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Register a new userThe effective potential and universality in GUT inspired gauge-Higgs unification
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The effective potential for the Aharonov-Bohm phase $theta_H$ in the fifth dimension in GUT inspired $SO(5)times U(1) times SU(3)$ gauge-Higgs unification is evaluated to show that dynamical electroweak symmetry breaking takes place with $theta_H ot= 0$, the 4D Higgs boson mass 125$,$GeV being generated at the quantum level. The cubic and quartic self-couplings $(lambda_3, lambda_4)$ of the Higgs boson are found to satisfy universal relations, i.e. they are determined, to high accuracy, solely by $theta_H$, irrespective of values of other parameters in the model. For $theta_H=0.1$ ($0.15$), $lambda_3$ and $lambda_4$ are smaller than those in the standard model by 7.7% (8.1%) and 30% (32%), respectively.
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We perform a detailed investigation of a Grand Unified Theory (GUT)-inspired theory of gauge-Higgs unification. Scanning the models parameter space with adapted numerical techniques, we contrast the scenarios low energy limit with existing SM and collider search constraints. We discuss potential modifications of di-Higgs phenomenology at hadron colliders as sensitive probes of the gauge-like character of the Higgs self-interactions and find that for phenomenologically viable parameter choices modifications of the order of 20% compared to the SM cross section can be expected. While these modifications are challenging to observe at the LHC, a future 100 TeV hadron collider might be able to constrain the scenario through more precise di-Higgs measurements. We point out alternative signatures that can be employed to constrain this model in the near future.
$SO(5) times U(1) times SU(3)$ 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 zero mode of an extra-dimensional component of gauge potentials serves as a 4D Higgs field in the gauge-Higgs unification. We examine QED on $M^4 times S^1$ and determine the mass and potential of a 4D Higgs field (the $A_5$ component) at the two loop level with gauge invariant reguralization. It is seen that the mass is free from divergences and independent of the renormalization scheme.
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.
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 leads 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.
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