Influence of the Polyakov loop on the chiral phase transition in the two flavor chiral quark model

TL;DR

This paper explores how the Polyakov loop influences the chiral phase transition in a two-flavor chiral quark model, analyzing various approximations and resummations to understand the phase diagram at finite temperature and chemical potential.

Contribution

It demonstrates that only a specific resummation of the pion propagator leads to a rapid crossover transition and the potential for a critical endpoint in the phase diagram.

Findings

A strict large-N_f resummation yields a rapid crossover transition.

Only certain approximations of the pion propagator produce a critical endpoint.

The renormalization within the large-N_f framework is feasible and well-defined.

Abstract

The SU(2)_L x SU(2)_R chiral quark model consisting of the (sigma,pi) meson multiplet and the constituent quarks propagating on the homogeneous background of a temporal gauge field is solved at finite temperature and quark baryon chemical potential mu_q using an expansion in the number of flavors N_f, both in the chiral limit and for the physical value of the pion mass. Keeping the fermion propagator at its tree-level, several approximations to the pion propagator are investigated. These approximations correspond to different partial resummations of the perturbative series. Comparing their solution with a diagrammatically formulated resummation relying on a strict large-N_f expansion of the perturbative series one concludes that only when the local part of the approximated pion propagator resums infinitely many orders in 1/N_f of fermionic contributions a sufficiently rapid crossover transition at mu_q=0 is achieved allowing for the existence of a tricritical point or a critical end point in the mu_q-T phase diagram. The renormalization and the possibility of determining the counterterms in the resummation provided by a strict large-N_f expansion are investigated.