Gauge-Higgs unification is the fascinating scenario solving the hierarchy problem without supersymmetry. In this scenario, the Standard Model (SM) Higgs doublet is identified with extra component of the gauge field in higher dimensions and its mass becomes finite and stable under quantum corrections due to the higher dimensional gauge symmetry. On the other hand, Yukawa coupling is provided by the gauge coupling, which seems to mean that the flavor mixing and CP violation do not arise at it stands. In this talk, we discuss that the flavor mixing is originated from simultaneously non-diagonalizable bulk and brane mass matrices. Then, this mechanism is applied to various flavor changing neutral current (FCNC) processes via Kaluza-Klein (KK) gauge boson exchange at tree level and constraints for compactification scale are obtained.

We discuss anomalous Higgs interactions in the scenario of gauge-Higgs unification. In the scenario Higgs originates from higher dimensional gauge field and has a physical meaning as AB phase or Wilson loop. As its inevitable consequence, physical observables are expected to be periodic in the Higgs field. In particular, the Yukawa coupling is expected to show some periodic and non-linear behavior as the function of the Higgs VEV. For a specific choice of the VEV, the Yukawa coupling of KK zero mode fermion even vanishes. On the other hand, the Yukawa coupling is originally provided by gauge interaction, which is linear in the Higgs field. We discuss how such two apparent contradiction about the non-linearity of the Yukawa coupling can be reconciled and at the same time how these two "pictures" give different predictions in the simplest framework of the scenario: SU (3) electroweak model in 5-dimensional flat space-time with orbifolding. The deviation of the Yukawa coupling from the standard model prediction is also calculated for arbitrary VEV. We study "H-parity", which guarantees the stability of the Higgs for a specific choice of the VEV. Also discussed is the Higgs interaction with W ± and Z 0 . It turns out that in our framework of flat space-time the interaction does not show deviation from the standard model prediction, except for the specific case of the VEV.

We discuss flavor mixing and resulting Flavor Changing Neutral Current (FCNC) in a five dimensional SU (3) color ⊗ SU (3) ⊗ U (1) gauge-Higgs unification. Flavor mixing is realized by the fact that the bulk and brane localized mass terms are not diagonalized simultaneously. As the concrete FCNC processes, we calculate the rate of B

Recent LHC experiments have revealed that Higgs is light. As an interesting candidate to accommodate light Higgs, in this paper we adopt the scenario of dimensional deconstruction, where Higgs is redarded as a pseudo-Nambu-Goldstone boson. Though the scenario is formulated in ordinary 4-dimensional space-time, it may also be interpreted as "latticized" gauge-Higgs unification. We point out that in this scenario Higgs interaction with matter field is anomalous, i.e. its coupling deviates from what the standard model predicts. The interplay between the periodicity of physical observables in the Higgs field and the violation of translational invariance along the extra-space due to the latticization is argued to play an essential role to get the anomalous interaction. Though the predicted anomalous Higgs interaction has much similarity to the one in the gauge-Higgs unification, in the case of dimensional deconstruction the anomaly exists even if we do not introduce bulk mass term for the chiral fermion realized by orbifolding, in clear contrast to the case of gauge-Higgs unification. It in turn means that the anomaly goes away in the continuum limit of the extra-space.

We discuss flavor mixing and resulting Flavor Changing Neutral Current (FCNC) in the SU (3) ⊗ SU (3) color gauge-Higgs unification. As the FCNC process we calculate the rate of D 0 −D 0 mixing due to the exchange of non-zero Kaluza-Klein gluons at the tree level. Flavor mixing is argued to be realized by the fact that the bulk mass term and brane localized mass term is not diagonalized simultaneously unless bulk masses are degenerate.It is shown that automatic suppression mechanism is operative for the FCNC processes of light quarks. We therefore obtain a lower bound on the compactification scale of order O(TeV) by comparing our prediction on the mass difference of neutral D meson with the recent experimental data, which is much milder than what we naively expect assuming only the decoupling of non-zero Kaluza-Klein gluons.