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

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.