QCD Phase Diagram in Polyakov-NJL Model

Wei-jie Fu

ITP, Chinese Academy of Science

August 11, 2009　

Workshop on RHIC Physics and CSR Physics at Weihai

Outline

Introduction The PNJL Model Numerical Results Inhomogeneous Phases Summary

Introduction

A semiquantitative QCD phase diagram

In term of temperature and density (chemical potential)

Experiments and observations: RHIC (temperature), Compact stars (density).

The Frontiers of Nuclear Science, A Long Range Plan 2007

QCD critical point

Phenomenological Models

Lattice Simulations

1. Reweighting2. Imaginary ch

emical potential

3.Taylor expansion

4…….

M. A. Stephanov, PoS, LAT2006, 024, 2006

An example: Taylor Expansion

C. R. Allton et al., PRD. 71, 054508, 2005

Does the QCD critical point really exist?

O. Philipsen, arXiv: 0808.0672, 2008

The PNJL Model

The 2+1 flavor NJL model with a Polyakov-loop is given by

where

is the Polyakov-loop effective potential, which is as function of the Polyakov-loop

Two kinds of Polyakov-loop effective potential

and

The other is

and

The Polyakov-loop effective potential as function of the real part and the imaginary part of the Polyakov-loop at two values of the temperature:

H. Hansen, et al., PRD. 75, 065004, 2007

Phase Transition at Finite Temperature

Phase Transition at Finite Temperature and Nonzero Chemical Potential

Phase Diagram (Effects of Flavor-mixing and Quark Current Mass)

Wei-jie Fu, Zhao Zhang, Yu-xin Liu., PRD. 77, 014006, 2008

Mesonic Excitations at Finite Temperature

Schematic representation of the effective interaction for the pseudoscalar modes in the RPA.

The pseudoscalar polarization function is

and the scalar polarization function is

Goldberger-Treiman（ GT） relation on the quark level at finite temperature:

Gell-Mann--Oakes--Renner （ GOR） relation at finite temperature:

Several critical temperatures

Wei-jie Fu, Yu-xin Liu., PRD. 79, 074011, 2009

The effect of color confinement screens the effect of temperature below the critical temperature

Scattering Lengths

Wei-jie Fu, Yu-xin Liu., PRD. 79, 074011, 2009

P. Deb et al., PRC 79,055208, 2009

P. Deb et al., PRC 79,055208, 2009

Inhomogeneous Phases

D. Nickel, arXiv: 0906.5295, 2009

Ginzburg-Landau Expansion

D. Nickel, arXiv: 0902.1778, 2009

Summary

The QCD phase diagram is calculated in the 2+1 flavor PNJL model. We have also investigated the dependence of the location of the QCD critical point on the strength of the ’t Hooft flavor-mixing interaction and the current mass of strange quarks.

Mesonic excitations is studied in the PNJL model. We find that the effect of color confinement screens the effect of temperature below the critical temperature.

Could the Polyakov dynamics affect the inhomogeneous phases, and how?

Thank you !