A thermodynamically consistent quasi-particle model without temperature-dependent infinity of the vacuum zero point energy

TL;DR

This paper introduces a thermodynamically consistent quasi-particle model that incorporates a classical background field to handle vacuum energy infinities, successfully fitting lattice QGP data without reformulating statistical mechanics.

Contribution

The paper presents a novel quasi-particle model that avoids temperature-dependent vacuum energy infinities using a classical background field, maintaining thermodynamic consistency.

Findings

Accurately fits lattice QGP data at finite temperature

Provides a general method extendable to chemical potential dependence

Ensures thermodynamic consistency without reformulating statistical mechanics

Abstract

In this paper, an improved quasi-particle model is presented. Unlike the previous approach of establishing quasi-particle model, we introduce a classical background field (it is allowed to depend on the temperature) to deal with the infinity of thermal vacuum energy which exists in previous quasi-particle models. After taking into account the effect of this classical background field, the partition function of quasi-particle system can be made well-defined. Based on this and following the standard ensemble theory, we construct a thermodynamically consistent quasi-particle model without the need of any reformulation of statistical mechanics or thermodynamical consistency relation. As an application of our model, we employ it to the case of (2+1) flavor QGP at zero chemical potential and finite temperature and obtain a good fit to the recent lattice simulation results of S. Borsanyi $et$ $al$. A comparison of the result of our model with early calculations using other models is also presented. It is shown that our method is general and can be generalized to the case where the effective mass depends not only on the temperature but also on the chemical potential.