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Register a new user126 GeV Higgs boson and universality relations in the $SO(5) times U(1)$ gauge-Higgs unification
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Yutaka Hosotani
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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.
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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 $theta_H$ 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.
$SO(5) times U(1) times SU(3)$ gauge-Higgs unification model inspired by $SO(11)$ gauge-Higgs grand unification is constructed in the Randall-Sundrum warped space. The 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Fermion multiplets are introduced in the bulk in the spinor, vector and singlet representations of $SO(5)$ such that they are implemented in the spinor and vector representations of $SO(11)$. The mass spectrum of quarks and leptons in three generations is reproduced except for the down quark mass. The small neutrino masses are explained by the gauge-Higgs seesaw mechanism which takes the same form as in the inverse seesaw mechanism in grand unified theories in four dimensions.
The Cabibbo-Kobayashi-Maskawa (CKM) mixing matrix and flavor-changing neutral currents (FCNCs) in the quark sector are examined in the GUT inspired $SO(5) times U(1) times SU(3)$ gauge-Higgs unification in which the 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Gauge invariant brane interactions play an important role for the flavor mixing in the charged-current weak interactions. The CKM matrix is reproduced except that the up quark mass needs to be larger than the observed one. FCNCs are naturally suppressed as a consequence of the gauge invariance, with a factor of order $10^{-6}$. It is also shown that induced flavor-changing Yukawa couplings are extremely small.
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 $theta_H$ 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.
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