CPphase 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.

Operator analysis of physical states on magnetized T2/ZN orbifolds

“…On these magnetized orbifolds, nontrivial (discrete) Scherk-Schwarz phases [64,65] and (discrete) Wilson line phases [52,66,67] play an important 1 See for string magnetized D-brane models [6,7] and references therein. 2 Another possible way to tackle these problems is to introduce point interactions (zero-thickness branes) in the bulk space of a five-dimensional theory on S 1 and consider various boundary conditions of fields on them [8][9][10]. 3 Within the framework of superstring theory, magnetized D-brane models are T-dual of intersecting D-brane models [6,7].…”

Dynamical generation of fermion mass hierarchy in an extra dimension

“…the SUð2Þ doublet fermion feels the point interactions at y ¼ L 1 , L 2 and the SUð2Þ singlet fermion feels the point interactions at [26][27][28]. Then the mode functions of the SUð2Þ-doublet zero mode G …”

“…It was pointed out in Refs. [26][27][28] that the gauge symmetry breaking due to the y-dependent VEV of the scalar field would cause a gauge universality violation. That is because the y-dependent VEV of the scalar modifies the flat profile of the zero-mode function of the gauge boson and thereby the values of the 4d gauge couplings change with respect to the generations through the overlap integrals.…”

“…5 As we discussed in [26], if the warped scalar VEV is provided in the Higgs doublet, a serious violation in the gauge universality is expected. Thereby, in the previous works [26][27][28], we introduced an additional singlet scalar with the warped VEV, while the Higgs doublet has the ordinary constant VEV, and considered "higher-dimensional" Yukawa terms where both the Higgs doublet and the singlet scalar appear. (Note that we prohibited the ordinary Yukawa terms by introducing the Z 2 discrete symmetry: odd parity for the two scalars, even parity for the others.)…”

“…In the papers [26][27][28]52], a new way to produce generations and a mass hierarchy was proposed with introducing zero-width branes, so-called point interactions, to the extra dimension. In this section, we briefly review a theory with point interactions at first.…”