T

B

Hadronic matter

Quark-Gluon Plasma

Chiral symmetrybroken

Chiral symmetryrestored

LH

C

A-A collisions fixed s

x

1st principle calculations: perturbation theory pQCD LGT

, :QCDT , :QCDT

:q T

QCD Phase diagram and its verification in HICKrzysztof Redlich University of Wroclaw

Collaboration: P. Braun-Munzinger, B. Friman , F. Karsch, K. Morita, C. Sasaki & V. Skokov

Chiral transition and O(4)

pseudo-critical line in LGT Probing O(4) criticality with Charge

fluctuations

theoretical expectations and

STAR data Deconfinement in SU(N) pure gauge

theory and in QCD from LGT

Collaboration: B. Friman, O. Kaczmarek,, F. Karsch, K. Morita, Pok. Man Lo, C. Sasaki & V. Skokov

QCD phase diagram and the O(4) criticality

In QCD the quark masses are finite: the diagram has to be modified

Expected phase diagram in the chiral limit, for massless u and d quarks:

Pisarki & Wilczek conjecture

TCP: Rajagopal, Shuryak, Stephanov Y. Hatta & Y. Ikeda

TCP

The phase diagram at finite quark masses

The u,d quark masses are small

Is there a remnant of the O(4) criticality at the QCD crossover line?

CPAsakawa-YazakiStephanov et al., Hatta & Ikeda

At the CP: Divergence of Fluctuations, Correlation Length and Specific Heat

The phase diagram at finite quark masses

Can the QCD crossover line appear in the O(4) critical region?

YES, It has been confirmed in LQCD calculations

TCP

CP

LQCD results: BNL-Bielefeld

Critical region

Phys. Rev. D83, 014504 (2011)Phys. Rev. D80, 094505 (2009)

O(4) scaling and magnetic equation of state

Phase transition encoded in

the magnetic equation

of state

Pqq

m

11/

/( ) ,sf z tz m

qq

m

pseudo-critical line

1/

qq

m

F. Karsch et al

universal scaling function common forall models belonging to the O(4) universality class: known from spin modelsJ. Engels & F. Karsch (2012)

mz

QCD chiral crossover transition in the critical region of the O(4) 2nd order

O(4)/O(2)

11 (2 ) /( , , ) ( , )Sq IRP T b b t bPP h

6

Due to expected O(4) scaling in QCD the free energy:

Consider generalized susceptibilities of net-quark number

Since for , are well described by the

search for deviations (in particular for larger n) from HRG

to quantify the contributions of , i.e. the O(4) criticality F. Karsch & K. R. Phys.Lett. B695 (2011) 136

B. Friman, et al. . Phys.Lett. B708 (2012) 179, Nucl.Phys. A880 (2012) 48

11 (2 ) /( , , ) ( ( ), )q IR SP T b b t bP hP

Quark fluctuations and O(4) universality class

4( ) ( / )

( / )

n

nB

nB

P Tc

T

(2 /2)/ ( )( )s 0 (| )n nn d h fc z

pcT T

with

( )nRc HRG

( )nSc

( )( )nR

nSc c

( )s 0

(2 )/ ( )| ( )nn ndc h f z

7

Only 3-parameters needed to fix all particle yields

Tests of equlibration of 1st “moments”: particle yields

resonance dominance: Rolf Hagedorn, Hadron Resonance

Gas (HRG) partition function

22ln ( , ) ( ) ( , )

2

iQB WT

i ii hadrons

VT sZ T d e ds s K F m s

T

����������������������������

��������������

Breit-Wigner res.

Re .[ ( , ) ( , )]KB BK

ti

h si

thiiV T TnN n

particle yield thermal density BR thermal density of resonances

Thermal yields and parameters and their energy dependence in HIC

Thermal origin of particle yields in HIC is well justified

A. Andronic, P. Braun-Munzinger & J. Stachel, Nucl. Phys. (06)

Phys.Rev. C73 (2006) 034905 J. Cleymans et al.

P. Braun-Munzinger et al.QM^12

Particle yields and their ratio, as well as LGT results

(F. Karsch, A. Tawfik, S. Ejiri & K.R.) well described by the HRG . A. Andronic et al., Nucl.Phys.A837:65-86,2010.

Budapest-Wuppertal

Chemical freezeout defines a lower bound for the QCD phase boundary

HotQCD Coll.

