We propose a new mechanism for generating a $CP$ phase via a Higgs 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.

• Received 4 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.115007