CPviolation from dimensional reduction: Examples in 4+1 dimensions

Abstract

We provide simple examples of the generation of complex mass terms and hence CP violation through dimensional reduction. This CP violation originates in the ''Hosotani mechanism,'' relying on nontrivial Wilson lines, assumed to appear in the dimensional reduction.

Complete CKM quark mixing via dimensional deconstruction

“…(23) In the previous section we have outlined the process diagonalizing the squared-mass matrix (6). The complete diagonalization process is complicated, but as we are concerned only with the zero eigenvalue problem, the computation can be done analytically in the general term (see Appendix A).…”

“…In this appendix we will work out the general expression of zero eigenstate of the matrix of the type (6). This mode plays a special role because it will be identified with the SM chiral fermions.…”

“…In this paper we look specifically into two such important mechanisms of extra dimension theories, namely the localization of matter fields in the bulk [3,4,5] and the dynamical breaking of CP symmetry by ED Wilson line [6,7,8,9]. Ultimately, the hybrid of these two mechanisms is just the well-known complex mixing of fermion flavors.…”

“…Interestingly, the above CP violation induction via deconstruction can also be visualized in extra dimensional view point. Indeed, because of having the same symmetry transformation property, DD link field can be identified with the Wilson line pointing along a latticized transverse direction (Appendix B), and the latter then can naturally acquire a complex VEV in the generalized Hosotani's mechanism [6,7,8,9] of dynamical symmetry breaking. Apparently, the source of CP violation in this approach comes from the complex effective Yukawa couplings so it can be classified as hard CP violation.…”

About Mass, CP and Extra Dimensions

“…In a simple example, we generate CP violation from a 4+1 theory with only real couplings. This work is based on reference [9], and its generalization to include grand unified structures [10].…”