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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 inthe scnenario of gauge-Higgs unification. In the scenario formulated on a flat5-dimensional space-time, the Higgs mass is calculable, being protected underthe quantum correction by gauge invariance, though the predicted Higgs mass isgenerally 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 thecorresponding prediction by the MSSM, $M_{H}$ leq (cos beta) $M_{Z}$. Wedemonstrate first by a general argument and secondly by explicit calculationsthat, even though the quantum correction to the quartic self-coupling of theHiggs 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 unificationscenario. The implication of the precise value 126 GeV to the compactificationscale and the bulk mass of the matter field in our model is also discussed.

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