Dynamical generation of low-energy couplings from quark-meson fluctuations

TL;DR

This paper derives low-energy pion interactions from quark-meson fluctuations using the Functional Renormalization Group, providing insights into the validity and scale of effective pion models.

Contribution

It introduces a method to dynamically generate low-energy couplings from quark-meson fluctuations within the FRG framework, extending previous work on the linear Quark-Meson Model.

Findings

Low-energy couplings are generated from quark and meson fluctuations.

Qualitative features inform the validity range of pion effective models.

The approach includes momentum-dependent interactions and self-interactions.

Abstract

We extend our recent computation of the low-energy limit of the linear O(4) Quark-Meson Model. The present analysis focuses on the transformation of the resulting effective action into a nonlinearly realized effective pion action, whose higher-derivative interaction terms are parametrized by so-called low-energy couplings. Their counterparts in the linear model are determined from the Functional Renormalization Group flow of the momentum-dependent four-pion vertex, which is calculated in a fully O(4)-symmetric approximation by including also momentum-dependent {\sigma}{\pi} interactions as well as {\sigma} self-interactions. Consequently, these higher-derivative couplings are dynamically generated solely from quark and meson fluctuations, initialized at a hadronic scale. Despite our restriction to low-energy degrees of freedom, we find that the qualitative features of the fluctuation dynamics allow us to comment on the range of validity and on appropriate renormalization scales for purely pionic effective models.