Abstract
Abstract Grand gauge-Higgs unification of 5D $SU(6)$ gauge theory on an orbifold $S^1/Z_2$ is discussed. The Standard Model (SM) fermions are introduced on one of the boundaries and some massive bulk fields are also introduced so that they couple to the SM fermions through the mass terms on the boundary. Integrating out the bulk fields generates SM fermion masses with exponentially small bulk mass dependences. The SM fermion masses except for the top quark are shown to be reproduced by mild tuning of the bulk masses. The one-loop Higgs potential is calculated and it is shown that electroweak symmetry breaking occurs by introducing additional bulk fields. The Higgs boson mass is also computed.
Highlights
Gauge-Higgs unification (GHU) [1] is one of the attractive scenarios among the physics beyond the Standard Model (SM), which solves the hierarchy problem by identifying the SM Higgs field with one of the extra spatial component of the higher dimensional gauge field
In the grand GHU previously discussed [13], a 5D SU (6) GHU with an orbifold S1/Z2 was considered and all the SM fermions were elegantly embedded into a minimal set of SU (6) bulk multiplets without massless exotic fermions, namely anomaly-free matter content
The down-type Yukawa couplings and the charged lepton Yukawa couplings were not allowed since the left-handed quark doublets and the right-handed down quark singlets were embedded into different SU (6) multiplets and Yukawa couplings in GHU is generated by the gauge interactions
Summary
Gauge-Higgs unification (GHU) [1] is one of the attractive scenarios among the physics beyond the Standard Model (SM), which solves the hierarchy problem by identifying the SM Higgs field with one of the extra spatial component of the higher dimensional gauge field. The scenario of grand gauge-Higgs unification was discussed by one of the present authors [13],1 where the five dimensional SU (6) grand gauge-Higgs unification was considered and the Standard Model (SM) fermions were embedded in zero modes of some SU (6) multiplets in the bulk. Yukawa coupling in GHU originated from the gauge coupling cannot be allowed This feature seems to be generic in GHU, we have to give up embedding all the SM fermions into the SU (6) multiplets in the bulk to obtain the SM Yukawa couplings. We calculate oneloop Higgs potential and study whether the electroweak symmetry breaking happens and Higgs mass can be obtained This issue is very nontrivial in GHU since the potential is generated at one-loop and strongly depends on matter fermion content. In Appendix B, calculations of the Kaluza-Klein (KK) mass spectrum of bulk fields are explained in some detail
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