To solve the doublet-triplet splitting problem in SU(5) grand unified theories, we propose a four dimensional orbifold grand unified theory by acting Z2 on the SU(5) gauge group. Without an adjoint Higgs, the orbifold procedure breaks the SU(5) gauge
symmetry down to the standard model gauge group, and removes the triplet component of the fundamental SU(5) Higgs. In the supersymmetric framework, we show that the orbifold procedure removes two triplet superfields of the Higgs multiplets and leaves us with the minimal supersymmetric standard model, which also solves the hierarchy problem and realizes gauge coupling unification. We also discuss possible UV completions of the orbifold theories.
We investigate a neutral gauge boson X originated from a hidden U(1) extension of the standard model as the particle dark matter candidate. The vector dark matter interacts with the standard model fermions through heavy fermion mediators. The interac
tions give rise to t-channel annihilation cross section in the XX to ff process, which dominates the thermal relic abundance during thermal freeze-out and produces measurable gamma-ray flux in the galactic halo. For a light vector dark matter, if it predominantly couples to the third generation fermions, this model could explain the excess of gamma rays from the galactic center. We show that the vector dark matter with a mass of 20 ~ 40 GeV and that annihilate into the bb and tautau final states provides an excellent description of the observed gamma-ray excess. The parameter space aimed at explaining the gamma-ray excess, could also provide the correct thermal relic density and is compatible with the constraints from electroweak precision data, Higgs invisible decay, and collider searches. We also show the dark matter couplings to the nucleon from the fermion portal interactions are loop-suppressed, and only contribute to the spin-dependent cross section. So the vector dark matter could easily escape the stringent constraints from the direct detection experiments.
To avoid possible electroweak vacuum instability in the vector-like fermion model, we introduce a new singlet scalar to the model, which couples to the vector-like fermion, and also mixes with the Higgs boson after spontaneous symmetry breaking. We i
nvestigate the vector-like fermion predominantly coupled to the third generation quarks, and its mass is generated from the vacuum expectation value of the new scalar field in the model. In this setup, as running towards high energies, the new scalar provides positive contribution to the running of the higgs quartic coupling, and the matching on the scale of the scalar mass gives rise to a threshod effect that lifts up the higgs quartic coupling strength. The two effects help stabilize the electroweak vacuum of the Higgs potential. Therefore, this setup could evade possible vacuum instability in the vector-like fermion model. We show that a large range of parameter space is allowed to have both stable Higgs vacuum and perturbativity of all the running couplings, up to the Planck scale. We also examine the experimental constraints from the electroweak precision observables such as oblique corrections S, T and non-oblique corrections to the Zbb coupling, the Higgs coupling precision measurements, and the current LHC direct searches.
