In the $SO(5) times U(1)$ gauge-Higgs unification the lightest, neutral component of $n_F$ $SO(5)$-spinor fermions (dark fermions), which are relevant for having the observed unstable Higgs boson, becomes the dark matter of the universe. We show that
the relic abundance of the dark matter determined by WMAP and Planck data is reproduced, below the bound placed by the direct detection experiment by LUX, by a model with one light and three heavier ($n_F=4$) dark fermions with the lightest one of a mass from 2.3$,$TeV to 3.1$,$TeV. The corresponding Aharonov-Bohm phase $theta_H$ in the fifth dimension ranges from 0.097 to 0.074. The case of $n_F=3$ ($n_F = 5, 6$) dark fermions yields the relic abundance smaller (larger) than the observed limit.
Signatures of the $SO(5)times U(1)$ gauge-Higgs unification at LHC and future colliders are explored. The Kaluza-Klein (KK) mass spectra of $gamma, Z, Z_R$ and the Higgs self-couplings obey universality relations with the Aharonov-Bohm (AB) phase $th
eta_H$ in the fifth dimension. The current data at low energies and at LHC indicate $theta_H <0.2$. Couplings of quarks and leptons to KK gauge bosons are determined. Three neutral gauge bosons, the first KK modes $Z_R^{(1)}$, $Z^{(1)}$, and $gamma^{(1)}$, appear as $Z$ bosons in dilepton events at LHC. For $theta_H = 0.114$, the mass and decay width of $Z_R^{(1)}$, $Z^{(1)}$, and $gamma^{(1)}$ are (5.73TeV, 482GeV), (6.07TeV, 342GeV), and (6.08TeV, 886GeV), respectively. For $theta_H = 0.073$ their masses are 8.00TeV$sim$8.61TeV. An excess of events in the dilepton invariant mass should be observed in the $Z$ search at the upgraded LHC at 14TeV.
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.
The SO(5) x U(1) gauge-Higgs unification in the Randall-Sundrum warped space with the Higgs boson mass m_H=126 GeV is constructed. An universal relation is found between the Kaluza-Klein (KK) mass scale $m_{KK}$ and the Aharonov-Bohm (AB) phase $thet
a_H$ in the fifth dimension; $m_{KK} sim 1350 GeV/(sin theta_H)^{0.787}$. The cubic and quartic self-couplings of the Higgs boson become smaller than those in the standard model (SM), having universal dependence on $theta_H$. The decay rates H -> gamma gamma, gg are evaluated by summing contributions from KK towers. Corrections coming from KK excited states are finite and about 0.2% (2%) for $theta_H= 0.12 (0.36)$, branching fractions of various decay modes of the Higgs boson remaining nearly the same as in the SM. The signal strengths of the Higgs decay modes relative to the SM are $sim cos^2 theta_H$. The mass of the first KK $Z$ is predicted to be $5.9 (2.4)$TeV for $theta_H= 0.12 (0.36)$. We also point out the possible enhancement of $Gamma(H -> gammagamma)$ due to the large $U(1)_X$ charge of new fermion multiplets.
When the extra dimensional space is not simply-connected, dynamics of the AB phase in the extra dimension can induce dynamical gauge symmetry breaking by the Hosotani mechanism. This opens up a new way of achieving unification of gauge forces. It lea
ds to the gauge-Higgs unification. The Hosotani mechanism can be established nonperturbatively by lattice simulations, in which measurements of the Polyakov line give a clue.
The gauge bosons and Englert-Brout-Higgs (EBH) boson are unified in the five dimensional RS spacetime. The EBH boson is identified with a part of the fifth dimensional component of the gauge potential. In the SO(5) x U(1) gauge-Higgs unification the
EW symmetry is dynamically broken. The EBH boson, predicted with a mass around 130 GeV, naturally becomes stable so that it appears as missing energy and momentum in collider experiments. Collider signatures such as gauge couplings of quarks and leptons and production of KK gamma and Z are also discussed.
In the $SO(5) times U(1)$ gauge-Higgs unification in the Randall-Sundrum (RS) warped space the Higgs boson naturally becomes stable. The model is consistent with the current collider signatures only for a large warp factor $z_L > 10^{15}$ of the RS s
pace. In order for stable Higgs bosons to explain the dark matter of the Universe the Higgs boson must have a mass $m_h = 70 sim 75$ GeV, which can be obtained in the non-SUSY model with $z_L sim 10^5$. We show that this discrepancy is resolved in supersymmetric gauge-Higgs unification where a stop mass is about $300 sim 320 $GeV and gauginos in the electroweak sector are light.
