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

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.

arXiv comment24 pages, prepared for submission to PTEP, accepted for publication in PTEP

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