Quark-meson model w/ FRG approach

Effective potential is obtained by solving the exact flow equation (Wetterich eq.) with the approximations resulting in the O(4) critical exponents

Full propagators with k < q <

q q

Integrating from k= to k= gives a full quantum effective potential

Put k=0(min) into the integral formula for P(N)

B. Stokic, B. Friman & K.R.

S classical

B.J. Schaefer & J. Wambach,;

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

4 2 3 1/ / 9c c c c / T

4,2 4 2/R c cRatios of cumulants at finite density: PQM +FRG

HRG

B. Friman, F. Karsch, V. Skokov &K.R. Eur.Phys.J. C71 (2011) 1694

HRGHRG

0/ pcT T T

STAR data on the first four moments of net baryon number

Deviations from the HRG

Data qualitatively consistent with the change of these ratios due to the contribution of the O(4) singular part to the free energy

4)2

(

(2)B

B

(3)

(2),B

B

S

HR

G

, 1| |p p

p p

HRG HRG

N N

N NS

STAR DATA Phys. Rev. Lett in print

Deviations of the ratios from their asymptotic, HRG values, are increasing with the order of the cumulants

Ratio of higher order cumulants in PQM modelB. Friman, V. Skokov &K.R. Phys. Rev. C83 (2011) 054904

Negative ratio!

4 2/B B 6 2/B B

6 2/B B

HRG

Theoretical predictions and STAR data 14

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

Lattice QCDPolyakov loop extendedQuark Meson Model

STAR Data

STAR Preliminary

L. Chen, QM 12

Strong deviatins of data from the HRG model (regular part ofQCD partition function) results: Remnant of O(4) criticality ?

Polyakov loop on the lattice needs renormalization Introduce Polyakov loop:

Renormalized ultraviolet

divergence

Usually one takes

as an order parameter

151/ V

c

c

0 deconfined T T

0 confined T<T

renren| | qFL e

NL c L 2 / ( )i k NNc e Z N

HotQCD Coll.

To probe deconfinement : consider fluctuations

Fluctuations of modulus of

the Polyakov loop

However, the Polyakov loop

Thus, one can consider fluctuations of the real and the imaginary part of the Polyakov loop.

SU(3) pure gauge: LGT data

R IL L Li

R

I

HotQCD Coll.

Compare different Susceptibilities:

Systematic differences/simi-larities of the Polyakov lopp susceptibilities

Consider their ratios!

Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement

In the deconfined phase

Indeed, in the real sector of Z(3)

Expand modulus

and find:

2 2 2| | | | ( )RL L L

Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) 1AR

0 0withR R RL L L L L

0 0with 0, thusI II IL L L L

2 2( ) , ( )L LR R I IV L V L

Expand the modulus,2

2 20 2

0 0

( )| | (1 )

2R I

R I

L LL L L L

L L

get in the leading order

thus A R

LA

A LR

R

Ratios of the Polyakov loop fluctuations as an excellent probe for deconfinement

In the confined phase

Indeed, in the Z(3) symmetric phase,

the probability distribution is Gaussian

to the first approximation,

with the partition function

consequently

Expand modulus

and find:

Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013) 0.43AR

In the SU(2) case

is in agreement with MC results

Thus and

LA

A LR

R

3 2 2[ ( )( )]R IVT T L LR IZ dL dL e

3 3

1 1,

2 2R IT T

3

1(2 ),

2 2A T

(3) (2 ) 0.4292

SUAR

(2) 2(2 ) 0.363SU

AR

Ratio Imaginary/Real of Polyakov loop fluctuations

In the confined phase for any symmetry breaking operator its average vanishes, thus

and

thus

2 2 0LL L L

LL R I R I

In deconfined phase the ratio of and its value is model dependent

/ 0I R

Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R. , PRD (2013)

LILR

Ratio Imaginary/Real and gluon screening In the confined phase

WHOT QCD Coll. (Y. Maezawa et al.)

and WHOT-coll. identified as the magnetic and electric mass:

Since

,(2

,( ) ) (4 )RR I Idr r C r

2 21/ , 1/RE MI m m

LILR

,( ) ,( ) ,( )( ) ( ) (0)R I R IR cIC L r Lr

,( )

