Polyakov loop, diquarks, and the two-flavor phase diagram

Abstract

An updated version of the PNJL model is used to study the thermodynamics of N f 2 quark flavors interacting through chiral four-point couplings and propagating in a homogeneous Polyakov loop background. Previous PNJL calculations are extended by introducing explicit diquark degrees of freedom and an improved effective potential for the Polyakov loop field. The mean field equations are treated under the aspect of accommodating group theoretical constraints and issues arising from the fermion sign problem. The input is fixed exclusively by selected pure-gauge lattice QCD results and by pion properties in vacuum. The resulting T; phase diagram is studied with special emphasis on the critical point, its dependence on the quark mass and on Polyakov loop dynamics. We present successful comparisons with lattice QCD thermodynamics expanded to finite chemical potential .

Inhomogeneous chiral condensates

“…When dealing with inhomogeneous phases, and¯ are naturally expected to be spatially dependent, presumably following the density profile in some way. 23 However, this would not only complicate the calculations, it would also create new ambiguities, because the standard parametrizations of the Polyakov-loop potential [136,142,128], do not contain kinetic contributions (i.e., gradient terms) which in principle should exist but are unknown. In the analysis of Ref.…”

“…In fact, some parametrizations of the potential, like those given in Refs. [128,137,142], have contributions from the Haar measure, which are not simply proportional to the number of gluons. Without Polyakov loop, the first replacement leaves the NJL-model gap equation, and hence the phase diagram N c -independent in mean-field approximation.…”

“…Furthermore, a local potential U( ,¯ ) is added to the thermodynamic potential, which is essentially constructed to reproduce ab-initio results of pure Yang-Mills theory at finite temperature [136,142]. When dealing with inhomogeneous phases, and¯ are naturally expected to be spatially dependent, presumably following the density profile in some way.…”

Quark–hadron matter at finite temperature and density in a two-color PNJL model

“…Dropping the sigma-diquark mixing terms in the full mass matrix (B.8), one arrives at an analytical expression for ω( q ) of the Bogoliubov mode. Consider the reduced mass matrix 15) and solve the dispersion relation det D(ω, q ) = 0 with respect to ω( q ) for the lowest mode:…”

“…The NJL model is further generalized by introducing the Polyakov loop to account for important thermodynamical aspects of color confinement [10][11][12]. This PNJL model is by now widely used for the discussion of quark-hadron matter at finite temperature and density [13][14][15][16][17]. The PNJL model results can be compared directly with lattice QCD at finite temperature and zero baryon density.…”