Is the 126 GeV Higgs Boson Mass Calculable in Gauge-Higgs Unification?

Abstract

We address a question whether the recently observed Higgs mass $M_H=126$ GeV, of the order of the weak scale $M_W$, is calculable as a finite value in the scnenario of gauge-Higgs unification. In the scenario formulated on a flat 5-dimensional space-time, the Higgs mass is calculable, being protected under the quantum correction by gauge invariance, though the predicted Higgs mass is generally too small compared with $M_W$. In the 6-dimensional SU(3) model, however, a suitable orbifolding is known to lead to a mass of the order of $M_W$: $M_H=2M_W$ at the tree level, which has some similarity to the corresponding prediction by the MSSM, $M_H$ leq (cos beta) $M_Z$. We demonstrate first by a general argument and secondly by explicit calculations that, even though the quantum correction to the quartic self-coupling of the Higgs field is UV-divergent, its deviation from that of $g^2$ is calculable, and therefore two observables, $M_H^2$ and Delta equiv $(M_H/2M_W{)}^2-1$, are both calculable in the gauge-Higgs unification scenario. The implication of the precise value 126 GeV to the compactification scale and the bulk mass of the matter field in our model is also discussed.

Comments: 24 pages, 2 figures, v2: Calculations of corrections to gauge kinetic terms added, v3: final version to be published