The pressure of strong coupling lattice QCD with heavy quarks, the hadron resonance gas model and the large N limit

TL;DR

This paper calculates the pressure in lattice QCD and Yang-Mills theories using strong coupling and hopping parameter expansions, validating the hadron resonance gas model and exploring large N behavior.

Contribution

It provides a first-principles calculation of pressure in lattice theories with heavy quarks, confirming the hadron resonance gas model and analyzing large N limits.

Findings

Results agree with the hadron resonance gas model in leading orders.

Pure Yang-Mills pressure corresponds to an ideal glueball gas.

Yang-Mills pressure remains order N^0 in the large N limit.

Abstract

In this paper we calculate the pressure of pure lattice Yang-Mills theories and lattice QCD with heavy quarks by means of strong coupling expansions. Dynamical fermions are introduced with a hopping parameter expansion, which also allows for the incorporation of finite quark chemical potential. We show that in leading orders the results are in full agreement with expectations from the hadron resonance gas model, thus validating it with a first principles calculation. For pure Yang-Mills theories we obtain the corresponding ideal glueball gas, in QCD with heavy quarks our result equals that of an ideal gas of mesons and baryons. Another finding is that the Yang-Mills pressure in the large N limit is of order $\sim N^0$ to the calculated orders, when the inverse 't Hooft coupling is used as expansion parameter. This property is expected in the confined phase, where our calculations take place.