The UV sensitivity of the Higgs potential in Gauge-Higgs Unification

TL;DR

This paper investigates the ultraviolet (UV) sensitivity of the Higgs potential within a Gauge-Higgs Unification model, revealing its dependence on UV theories due to divergences at higher loop levels.

Contribution

It demonstrates that the Higgs effective potential in GHU models is UV-sensitive, with divergences appearing at two-loop and four-loop levels, highlighting the non-renormalizable nature of the theory.

Findings

Four-Fermi diagrams are logarithmically divergent at two loops.

Counter terms contribute to the Higgs potential at four loops.

Higgs potential depends on UV theories in GHU models.

Abstract

In this paper, we discuss the UV sensitivity of the Higgs effective potential in a Gauge-Higgs Unification (GHU) model. We consider an $SU(\mathcal N)$ GHU on $\mathbf M^4\times S^1$ spacetime with a massless Dirac fermion. In this model, we evaluate the four-Fermi diagrams at the two-loop level and find them to be logarithmically divergent in the dimensional regularization scheme. Moreover, we confirm that their counter terms contribute to the Higgs effective potential at the four-loop level. This result means that the Higgs effective potential in the GHU depends on UV theories as well as in other non-renormalizable theories.