Relation between the Polyakov loop and the chiral order parameter at strong coupling

1. 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

2. 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?

3. 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

4. Effective Model Study • Effective action • Schematic representation r = fund. or adj. Quasi Quark Energy: Quasi-quarks exciting thermally along the temporal axis. Confined mesons propagating in the spatial directions.

5. Mean-Field Analyses • With imposed (in a confined phase); • With assumed (in a deconfined phase) ; In the confined phase (), the chiral symmetry must be broken spontaneously () at any temperature. Chiral phase transition is hindered with the Polyakov loop decreasing.

6. Parameter Fixing • Two typical cases (MeV) Parameter I ~ Deconfinement Dominance Parameter II ~ Simultaneous Transitions (Chiral + Deconfinement) Chiral Dominance is impossible becausethe chiral phase transition occurs at higher temperature.

7. Order Parameters Which curve is responsible for the simultaneous crossovers?

8. Temperature Slopes Deconfinement Dominance (Theoretical possibility) Chiral + Deconfinement (Realistic case)

9. Susceptibilities

10. 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)]

11. 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 .

12. 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.