We discuss anomalous Higgs interactions in the scenario of gauge-Higgs unification. In the scenario Higgs originates from a higher dimensional gauge field and has a physical meaning as an Aharonov-Bohm phase or Wilson loop. As its inevitable consequence, physical observables are expected to be periodic in the Higgs field. In particular, the Yukawa coupling is expected to show some periodic and nonlinear behavior as the function of the Higgs vacuum expectation value (VEV). For a specific choice of the VEV, the Yukawa coupling of the Kaluza-Klein zero mode fermion even vanishes. On the other hand, the Yukawa coupling is originally provided by gauge interaction, which is linear in the Higgs field. We discuss how such two apparent contradictions about the nonlinearity of the Yukawa coupling can be reconciled and at the same time how these two “pictures” give different predictions in the simplest framework of the scenario: $SU(3)$ electroweak model in 5-dimensional flat space-time with orbifolding. The deviation of the Yukawa coupling from the standard model prediction is also calculated for arbitrary VEV. Also discussed is the Higgs interaction with $W^{\pm }$ and $Z^0$. It turns out that in our framework of flat space-time the interaction does not show deviation from the standard model prediction, except for the specific case of the VEV.

• Received 27 January 2012

DOI:https://doi.org/10.1103/PhysRevD.87.016011