Phase structure of quark matter and in-medium properties of mesons from Callan-Symanzik flows

TL;DR

This paper uses a Callan-Symanzik functional renormalization group approach to analyze meson spectral functions and phase structure in quark matter at finite temperature and density, providing insights into non-analytic features and symmetry breaking.

Contribution

It introduces a novel Callan-Symanzik flow method for studying meson properties and phase diagrams in the quark-meson model, preserving key symmetries and causality.

Findings

Detailed meson spectral functions at finite T and density

Insights into non-analytic structures of two-point functions

Framework for studying chiral symmetry breaking

Abstract

We compute meson spectral functions at finite temperature and density in the quark-meson model, supplemented with a computation of the phase diagram. In particular, we provide a detailed analysis of the non-analytic structure of the meson two-point functions which is of great relevance for phenomenological applications, such as moat regimes and inhomogeneous phases. Furthermore, it is also relevant from a field-theoretical standpoint as it provides an insight into the applicability of derivative expansions of the effective action to studies of general fermion-boson models, both at zero and finite chemical potential. Our computation is based on a functional renormalization group setup that preserves causality, all spacetime symmetries, and the Silver-Blaze property. The combination of these properties can only be achieved by a Callan-Symanzik regulator. Instead of momentum shell integrations, renormalization group flows generated by such a regulator describe the change of the theory induced by a change of the masses of the mesons and quarks. A particular focus of our work lies on the construction of controlled Callan-Symanzik flows in the presence of spontaneous and explicit chiral symmetry breaking by means of chiral Ward-Takahashi identities.