2006/05/31 by C. C. Nishi · 6 citations
Mathematics · Physics and Astronomy · #Algorithm #Basis (linear algebra) #CP violation #Geometry #Higgs boson #Invariant (physics) #Mathematical physics #Mathematics #Meson #Neutrino Physics Research #Particle physics #Particle physics theoretical and experimental studies #Physics #Pseudoscalar #Quantum Chromodynamics and Particle Interactions #Scalar (mathematics) #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.74.036003
published as Phys.Rev.D74:036003,2006; Erratum-ibid.D76:119901,2007 · RevTeX4 used. Minor modifications, in particular, the parameter counting of $Z$. v3: Eqs.(28)-(31) corrected
openalex publication_date 2006/08/10 · arxiv created 2007/10/26 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31
Conditions for CP violation in the scalar potential sector of general N-Higgs-doublet models are analyzed from a group theoretical perspective. For the simplest two-Higgs-doublet model potential, a minimum set of conditions for explicit and spontaneous CP violation is presented. The conditions can be given a clear geometrical interpretation in terms of quantities in the adjoint representation of the basis transformation group for the two doublets. Such conditions depend on CP-odd pseudoscalar invariants. When the potential is CP invariant, the explicit procedure to reach the real CP-basis and the explicit CP transformation can also be obtained. The procedure to find the real basis and the conditions for CP violation are then extended to general N-Higgs-doublet model potentials. The analysis becomes more involved and only a formal procedure to reach the real basis is found. Necessary conditions for CP invariance can still be formulated in terms of group invariants: the CP-odd generalized pseudoscalars. The problem can be completely solved for three Higgs-doublets.