Weinberg power counting and the quark determinant at small chemical potential

TL;DR

This paper develops a gauge-invariant effective action for QCD at finite temperature and small chemical potential, using Weinberg power counting to expand the quark determinant and analyze phase fluctuations.

Contribution

It introduces a minimal effective action for QCD at finite temperature and chemical potential, incorporating gauge invariance and nonperturbative effects within a systematic expansion.

Findings

Derived a gauge-invariant expression for the phase of the quark determinant.

Recovered dimensional reduction in the high-temperature limit.

Analytically computed <theta^2> including perturbative and nonperturbative contributions.

Abstract

We construct an effective action for QCD by expanding the quark determinant in powers of the chemical potential at finite temperature in the case of massless quarks. To cut the infinite series we adopt the Weinberg power counting criteria. We compute the minimal effective action (~p^4), expanding in the external momentum, which implies the use of the hard thermal loop approximation. Our main result is a gauge invariant expression for the phase theta of the functional determinant in QCD, and recovers dimensional reduction in the high-temperature limit. We compute, analytically, <theta^2> in the range of p << 2 pi T, including perturbative and nonperturbative contributions, the latter treated within the mean field approximation. Implications for lattice simulations are briefly discussed.