Few remarks on the Higgs boson decays in gauge-Higgs unification

In the scenario of gauge-Higgs unification, the origin of the Higgs boson is the higher-dimensional gauge boson. Very characteristic predictions are made of the Higgs boson interactions in this scenario, reflecting its origin. In particular, a remarkable claim has been made: the contribution of nonzero Kaluza-Klein modes to the Higgs decay $H\to Z\gamma$ exactly vanishes in the minimal SU(3) electroweak unified model, at least at the one-loop level. In this brief paper, in order to see whether this prediction is a general feature of the scenario or the consequence of the specific choice of the model, matter content, or the order of perturbative expansion, we perform an operator analysis. We demonstrate that no relevant operator exists, respecting the gauge symmetry SU(3) in the bulk. We also comment on the possibly important contribution to the photonic decay $H\to \gamma \gamma$ due to the nonzero Kaluza-Klein modes of light quarks.