Charge fluctuations in heavy ion collisions and QCD phase diagram

K. Redlich, Uni Wroclaw & EMMI

crossover HIC CP or Triple Point Qarkyonic Matter    QCD phase boundary, its O(4) „scaling” & relation to freezeout in HIC Moments and probablility distributions of conserved charges as probes of the O(4) criticality in QCD Xu Nu -STAR data & expectations with: P. Braun-Munzinger, B. Friman F. Karsch, V. Skokov



T

Particle yields and their ratio, as well as LGT results at 

T c

are well described by the Hadron Resonance Gas Partition Function . Budapest-Wuppertal LGT data O(4) universality

T T c



c

1 0.006

. 2 HRG model Thermal and chemical equilibrium: H. Barz, B. Friman, J Knoll & H.Schultz P. Braun-Munzinger, J. Stachel, Ch. Wetterich C. Greiner & J. Noronha-Hostler, ……..

O(4) scaling and critical behavior



F

singular part of the free energy density 

F reg



F S

with

F S t

with 

t



T



T c T c

 

T c

2 Phase transition encoded in  

d

1/  

t

, 

h

1/

b

    the “equation of state”    

F s



h

 pseudo-critical line  

h

1 /   

h z



th

 1/  F. Karsch et al

h

)

O(4) scaling of net-baryon number fluctuations

  The fluctuations are quantified by susceptibilities

B

   (

n



B

4

n

) : 

c n

with

P



P reg



P Singular

 

B



B

From free energy and scaling function one gets   

r



r



c h

2 

c h

2

n n

/2

f

 ( /2)

f

 ( ) (

z

)

for

for

  0   0

and n even

 Resulting in singular structures in n-th order moments   

n

 3

at

  0 since    0.2

in O(4) univ. class

Effective chiral models and their non-perturbative thermodynamics: Renormalisation Group Approach

S

   1/ 0

T

 

V

3 [ (  ( , * ) 

A

 4 )

q



V

i nt ( )  

q



q q



L

* ) ]

V

int   through:  Nambu-Jona-Lasinio model PNJL chiral model K. Fukushima ; C. Ratti & W. Weise; B. Friman , C. Sasaki ., ….

  coupling with meson fileds PQM chiral model B.-J. Schaefer, J.M. Pawlowski & J. Wambach; B. Friman, V. Skokov, ...

FRG thermodynamics of PQM model: B. Friman, V. Skokov, B. Stokic & K.R.

Kurtosis of net quark number density in PQM model

V. Skokov, B. Friman &K.R.

 For

T



T c

the assymptotic value due to „ confinement” properties 9

c

4 /

c

2

P q q T

4  2

N f N c

2   3

m q T

  2

K

2   3

m q T

  cosh 3 

q T c

4 /

c

2  9 

P q q T

4 For

T



c

4 /

c

2 

T c

1

c

[ 2  2    4  1 6  6 /  2 2  7  2 180 ]  Smooth change with a very weak dependence on the pion mass

Ratio of cumulants at finite density

R

4,2 

c

4 /

c

2

HRG HRG Deviations of the ratios of odd and even order cumulants from their asymptotic, low

c

/

c



c

/

c

 9

with

 /

T

and the cumulant order Properties essential in HIC to discriminate the phase change by measuring baryon number fluctuations !

Comparison of the Hadron Resonance Gas Model with STAR data

 Frithjof Karsch & K.R.

 

B

(2) (1)

B

 coth( 

B

  

B B

(4) (2)  1 RHIC data follow generic properties expected within HRG model for different ratios of the first four moments of baryon number fluctuations  (3) 

B B

(2)  tanh( 

B

Error Estimation for Moments Analysis : Xiaofeng Luo arXiv:1109.0593v

Ratio of higher order cumulants

Deviations of the ratios from their asymptotic, low T-value, are increasing with the order of the cumulant Properties essential in HIC to discriminate the phase change by measuring baryon number fluctuations !

Fluctuations of 6th and 8th order moments exhibit strong variations from HRG predictions: Their negative values near chiral transition to be seen in heavy ion collisions at LHC & RHIC

The range of negative fluctuations near chiral cross-over: PNJL model results with quantum fluctuations being included : These properties are due to O(4) scaling , thus should be also there in QCD. 10

Theoretical predictions and STAR data

Deviation from HRG if freeze-out curve close to Phase Boundary/Cross over line

11

L. Chen, BNL workshop, CPOD 2011 STAR Data Lattice QCD Polyakov loop extended Quark Meson Model Strong deviations of data from the HRG model (regular part of QCD partition function) results: Remnant of O(4) criticality!!??

STAR Preliminary

Moments obtained from probability distributions

 Moments obtained from probability  distribution 

N k

 

N N k

Probability quantified by all cumulants

P

 1 2  2  0 

dy

exp [

i yN

  (

iy

) ] Cumulants generating function:      )   In statistical physics

P

(

N

) 

Z C

(

N

)

e Z GC



N T

 ) ]  

k



k y k

Probability distribution of the net baryon number

 For the net baryon number P(N) is described as Skellam distribution

P



B

 

N

/ 2

I N

(2

B B B B

)]

B

,  P(N) for net baryon number N entirely given by measured mean number of

B

(

T f



f

Chemical Freezeout

Comparing HRG Model with Preliminary STAR data:

efficiency uncorrected

Data presented at QM’11 Data described by Skellam distribution: No sign for criticality

Observed schrinking of the probability distribution already expected due to deconfinement properties of QCD In the first approximation the 

B

quantifies the width of P(N)  exp( 

N

2 / 2

VT

3 

B

) HRG LGT hotQCD Coll.

Similar: Budapest-Wuppertal Coll At the critical point ( CP ) the width of P(N) should be larger than expected in 

Conclusions:

  Probability distributions and higher order cumulants are excellent probes of O(4) criticality in HIC Hadron resonance gas provides reference for O(4) critical behavior in HIC and LGT results     value as expected at the O(4) pseudo-critical line Deviation of P(N) from HRG seems to set in at

s

 39

GeV