Hosotani mechanism on the lattice

We explore the phase structure and symmetry breaking in four-dimensional SU(3) gauge theory with one spatial compact dimension on the lattice in the presence of fermions in the adjoint and fundamental representations with general boundary conditions. The eigenvalue phases of Polyakov loops and the associated susceptibility are measured on 16^3 x 4 lattice. We establish a correspondence between the phases found on the lattice and the gauge symmetry breaking by the Hosotani mechanism.Comment: 7 pages, 4 figures, prepared for the 31st International Symposium on Lattice Field Theory - LATTICE 2013 Added preprint number

Distinct signals of the gauge-Higgs unification in e+e−e^+e^- collider experiments

Effects of Kaluza-Klein excited neutral vector bosons ($Z'$ bosons) in the gauge-Higgs unification on $e^+e^- \to \bar{q}q, \ell^+\ell^-$ cross sections are studied, particularly in future $e^+ e^-$ collider experiments with polarized beams. Significant deviations in the energy and polarization dependence in $\sigma(\mu^+\mu^-)$, the lepton forward-backward asymmetry, $R_b(\mu) \equiv \sigma(\bar{b}b)/\sigma(\mu^+\mu^-)$ and the left-right asymmetry from the standard model are predicted.Comment: 16 pages, 5 figures, 7 tables (v3) numerical evaluations renewed, comments and references added, 4 tables adde

Coupling Sum Rules and Oblique Corrections in Gauge-Higgs Unification

In GUT inspired $SO(5) \times U(1)_X \times SU(3)_C$ gauge-Higgs unification (GHU) in the Randall-Sundrum warped spacetime, the $W$ and $Z$ couplings of all 4D fermion modes become nontrivial. The $W$ and $Z$ couplings of zero-mode quarks and leptons slightly deviate from those in the SM, and the couplings take the matrix form in the space of Kaluza-Klein (KK) states. In particular, the 4D couplings and mass spectra in the KK states depend on the Aharonov-Bohm phase $\theta_H$ in the fifth dimension. Nevertheless there emerge three astonishing sum rules among those coupling matrices, which guarantees the finiteness of certain combinations of corrections to vacuum polarization tensors. We confirm by numerical evaluation that the equality in the sum rules holds with 5 to 7 digits accuracy. Based on the sum rules we propose improved oblique parameters in GHU. Oblique corrections due to fermion 1-loop diagrams are found to be small.Comment: 39 page

WW and ZZ Boson Pair Production at Electron-Positron Colliders in Gauge-Higgs Unification

We examine $W$ and $Z$ boson pair production processes at electron-positron collider experiments in the $SU(3)_C\times SO(5)_W\times U(1)_X$ gauge-Higgs unification (GHU) model. We find that the deviation of the total cross section for the $e^-e^+\to W^-W^+$ process from the Standard Model (SM) in the GHU model with parameter sets, which are consistent with the current experiments, is about 0.5% to 1.5% and 0.6% to 2.2% for $\sqrt{s}=250$GeV and 500GeV, respectively, depending on the initial electron and positron polarization. We find that for the $e^-e^+\to ZZ$ process the deviation from the SM in the GHU model is at most 1%. We find that unitality bound for the $e^-e^+\to W^-W^+$ process is satisfied in the GHU model as in the SM, as a consequence of the relationship among coupling constants.Comment: 32 pages, 8 tables, 12 figures. arXiv admin note: substantial text overlap with arXiv:2301.0783