Asymptotic freedom in ${Z}_2$-Yukawa-QCD models

TL;DR

This paper explores new asymptotically free trajectories in ${Z}_2$-Yukawa-QCD models, revealing additional regimes where all couplings become free at high energies through various analytical and numerical methods.

Contribution

It uncovers previously unknown asymptotically free trajectories in ${Z}_2$-Yukawa-QCD models using generalized boundary conditions and multiple approximation schemes.

Findings

Discovery of new asymptotically free trajectories.

Construction of quasi-fixed points for the Higgs potential.

Numerical validation using pseudo-spectral and shooting methods.

Abstract

${Z}_2$-Yukawa-QCD models are a minimalistic model class with a Yukawa and a QCD-like gauge sector that exhibits a regime with asymptotic freedom in all its marginal couplings in standard perturbation theory. We discover the existence of further asymptotically free trajectories for these models by exploiting generalized boundary conditions. We construct such trajectories as quasi-fixed points for the Higgs potential within different approximation schemes. We substantiate our findings first in an effective-field-theory approach, and obtain a comprehensive picture using the functional renormalization group. We infer the existence of scaling solutions also by means of a weak-Yukawa-coupling expansion in the ultraviolet. In the same regime, we discuss the stability of the quasi-fixed point solutions for large field amplitudes. We provide further evidence for such asymptotically free theories by numerical studies using pseudo-spectral and shooting methods.