Thermodynamics and quark susceptibilities: a Monte-Carlo approach to the PNJL model

TL;DR

This paper employs a Monte-Carlo approach to the PNJL model, incorporating fluctuations around mean fields to improve the understanding of thermodynamics and quark susceptibilities, aligning better with lattice QCD results.

Contribution

It introduces a Monte-Carlo method to the PNJL model, moving beyond mean-field approximation by including fluctuations, especially pion fields, to better match lattice QCD data.

Findings

Fluctuations cause small changes in order parameters for phase transitions.

Including fluctuations improves agreement with lattice QCD for quark susceptibilities.

Pion fields are crucial for reproducing flavor non-diagonal susceptibilities.

Abstract

The Monte-Carlo method is applied to the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. This leads beyond the saddle-point approximation in a mean-field calculation and introduces fluctuations around the mean fields. We study the impact of fluctuations on the thermodynamics of the model, both in the case of pure gauge theory and including two quark flavors. In the two-flavor case, we calculate the second-order Taylor expansion coefficients of the thermodynamic grand canonical partition function with respect to the quark chemical potential and present a comparison with extrapolations from lattice QCD. We show that the introduction of fluctuations produces only small changes in the behavior of the order parameters for chiral symmetry restoration and the deconfinement transition. On the other hand, we find that fluctuations are necessary in order to reproduce lattice data for the flavor non-diagonal quark susceptibilities. Of particular importance are pion fields, the contribution of which is strictly zero in the saddle point approximation.