Functional Renormalization Group Study of Phonon Mode Effects on Chiral Critical Point

TL;DR

This study uses the functional renormalization group to analyze how phonon mode effects influence the nature and size of the QCD critical point by considering coupled fluctuations of chiral condensate and quark-number density.

Contribution

It introduces an extended quark-meson model with coupled chiral and quark-number density fields and analyzes their impact on the QCD critical point beyond mean-field approximation.

Findings

Coupling of density and chiral fluctuations causes level repulsion.

Expansion of the critical region of the QCD critical point.

Dependence of critical region size on model coupling constants.

Abstract

We apply the functional renormalization-group (FRG) equation to analyze the nature of the QCD critical point beyond the mean-field approximation by taking into consideration the fact that the soft mode associated with the QCD critical point is a linear combination of fluctuations of the chiral condensate and the quark-number density, rather than the pure chiral fluctuations. We first construct an extended quark-meson model in which a new field corresponding to quark-number density is introduced to the conventional one composed of the chiral fields sigma, pi and the quarks. The fluctuations of the quark-number density as well as the chiral condensate are taken into account by solving the FRG equation which contains sigma and the new field as coupled dynamical variables. It is found that the mixing of the two dynamical variables causes a kind of level repulsion between the curvature masses, which in turn leads to an expansion of the critical region of the QCD critical point, depending on the coupling constants in the model yet to be determined from microscopic theories or hopefully by experiments.