Field dependence of the Yukawa coupling in the three flavor quark-meson model

TL;DR

This paper explores how the Yukawa coupling in the three flavor quark-meson model varies with energy scale, revealing complex quantum effects that influence its renormalization beyond simple perturbative predictions.

Contribution

It demonstrates the nontrivial scale dependence of the field-dependent Yukawa coupling using the functional renormalization group, highlighting the generation of new operators affecting its flow.

Findings

Yukawa coupling exhibits nontrivial scale dependence.

Quantum fluctuations generate new chirally invariant operators.

Distinguishing Yukawa flow from other operators is complex.

Abstract

We investigate the renormalization group flow of the field-dependent Yukawa coupling in the framework of the three flavor quark-meson model. In a conventional perturbative calculation, given that the field rescaling is trivial, the Yukawa coupling does not get renormalized at the one-loop level if it is coupled to an equal number of scalar and pseudoscalar fields. Its field-dependent version, however, does flow with respect to the scale. Using the functional renormalization group technique, we show that it is highly nontrivial how to extract the actual flow of the Yukawa coupling as there are several new chirally invariant operators that get generated by quantum fluctuations in the effective action, which need to be distinguished from that of the Yukawa interaction.