Effective Potential of Higgs Field in Warped Gauge-Higgs Unification

TL;DR

This paper derives formulas to calculate the Higgs effective potential in warped gauge-Higgs unification models, enabling realistic model construction by analyzing contributions from bulk fermions with various boundary conditions.

Contribution

It provides new analytical formulae for the Higgs effective potential on warped backgrounds, facilitating model building in gauge-Higgs unification scenarios.

Findings

Derived useful formulae for the effective potential calculation.

Calculated contributions from bulk fermions with different boundary conditions.

Showed certain boundary conditions do not contribute to the potential.

Abstract

The gauge-Higgs unification is one of influential scenarios to solve the hierarchy problem in the Standard Model. Recently, the scenario on the warped background attracts many attentions due to a large possibility to construct a realistic model naturally in this framework. It is, however, well known that the effective potential for the Higgs field, which is the most important prediction of the scenario, is not easy to calculate on the warped background, because masses of Kaluza-Klein particles are not obtained analytically. In this article, we derive useful formulae for the effective potential. The formulae allow us to calculate the Higgs mass easily, thus to construct a realistic model in the gauge-Higgs unification scenario on the warped background. Using obtained formulae, we calculate contributions from bulk fermions with several boundary conditions. We also show bulk fermions, which have boundary conditions not allowed in the orbifold picture, do not contribute to the effective potential.