The Higgs boson mass and top quark mass imply that the Higgs quartic coupling vanishes around the scale of $10^9 - 10^{13}$ GeV, depending on the precise value of the top quark mass. The vanishing quartic coupling can be naturally addressed if the Higgs field originates from a 5-dimensional gauge field and the 5th dimension is compactified at the scale of the vanishing Higgs quartic coupling, which is a scenario based on gauge-Higgs unification. We present a general prediction of the scenario on the proton decay process $p \to π^0 e^+$. In many gauge-Higgs unification models, the 1st generation fermions are localized towards an orbifold fixed point in order to realize the realistic Yukawa couplings. Hence, four-fermion operators responsible for the proton decay can appear with a suppression of the 5-dimensional Planck scale (not the 4-dimensional Planck scale). Since the 5-dimensional Planck scale is connected to the compactification scale, we have a correlation between the proton partial decay width and the top quark mass. We show that the future Hyper-Kamiokande experiment may discover the proton decay if the top quark pole mass is larger than about 172.5 GeV.
We consider the triple coupling of the Higgs boson in the context of the gauge-Higgs unification scenario. We show that the triple coupling of the Higgs boson in this scenario generically deviates from SM prediction since the Higgs potential in this scenario has a periodicity. We calculate the coupling in the five-dimensional $SU(3)$ x $U(1)_X$ gauge-Higgs unification model and obtain 70% deviation from the SM prediction.
We discuss the Yukawa coupling unification, a very interesting prediction of the grand unified theory, in the context of scenarios with more than one pair of Higgs doublet since the current LHC constraint has become a problem for the Yukawa unification scenarios with just one pair of Higgs doublet. More than one pair of Higgs doublets can easily arise in missing partner mechanism which solves the doublet-triplet splitting problem. In such a scenario, the Yukawa unification occurs at a medium $\tanβ$ value, e.g., $\sim$ 30, which corresponds to much smaller threshold corrections compared to usu…
We analyze the structure of the Higgs potential in gauge-Higgs unification with a flat extra dimension. As a concrete model, we first consider the cases where the Standard Model Higgs doublet is embedded into a higher-dimensional $SU(3)_{w}^{}$ gauge multiplet with five-dimensional Lorentz symmetry relaxed. In this $SU(3)_{w}^{}$ model with Lorentz violation, the deviation of the resulting triple Higgs boson coupling from its SM prediction is shown to be less than $10\%$ when the compactification scale is larger than the experimental lower bound, which is around 5 TeV. Next, we examine the Hig…
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 …
We propose a new model of 5D $SU(3)\otimes U(1)_X$ gauge-Higgs unification with a successful electroweak symmetry breaking and a realistic Higgs boson mass. In our model, the representations of the fermions are very simple, the ${\bf 3}, \overline{\bf 3}$ and $\bf \overline{15}$ representations of $SU(3)$ gauge group. Employing the anti-periodic boundary conditions for $\bf \overline{15}$ reduces massless exotic fermions and simplifies the brane localized mass terms. We calculate the 1-loop Higgs potential in detail and find that a realistic electroweak symmetry breaking and the observed Higgs…
In this paper, we investigate the finiteness of the Higgs effective potential in an ${\rm SU}(\mathcal N)$ Gauge-Higgs Unification (GHU) model defined on ${\bf M}^4\times S^1$. 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 ${\rm SU}(\mathcal N)$ gauge theory on ${\bf M}^5\times S^1$, where the one-loop corrections to the four-Fermi operators are divergent. We find that the Higgs effective potential depends on the…
$SO(5) \times U(1) \times SU(3)$ gauge-Higgs unification model inspired by $SO(11)$ gauge-Higgs grand unification is constructed in the Randall-Sundrum warped space. The 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Fermion multiplets are introduced in the bulk in the spinor, vector and singlet representations of $SO(5)$ such that they are implemented in the spinor and vector representations of $SO(11)$. The mass spectrum of quarks and leptons in three generations is reproduced except for the down quark mass. The small neutrino masses are explained by the ga…
