Regulator scheme dependence of the chiral phase transition at high densities

TL;DR

This paper investigates how the choice of regulator scheme affects the observed back-bending of the chiral phase transition line and negative entropy density in low-energy QCD models, revealing scheme dependence and artifacts.

Contribution

It demonstrates that the regulator shape function's momentum dependence causes the back-bending and negative entropy phenomena, highlighting artifacts in the derivative expansion.

Findings

Back-bending behavior depends on regulator scheme.

Negative entropy density is scheme-dependent.

Callan-Symanzik regulators eliminate the artifacts.

Abstract

A common feature of recent functional renormalization group investigations of effective low-energy QCD is the appearance of a back-bending behavior of the chiral phase transition line at low temperatures together with a negative entropy density in the symmetric regime. The regulator scheme dependence of this phenomenon and the necessary modifications at finite densities are analyzed within a two-flavor quark-meson model. The flows at finite densities for three different regulators of three- or four-dimensional momenta are confronted to each other. It is found that the back-bending behavior and the negative entropy density can be traced back to the explicit momentum dependence of the regulator shape function. While it persists for the often-used three-dimensional flat regulator, it vanishes for Callan-Symanzik type regulators. This points to truncation artifacts in the lowest order of the derivative expansion. A careful theoretical as well as numerical exploration is given.