$CP$ phase from twisted Higgs vacuum expectation value in extra dimension

Abstract

We propose a new mechanism for generating a CP phase via Higgs a vacuum expectation value originating from geometry of an extra dimension. A twisted boundary condition is the key to produce an extra-dimension coordinate-dependent vacuum expectation value, which contains a CP phase degree of freedom and can be a new source of a CP phase in higher-dimensional gauge theories. As an illustrative example, we apply our mechanism to a five-dimensional gauge theory with point interactions and show that our mechanism can dynamically produce a nontrivial CP-violating phase with electroweak symmetry breaking, even though the five-dimensional model does not include any CP-violating phases of Yukawa couplings in the five-dimensional Lagrangian because of a single generation of five-dimensional fermions. We apply our mechanism to a model with point interactions, which has no source of CP-violating phases in the couplings of the higher-dimensional action, and show that a nontrivial CP phase dynamically appears.

Comments: 14 pages, 2 figures, 1 table (v1); 15 pages, 2 figures, 1 table, some representations modified, typos fixed, some references added (v2); published version in PRD, 19 pages, 5 figures, 2 tables, title changed, discussion improved, typos fixed, an appendix added (v3)