Is the 126 GeV Higgs boson mass calculable in gauge-Higgs unification?

We address the question of 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 scenario of gauge–Higgs unification. In the scenario formulated on a flat five-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 six-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 minimal supersymmetric standard model, |$M_{H} \leq (\cos \beta ) M_{Z}$|⁠. 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 |$\Delta \equiv \left ( \frac {M_{H}}{2M_{W}}\right ) ^{2}-1$|⁠, 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.