H$\to Z\gamma$ in the gauge-Higgs unification

The decay rate of the Higgs decay $H \to Z \gamma$ is evaluated at the one-loop level in the $SO(5)\times U(1)$ gauge-Higgs unification. Although an infinite number of loops with Kaluza-Klein states contribute to the decay amplitude, there appears the cancellation among the loops, and the decay rate is found to be finite and non-zero. It is found that the decay rate is well approximated by the decay rate in the standard model multiplied by $\cos^2\theta_H$, where $\theta_H$ is the Aharonov-Bohm phase induced by the vacuum expectation value of an extra-dimensional component of the gauge field.