126 GeV Higgs boson and universality relations in the $SO(5) \times U(1)$ gauge-Higgs unification

Abstract: The Higgs boson mass $m_H=126 $GeV in the $SO(5) \times U(1)$ gauge-Higgs unification in the Randall-Sundrum space leads to important consequences. An universal relation is found between the Kaluza-Klein (KK) mass scale $m_{KK}$ and the Aharonov-Bohm phase $\theta_H$ in the fifth dimension; $m_{KK} \sim 1350\,{\rm GeV}/(\sin \theta_H)^{0.787}$. The cubic and quartic self-couplings of the Higgs boson become smaller than those in the SM, having universal dependence on $\theta_H$. The decay rates $H \rightarrow \gamma \gamma, gg$ are evaluated by summing contributions from KK towers. Corrections coming from KK excited states turn out very small. With $\theta_H= 0.1 \sim 0.35$, the mass of the first KK $Z$ is predicted to be $2.5 \sim 6 \, $TeV.