Relation between the Polyakov loop and the chiral order

parameterat strong coupling

Kenji Fukushima

Department of Physics, University of Tokyo

e-mail: fuku@nt.phys.s.u-tokyo.ac.jp

Refs: Phys.Lett.B553, 38 (2003); hep-ph/0303225 to appear in Phys.Rev.D

Objective and Obstacle

The nature of the QCD phase transitions should be determined by the Polyakov loop and the chiral condensate at finite T.

How and why are the deconfinement and chiral phase transition observed on the lattice at the same Tc ?

Model study with both two order parameters.♦ NJL, LSM, Chiral RM, ... Only Chiral Dynamics

♦ PLM, ... Only Polyakov Loop Dynamics

♦ Instanton, ... How to make the string tension?

Strong Coupling Approach

Deconfinement Transition O.K.◊ A.M. Polyakov, Phys.Lett.B72, 477 (1978)

◊ L. Susskind, Phys.Rev.D20, 2610 (1979)

◊ J. Polonyi, K. Szlachanyi, Phys.Lett.B110, 395 (1982)

Chiral Phase Transition O.K.◊ N. Kawamoto, J. Smit, Nucl.Phys.B192, 100 (1981)

◊ H. Kluberg-Stern, A.Morel, B.Petersson, Nucl.Phys.B215 [FS7], 527 (1983)

◊ P.H. Damgaard, N. Kawamoto, K. Shigemoto, Phys.Rev.Lett.53, 2211 (1984)

Deconfinement and Chiral Phase Transition◊ F. Green, F. Karsch, Nucl.Phys.B238, 297 (1984)

◊ A. Gocksch, M. Ogilvie, Phys.Rev.D31, 877 (1985)

◊ E-M. Ilgenfritz, J.Kripfganz, Z.Phys.C29, 79 (1985)

A prosperous model approach based on QCD

Effective Model Study

Effective action

Schematic representation

n

rr

nm

r

LLENN

mmnVnr

mLnLJLS

)()(c

f

,n.n.cc

)(eff

2

1coshlnTr

4

)(),()(2

)dim()(Tr)(Tr],[

m

dE

2

1sinh 1 r = fund. or adj. Quasi Quark

Energy:

Confined mesons propagatingin the spatial directions.

Quasi-quarks exciting thermally along the temporal axis.

Mean-Field Analyses

With imposed (in a confined phase) ;

With assumed (in a deconfined phase) ;

0Trc L

||22

1const.)(

||122

1const.)(

2c(adj.)

mf

c(fund.)mf

NNd

f

NNd

f

In the confined phase ( ), the chiral symmetry must be broken spontaneously ( ) at any temperature.

0Trc L0

vL cTr

12

(adj.)

1(fund.)

)1(4

1)1(4

1

av

dT

av

dT

Chiral phase transition is hindered with the Polyakov loop decreasing.

Parameter Fixing

Two typical cases

a mq m m Td Tc

Parameter I 432 5.7 *140 *770 208 187

Parameter II 333 7.4 *140 597 *270 230

Parameter I ~ Deconfinement DominanceParameter II ~ Simultaneous Transitions (Chiral + Deconfinement)

Chiral Dominance is impossible becausethe chiral phase transition occurs at higher temperature.

(MeV)

Order Parameters

Which curve is responsible for the simultaneous crossovers?

Temperature Slopes

Deconfinement Dominance(Theoretical possibility)

Chiral + Deconfinement(Realistic case)

Susceptibilities

Adjoint Quarks

First order deconfinement transition persists ;

Deconfinement temperature is lowered in the presence of dynamical quarks.

Quark mass dependence is manifested in the chiral order parameter above the deconfinement temperature.

Qualitative agreement with the lattice aQCD result [Karsch-Lutgemeier (’99)]

Further Discussions

The theoretical requirement that the confine phase must have non-vanishing chiral condensate might be tested on the lattice? Simulation with

Deconfinement Dominance would be interesting; we can see two phase transitions separately in the simulations.

Critical End Point in the deconfinement phase transition is located around .

Summary

The effective model with the Polyakov loop and the chiral condensate is investigated.

Simultaneous transitions of deconfinement and chiral restoration is caused in two steps.

□ Chiral restoration (~150MeV) must occur at higher temperature than the deconfinement transition does (in accordance with the theoretical requirement).

□ Deconfinement transition (~270MeV) is originally located at higher temperature.

Physics of confinement plays an important role.