Chemical potential and the gap equation

TL;DR

This paper investigates the behavior of the QCD gap equation at nonzero chemical potential, showing that solutions can be obtained via analytic continuation within a certain domain, and explores chiral symmetry restoration and deconfinement transitions.

Contribution

It demonstrates that the gap equation's solution at nonzero chemical potential can be derived from the vacuum solution through analytic continuation within a specific domain, using two infrared-focused models.

Findings

Solutions are mu-independent within the analyticity domain.

Chiral symmetry is restored via a first-order transition at mu~M(0).

Deconfinement transition is likely coincident with chiral restoration.

Abstract

In general the kernel of QCD's gap equation possesses a domain of analyticity upon which the equation's solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the single-quark number- and scalar-density distribution functions are mu-independent. This is illustrated via two models for the gap equation's kernel. The models are alike in concentrating support in the infrared. They differ in the form of the vertex but qualitatively the results are largely insensitive to the Ansatz. In vacuum both models realise chiral symmetry in the Nambu-Goldstone mode and in the chiral limit, with increasing chemical potential, exhibit a first-order chiral symmetry restoring transition at mu~M(0), where M(p^2) is the dressed-quark mass function. There is evidence to suggest that any associated deconfinement transition is coincident and also of first-order.