Abstract
We analyze the electroweak phase transition at finite temperature in a model of gauge-Higgs unification where the fermion mass hierarchy including top quark mass, a viable electroweak symmetry breaking and an observed Higgs mass are successfully reproduced. To study the phase transition, we derive the general formula of the 1-loop effective potential at finite temperature by using the $\zeta$ function regularization method. It is remarkable that the functions determining the Kaluza-Klein mass spectrum have only to be necessary in calculations. This potential can be applicable to any higher dimensional theory in flat space where one extra spatial dimension is compactified. Applying to our model of gauge-Higgs unification, the strong first phase transition compatible with 125 GeV Higgs mass is found to happen.
Highlights
Gauge-Higgs unification (GHU) [1,2] is one of the attractive scenarios that solves the hierarchy problem without invoking supersymmetry, where the Standard Model (SM) Higgs boson mass and its potential are calculable thanks to the higher dimensional gauge symmetry [2]
We have studied the electroweak phase transition at finite temperature in a model proposed by the authors, 5D SUð3Þ ⊗ Uð1ÞX GHU with a realistic fermion mass hierarchy including top quark mass, a successful electroweak symmetry breaking and an observed Higgs boson mass [12]
We adopted the ζ function regularization method which is well-known technique and extend it to analyze the 1-loop effective potential at finite temperature in our model. The advantage of this method is that even if the KK mass spectrum cannot be found, the 1-loop effective potential can be calculated if we have the functions determining the KK mass spectrum
Summary
Gauge-Higgs unification (GHU) [1,2] is one of the attractive scenarios that solves the hierarchy problem without invoking supersymmetry, where the Standard Model (SM) Higgs boson mass and its potential are calculable thanks to the higher dimensional gauge symmetry [2]. In order to obtain an observed Higgs mass and a realistic electroweak symmetry breaking, a very small Higgs vacuum expectation value (VEV) is required in GHU It is well known for getting small Higgs VEV that Higgs potential has to be generated by various contributions from higher rank representations of the gauge group [10,11]. It is very nontrivial to calculate the 1-loop effective potential at finite temperature because of the brane localized fermions and their coupling to the bulk fermions. In such a case, the Kaluza-Klein (KK) mass spectrum cannot be exactly solved in general.
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