1

Debye screened

QGP

QCD :

confined

rrV )(

Chiral Condensate

0qq

Quark Potential

r

rrV D )exp(

~)(

0qq

Deconfinement and

Chiral Symmetry restoration

expected within QCD

( , , , )c c cf f fL q q A m(3) (2)c fSU SU

m m 0 symmetry )3(Z Chiral

symmetry )2()2( RL SUSU

HG

Global symmetries

111QSB UUU

2

Phases of QCD and charge fluctuations

quark-gluon plasma

hadron gas color

superconductor

B

Effective Chiral Models and QCD phase diagram: Charge fluctuations - probe of chiral phase transition : how to possibly search for TCP in heavy ion collisions?

T

K. Redlich

m=0O(4) 2nd order

TCP Z(2), 2nd order

1st order

Crossover m=0

(B. Friman, Ch. Sasaki &K.R)

3

Chiral Transformations of QCD-Langrangian

ˆ | , | ,s p p h h p h

qqqq LR )1(2

1)1(

2

155

( )quarq

k a aQCDL q i m qgA q q

L R R Lqq q q q q

L L R Rq D q q D q q D q

Chiral transformations:

Decompose:

Li

LRi

R qeqqeq LR 2/2/

(2) (2)R LSU SUBreaks chiral symmetry: invariant under

(2) ( )RV LSU In QCD vacuum chiral symm. spontaneously broken

33qq fm

L Rq q q

4

Order parameter of chiral symmetry restoration

Consider chiral susceptibility:

to determine the position of

the chiral phase transition:

qq { csymmetry0 restored T >Tchiral

c symmet0 brokry T<n Techiral

2

2

( , , )qq

q

q

P T m

m

Measures dynamically generated „constituent” quark mass: T=0 quarks „dress” with gluons

in hot medium dressing „melts”

effective quark mass shift

2 2( )qq qq

5

Extendet PNJL model and its mean field dynamics

2 2 25

2

( )

(3

4

)

( ) [( ) ( ) ] ( )

( ) ( [ ], [ ], )

1( exp[ ( , )])

SNJL

c

V

q I

S

VV

L q i m q qq qi q q q

q q q q q q U A A T

Tr P i d A x

G

NiA

G

D

G

D

Thermodynamic potential: mean-field approximation

, ,S VS V VG G G : Strength of quarks interactions in scalar and vector sector

Polyakov loop

( , )( , , , , , )u d q IT M dynamical (u,d)-quark masses, shifted chemical , :u dM qq

ipotentials and thermal averages of Polyakov loops

obtained from the stationary conditions:

( , ) / 0iT x x

6

Chiral Symmetry Restoration – Order Parameterd

isco

nti

nu

ity

Divergence of the chiral susceptibility at the 2nd order transition and at the TCP

Discontinuity of the chiral susceptibility: at the 1st order transition

dis

con

tin

uit

y

discontinuity

Fixed q

Different Slopes

7

Generic Phase diagram for effective chiral Lagrangians

Generic structure of the

phase diagram as expected

in different chiral models:

see eg. Y. Hatta & T. Ikeda;

M. Stephanov, K. Rajagopal, Fuji,.. Quantitative properties of the

phase diagram and the position of

TCP are strongly model dependent

Large no TCP at finite

temperature !VG

TCP

2nd order transition

1st order transition

8

Effective Thermodynamic Potentials

Flattening of the potential at TCP: indeed expanding thermodynamic near

0M

62 4

26

4( , , ) ( , ) ( , ) ( , )aT TM M Ma MT a T

at TCP

Landau – Ginzburgpotential

finds: 42

42

( , ) 0 ( , ) 0

( , ) 0 ( , ) 0

c c c c

c c c c

a

a

T T

T T

a

a

2nd order TCP

2nd order

1st order

cT T

cT T

cT TTCPT T

cT T

cT T

cT T

6 0a

9

Susceptibilities of conserved charges

Net quark-number ,isovector

and electric charge

fluctuations

21 1 1

36 4 6Q q Iq I

P

2

2II

P

2

2qq

P

qQ

I

2 2A A A

No mixing of isospin density with thesigma field due to isospin conservation Hatta & Stephanov

300q MeV

305TCPq MeV

310q MeV

TCP

1st order

2nd order

10

Critical structure of the quark susceptibility

Quark number susceptibility at

Divergence of quark susc. at TCP is

directly related with the flattening ( ) of the thermodynamic potential

2(

(0

0

)0)

( )

1

( )2

2VS

q q SS sG

G

qS

qq

m

Scalar susceptibility

qVS

qq

vector-scalar susc.