,( ),( ) ( )( )R I

I

m

Ir RR

reC

rTr T

( )R Im

2 2M RE Im m

Phys. Rev. D81 091501 (2010)

316 4 / 0.6PS Vm m

WHOT QCD Coll:

2-flavors of improved Wilson quarks

String tension from the PL susceptibilities

Common mass scale for

In confined phase a natural choose for M

c I RT T

,(2

,( ) ) (4 )RR I Idr r C r

,( ) ( )4R I

rMe

rC

Tr

,( ) ( )R IC r

/M Tbstring tension

2 2 3 1(

/2, )( ) / ( / ) ( )Ic c RT T Tb T T

Pok Man Lo, et al. ( in preparation)

O. Kaczmarek, et al. 99

Polyakov loop and fluctuations in QCD

Smooth behavior for the Polyakov loop and fluctuations

difficult to determine where is “deconfinement”

The inflection point at 0.22decT GeV

HOT QCD Coll

The influence of fermions on the Polyakov loop susceptibility ratio

Z(3) symmetry broken, however ratios still showing deconfinement

Dynamical quarks imply smoothening of the susceptibilities ratio, between the limiting values as in the SU(3) pure gauge theory

Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R.

LA

A LR

R

Change of the slope in the

narrow temperature range signals color deconfinement

/ pcT T

this work

Probing deconfinement in QCD

Kurtosis measures the squared of the baryon

number carried by leading

particles in a medium S. Ejiri, F. Karsch & K.R. (06)

2

2

2 4

1

1

9

PC

BPC

B T T

T TB

Pok Man Lo, B. Friman, (013)O. Kaczmarek, C. Sasaki & K.R.

S. Ejiri, F. Karsch & K.R. (06)

316 4 lattice with p4 fermion action

0.77GeV, =0Bm

S. Ejiri, F. Karsch & K.R. (06) ( , ) ( ) cosh( / )Bq BP T F BT T

HRG factorization of pressure:

4

2

B

B

200 MeVpcT

2 770fN m MeV

Kurtosis of net quark number density in PQM modelV. Skokov, B. Friman &K.R.

For

the assymptotic value

2

24 2

( ) 2 3 3cosh

3qq f q q

c

qP T N m

KT T T

m

N T

due to „confinement” properties

Smooth change with a very weak dependence on the pion mass

cT T9

4 2/ 9c c

For cT T

4

( )qq

P T

T

4 22/ 6 /c c

4 2/c c

4 2 2

2

1 1 7[ ]2 6 180f cN N

T T

Probing deconfinement in QCD

The change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value

In the presence of quarks

there is “remnant” of Z(N)

symmetry in the

ratio, indicating deconfi-

nement of quarks

Pok Man Lo, B. Friman, (013)O. Kaczmarek, C. Sasaki & K.R.

S. Ejiri, F. Karsch & K.R. (06)

316 4 lattice with p4 fermion action

0.77GeV, =0Bm /L LA R

/L LA R

/L LA R

4

2

B

B

200 MeVpcT

Probing deconfinement in QCD

Change of the slope of the ratio of the Polyakov loop susceptibilities appears at the same T where the kurtosis drops from its HRG asymptotic value In the presence of quarks

there is “remnant” of Z(N)

symmetry in the

ratio, indicating deconfi-

nement

Still the lattice finite size effects need to be studied

Pok Man Lo, B. Friman, O. Kaczmarek, C. Sasaki & K.R.

S. Ejiri, F. Karsch & K.R. (06)

0.77GeV, =0Bm /L L

A R

/L LA R

/L LA R

4

2

B

B

Ch. Schmidt

This paper

150 200 T[MeV]

Polyakov loop susceptibility ratios still away from the continuum limit:

The renormalization of the Polyakov loop susceptibilities is still not well described:

Still strong dependence on in the presence of quarks.

N

Ch. Schmidt et al.

Conclusions:

Chiral transition in QCD belong to the O(4) universality class Ratios the Net-charge susceptibilities are excellent probes of the

O(4) chiral crossover in QCD Systematics of the net-proton number fluctuations and their

probability distributions measured by STAR are qualitatively consistent with the expectation, that they are influenced by the O(4) criticality.

Ratios of different Polyakov loop susceptibilities are excellent and novel probe of deconfinement in QCD

There is a coincident between deconfinement and O(4) chiral crossover in QCD at small baryon density