Asymptotically free scaling solutions in nonabelian Higgs models

TL;DR

This paper constructs and analyzes asymptotically free trajectories in nonabelian Higgs models, revealing new UV completions and potential solutions to naturalness issues, with implications for the standard model Higgs sector.

Contribution

It introduces a novel class of asymptotically free solutions in nonabelian Higgs models, extending the understanding of UV completions beyond perturbative methods.

Findings

Identification of a three-parameter family of RG trajectories connecting UV and Higgs phases.

Estimation of low-energy properties relevant to the standard model Higgs sector.

Discovery of a two-parameter subclass of Coleman-Weinberg trajectories free from naturalness problems.

Abstract

We construct asymptotically free renormalization group trajectories for the generic nonabelian Higgs model in four-dimensional spacetime. These ultraviolet-complete trajectories become visible by generalizing the renormalization/boundary conditions in the definition of the correlation functions of the theory. Though they are accessible in a controlled weak-coupling analysis, these trajectories originate from threshold phenomena which are missed in a conventional perturbative analysis relying on the deep Euclidean region. We identify a candidate three-parameter family of renormalization group trajectories interconnecting the asymptotically free ultraviolet regime with a Higgs phase in the low-energy limit. We provide estimates of their low-energy properties in the light of a possible application to the standard model Higgs sector. Finally, we find a two-parameter subclass of asymptotically free Coleman-Weinberg-type trajectories that do not suffer from a naturalness problem.