0VG

42 4 6

2 6M aaa M M 4 0a

(0)4

(0

2

)

1 2

S

S S

V

MG a

M

4

1q a

{= finite at 2nd order

at TCP

Change of the universality class

11

The universality class and T-dependence of M

Criticality of

directly related with the scalling of and with

(0) 2(0)

(

2

0) 2

( )2

1 2VS

q q SS s

GG

M

m

1 2 20 2

2 1/ ( )|M cmD M a T T

2M { at TCP

2M 2m ( )cT T

at 2nd1( )cT T

| |TCPT T

The critical exponents of determined

by the slope of the order parameter

as a function of near

qM

TcT

| |cT T

1| |cT T

2 42 ( ) ( )a T M O M

TCP

2nd

12

Critical exponents near TCP

1 1

2 | |TCPT T

The strength of singularity at TCP depends on direction in plane( , )BT

1( )Cq T PT T along 1st order line

any direction not parallel

along 2nd order line 11

( )2 Tq CPT T

1/ 2( )Tq CPT T

Ising Model 1.25

Going beyond mean field:B.-J. Schaefer & J. Wambach

| |q TCPT T

Z(2) univer. class

1| |TCPT T

11| |

2 TCPT T

1/ 2| |TCPT T

(2 ) 0| |ndcT T

13

Free energy: expected 2-order transition in 3-d, O(4)

universality class:

1( )1 2( , , ) ( )Analitic q SiI ngularF b tF F T b

2 ,( ) ~ 0F t t and small 2

| |: q

c c

cTTscaling field c

T Tt

Net Quark

Fluctuations

2( )qN

1 0

0 0

0

q

qt for vanishes t

t for cusp structure t

4( )qN (2 )

0

0 0

0

q

qt

t fo

for vanishes t

r diverges t

2 (( 2) 2)q diverges at Z nd order p tN oin

(2)Z

(4)O

1st order

T

Quark fluctuation and O(4) universality

/q T fix

14

How to search for TCP

2/q T

2

2

2(1 )

3 qfN

T

( ) /q TMe

LGT-Bielefeld

An increase of is only necessary but not sufficient condition to verify the existence of TCP

2/q T

PNJL model, Sasaki et al..0qm

15

Quark and isovector fluctuations along critical line

sensitive probes of TCP( , ( ))q c c cT T Non-singular behavior at TCP of ( , ( ))I c c cT T

Non-monotonic behavior of the net quark susceptibility in the vicinity to TCP

16

Critical region near TCP

The critical window near TCP is elongated on the critical line

This window is quite

narrow in the direction

of fixed T and corresponds to

In heavy ion collisions

the

corresponds to change in

3q MeV

30T MeV

1s GeV

T

20q MeV

Sfix

B

17

Finite quark mass and QCD phase diagram

0qm

surface of 1st order transitions

line of end pointCEP

TCP

0qm

T

q

qm

crossover line 2nd

qq

T

0qm

0qm

acts as an external magnetic field and destroys the 2nd order transition preserving the 1st order below CEP

0qm

0qm

changes the effective thermodynamic potential 2 4 6

2 4 6( , , , )q qT M m a M a MM M ma

consequently the modification of the critical properties is to be expected:

18

Conclusions

The effective chiral Lagrangians provide a powerful tool (due to universality) to study the critical consequences of chiral symmetry restoration in QCD, however

The quantitative verification of the phase diagram and the existence of the CEP/TCP in QCD requires the first principle LGT calculations and CBM experiment

19

Phase boundary of the fixed energy density versus chemical freezeout

30.6c

GeV

fm

Splitting of the chemical freeze-out and the phase boundary surface appears when the densities of mesons and baryons are comparable?

particles production processes

0.77m GeV 0.14m GeV

LGT (Allton et al..)

1meson

baryon

MesonDominated

BaryonDominated

(6 8)NNs GeV

Z. Fodor et al..

: QGP hadronization

(6 8)NNs GeV : Hadronic rescattering

R. Gavai, S. Gupta

20

Charge Fluctuations Near Deconfinement

S.N Jeon & V. KochE. Shuryak & M. Stephanov M. Asakawa. U. Heinz & B. Muller ….

Mass and quantum numbergap between confinedand deconfined phase

2( )x x x