Towards A Realistic Grand Gauge-Higgs Unification Scenario
Nobuhito Maru
备注：
11 pages, 5 eps figures, To appear in the proceeding of International Workshop on Grand Unified Theories: Current Status and Future Prospects (GUT07), December 17-19 2007, Kusatsu, Japan
In this talk, we discuss an attempt to construct a realistic model of the grand gauge-Higgs unification. We investigate a 5D SU(6) grand gauge-Higgs unification model compactified on an orbifold S^1/Z_2. Ordinary quarks and leptons, together with right-handed neutrinos, are just accommodated into a minimal set of representations of the gauge group, without introducing any exotic states in the same representations. The proton decay turns out to be forbidden at least at the tree level. We also find a correct electroweak symmetry breaking SU(2)_L \times U(1)_Y \to U(1)_{em} is easily realized by introducing suitable number of adjoint fermions.
We discuss renormalization group equations for gauge coupling constants in gauge-Higgs grand unification on five-dimensional Randall-Sundrum warped space. We show that all the four-dimensional Standard Model gauge coupling constants are asymptotically free and are effectively unified in $SO(11)$ gauge-Higgs grand unified theories on 5D Randall-Sundrum warped space.
The effective Higgs theories at the TeV scale in supersymmetric $SU(5)$ grand unification models are systematically derived. Restricted to extensions on $\mathbf{5}_{H}$ containing the Higgs sector we show that only two types of real (vector-like) models and one type of chiral model are found to be consistent with perturbative grand unification. While the chiral model has been excluded by the LHC data, the fate of perturbative unification will be uniquely determined by the two classes of vector-like models.
We apply the perturbative grand unification due to renormalization to distinguish TeV-scale relics of supersymmetric $\rm{SO}(10)$ scenarios. With rational theoretical constraints taken into account, we find that for the breaking pattern of either $\rm{SU}(5)$ or Pati-Salam only extra matter $\mathbf{16}$ supermultiplet of $SO(10)$ can appear at TeV scale, apart from MSSM spectrum.
SU(5) $\otimes$ SU(5) provides a minimal grand unification scheme for fermions and gauge forces if there are vector-like quarks and leptons in nature. We explore the gauge coupling unification in a non-supersymmetric model of this type, and study its implications for proton decay. The properties of vector-like quarks and intermediate scales that emerge from coupling unification play a central role in suppressing proton decay. We find that in this model, the familiar decay mode $p \to e^+ π^0$ may have a partial lifetime within the reach of currently planned experiments.
Supersymmetric grand unification based on $SO(10)$ is one of the most attractive paradigms in physics beyond the Standard Model. Inspired by the recent NANOGrav signal, we discuss the implications of detecting a stochastic gravitational wave background emitted by a network of cosmic strings for the $SO(10)$ grand unification. Starting from a minimal model with multiple steps of symmetry breaking, we show that it generally prefers a high intermediate scale above $10^{14}\, \mathrm{GeV}$ that is favored by observable primordial gravitational waves. The observed spectrum can potentially narrow th…
We explicitly test the asymptotic grand unification of a minimal 5-dimensional model with SO(10) gauge theory compactified on an $S^{1}/Z_{2}\times Z^{\prime}_{2}$ orbifold. We consider all matter fields as propagating in the bulk and show that the gauge couplings asymptotically run to a fixed point in the UV. However, the Yukawa couplings will typically hit a Landau pole right above the compactification scale in this class of SO(10) models.
4D Higgs field is identified with the extra-dimensional component of gauge potentials in the gauge-Higgs unification scenario. $SO(5) \times U(1)$ gauge-Higgs EW unification in the Randall-Sundrum warped space is successful at low energies. The Higgs field appears as an Aharonov-Bohm phase $θ_H$ in the fifth dimension. Its mass is generated at the quantum level and is finite. The model yields almost the same phenomenology as the standard model for $θ_H < 0.1$, and predicts $Z'$ bosons around 6 - 10 TeV with very broad widths. The scenario is genelarized to $SO(11)$ gauge-Higgs grand unificatio…
