$H$ parity and the stable Higgs boson in the $SO(5)\times U(1)$ gauge-Higgs unification

In the $SO(5)\times U(1)$ gauge-Higgs unification model in the Randall-Sundrum warped space, there results the conservation of the $H$ parity. The $H$ parity is assigned to all 4D fields including excited modes in Kaluza-Klein towers. The neutral Higgs boson is the lightest particle of odd $H$ parity, consequently becoming absolutely stable. Its mass is found to be $70–135\mathrm{GeV}$ for the warp factor $z_L={10}^5–{10}^{15}$.

Figure 1

The effective potential $V_{\mathrm{eff}}({\theta }_H)$ in the model. The plot is for $U({\theta }_H/\pi )=(4\pi {)}^2(k{z}_L^{-1}{)}^{-4}{V}_{\mathrm{eff}}$ at $z_L={10}^5$ (left) and $z_L={10}^{15}$ (right). Green, blue, and red curves represent $V_{\mathrm{eff}}^{\mathrm{gauge}}$, $V_{\mathrm{eff}}^{\mathrm{fermion}}$, and $V_{\mathrm{eff}}$, respectively. The global minima are located at ${\theta }_H=\frac{1}{2}\pi$ and $\frac{3}{2}\pi$, where the EW symmetry dynamically breaks down to $U(1{)}_{\mathrm{EM}}$.

Figure 2

The critical behavior near $z_L=1.67$, below which $V_{\mathrm{eff}}$ is minimized at ${\theta }_H=0,\pi$.

Figure 3

Two types of spectra where the horizontal axis is ${\theta }_H/\pi$.