Predictions of the Higgs mass and the weak mixing angle in the 6D gauge-Higgs unification

In the gauge-Higgs unification with multiple extra spaces, the Higgs self-coupling is of the order of $g^2$ and Higgs is predicted to be light, being consistent with the LHC results. When the gauge group is simple, the weak mixing angle is also predictable. We address a question whether there exists a model of gauge-Higgs unification in 6-dimensional space-time, which successfully predicts the mass ratios of the Higgs boson and weak gauge bosons. First, by use of a useful formula we give a general argument on the condition to get a realistic prediction of the weak mixing angle $sin^{2}theta_{W} = 1/4$, and find that triplet and sextet representations of the minimal SU(3) gauge group lead to the realistic prediction. Concerning the Higgs mass, we notice that in the models with one Higgs doublet, the predicted Higgs mass is always the same: $M_H = 2 M_W$. However, by extending our discussion to the models with two Higgs doublets, the situation changes: we obtain an interesting prediction $M_{H} leq 2M_{W}$ at the leading order of the perturbation. Thus it is possible to recover the observed Higgs mass, 125 GeV, for a suitable choice of the parameter. The situation is in clear contrast to the case of the minimal supersymmetric standard model, where $M_{H} leq M_{Z}$ at the classical level and the predicted Higgs mass cannot recover the observed value.