To be, or not to be finite? The Higgs potential in Gauge-Higgs Unification

Abstract

In this paper, we investigate the finiteness of the Higgs effective potential in an $\mathrm{SU}(\mathcal{N})$ Gauge-Higgs Unification (GHU) model defined on ${\mathbf{M}}^4\times S^1$. We obtain the Higgs effective potential at the two-loop level and find that it is finite. We also discuss that the Higgs effective potential is generically divergent for three- or higher-loop levels. As an example, we consider an $\mathrm{SU}(\mathcal{N})$ gauge theory on ${\mathbf{M}}^5\times S^1$, where the one-loop corrections to the four-Fermi operators are divergent. We find that the Higgs effective potential depends on their counter terms at the three-loop level.

arXiv comment23 pages. Accepted for publication in JHEP

References in corpus (3)

• Finite Higgs mass without Supersymmetry
• Two loop finiteness of Higgs mass and potential in the gauge-Higgs unification
• Two-loop Calculation of Higgs Mass in Gauge-Higgs Unification: 5D Massless QED Compactified on S^1

Cited by in corpus (4)

• On representation matrices of boundary conditions in $SU(n)$ gauge theories compactified on two-dimensional orbifolds
• UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
• The UV sensitivity of the Higgs potential in Gauge-Higgs Unification
• Graviton loop contribution to Higgs potential in gauge-Higgs unification