Geometrical CP violation in multi-Higgs models

Understand

We introduce several methods to obtain calculable phases with geometrical values that are independent of arbitrary parameters in the scalar potential.

• These phases depend on the number of scalars and on the order of the discrete non-Abelian group considered.
• Using these methods we present new geometrical CP violation candidates with vacuum expectation values that must violate CP (the transformation that would make them CP conserving is not a symmetry of the potential).
• We also extend to non-renormalisable potentials the proof that more than two scalars are needed to obtain these geometrical CP violation candidates.