 2 @ lhc2
<dNB2> and <dNp2 > @ LHC ?

should have different Dh dependence.

Baryon # cumulants are experimentally observable! MK, Asakawa, 2011;2012

d n q 4 @ lhc
<dNQ4> @ LHC ?

How does behave as a function of Dh?

enhancement

suppression

or

three non s
Three “NON”s

Physics of non-Gaussianity in heavy-ion

is a particularproblem!

Non-Gaussianitiy is

irrelevant in large systems

  • Non-Gaussian
  • Non-critical
  • Non-equilibrium

critical enhancement is

not observed in HIC so far

Fluctuations are not

equilibrated in HIC

three non s1
Three “NON”s

Physics of non-Gaussianity in heavy-ion

is a particularproblem!

Non-Gaussianitiy is

irrelevant in large systems

  • Non-Gaussian
  • Non-critical
  • Non-equilibrium

critical enhancement is

not observed in HIC so far

Fluctuations are not

equilibrated in HIC

It is impossible to directly extend the theory

ofhydro fluctuationsto treat higher orders.

diffusion master equation
Diffusion Master Equation

Divide spatial coordinate into discrete cells

probability

diffusion master equation1
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
Solution of DME

1st

initial

Deterministic part  diffusion equation

at long wave length (1/a<<k)

Appropriate continuum limit with ga2=D

solution of dme1
Solution of DME

1st

initial

Deterministic part  diffusion equation

at long wave length (1/a<<k)

Appropriate continuum limit with ga2=D

2nd

Consistent with stochastic diffusion eq.

(for smooth initial condition)

Shuryak, Stephanov, 2001

net charge number
Net Charge Number

Prepare 2 species of (non-interacting) particles

Let us investigate

at freezeout time t

time evolution in hadronic phase
Time Evolution in Hadronic Phase

Hadronization(initial condition)

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

suppression owing to

local charge conservation

strongly dependent on

hadronization mechanism

time evolution in hadronic phase1
Time Evolution in Hadronic Phase

Hadronization(initial condition)

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

Time evolution via DME

suppression owing to

local charge conservation

strongly dependent on

hadronization mechanism

Freezeout

dh dependence at freezeout
Dh Dependence at Freezeout

Initial fluctuations:

2nd

4th

parameter

sensitive to

hadronization

dh dependence at freezeout1
Dh Dependence at Freezeout

Initial fluctuations:

2nd

4th

parameter

sensitive to

hadronization

d n q 4 @ lhc1
<dNQ4> @ LHC
  • boost invariant system
  • small fluctuations of CC at hadronization
  • short correlation in hadronic stage

Assumptions

1

4th-order cumulant will besuppressed at LHC energy!

Dh dependences encode various information on the dynamics of HIC!

0.5

summary
Summary

Plenty of physics in Dhdependences of

various cumulants

  • Diagnosing dynamics of HIC
  • history of hot medium
  • mechanism of hadronization
  • diffusion constant

Physical meanings

of fluctuation obs.

in experiments.

summary1
Summary

Plenty of physics in Dhdependences of

various cumulants

  • Diagnosing dynamics of HIC
  • history of hot medium
  • mechanism of hadronization
  • diffusion constant

Physical meanings

of fluctuation obs.

in experiments.

Search of QCD Phase Structure

open questions future work
Open Questions & Future Work
  • Why the primordial fluctuations are observed only at LHC, and not RHIC ?
  • Extract more information on each stage of fireballs using fluctuations
  • Model refinement
  • Including the effects of
  • nonzero correlation length / relaxation time
  • global charge conservation
  • Non Poissonian system  interaction of particles
dh dependence at star
Dh Dependence at STAR

STAR, QM2012

decreases as Dh becomes larger at RHIC energy.

chemical reaction 1
Chemical Reaction 1

x: # of X

a: # of A (fixed)

Master eq.:

Cumulants with fixed initial condition

equilibrium

initial

chemical reaction 2
Chemical Reaction 2

2nd

3rd

4th

Higher-order

cumulants

grow slower.

time evolution in hic
Time Evolution in HIC

Quark-Gluon Plasma

Hadronization

Freezeout

hydrodynamic fluctuations
Hydrodynamic Fluctuations

Landau, Lifshitz, Statistical Mechaniqs II

Kapusta, Muller, Stephanov, 2012

Diffusion equation

Stochastic diffusion equation

Stochastic Force

determined by fluctuation-dissipation relation

d h dependence
Dh Dependence

Shuryak, Stephanov, 2001

  • Initial condition:
  • Translational invariance

equilibrium

initial

equilibrium

initial

non gaussianity in fluctuating hydro
Non-Gaussianity in Fluctuating Hydro?

It is impossible to directly extend the theory

ofhydro fluctuations to treat higher orders.

  • No a priori extension of FD relations to higher orders

Markov process+continuous variable

  • Theorem

Gaussian random force

cf) Gardiner, “Stochastic Methods”

event by event analysis @ hic
Event-by-Event Analysis @ HIC

Fluctuationscan be measured by e-by-e analysis in HIC.

STAR, PRL105(2010)

Detector

non gaussianity
Non-Gaussianity

fluctuations (correlations)

Non-Gaussianity

PLANCK

: statistics insufficient to see non-Gaussianity…(2013)