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

Abstract

In the gauge-Higgs unification with multiple extra spaces, the Higgs self-coupling is on the order of g2 and the Higgs boson 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 on whether there exists a model of gauge-Higgs unification in sixdimensional space-time, which successfully predicts the mass ratios of the Higgs boson and weak gauge bosons. First, using a useful formula, we give a general argument on the condition for obtaining a realistic prediction of the weak mixing angle sin2θW =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: MH =2MW . However, by extending our discussion to the models with two Higgs doublets, the situation changes: we obtain an interesting prediction MH ≤ 2MW 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 MH ≤ MZ at the classical level and the predicted Higgs mass cannot recover the observed value.