Constraining multi-Higgs flavour models

Understand

To study a flavour model with a non-minimal Higgs sector one must first define the symmetries of the fields; then identify what types of vacua exist and how they may break the symmetries; and finally determine whether the remnant symmetries are compatible with the experimental data.

• Here we address all these issues in the context of flavour models with any number of Higgs doublets.
• We stress the importance of analysing the Higgs vacuum expectation values that are pseudo-invariant under the generators of all subgroups.
• It is shown that the only way of obtaining a physical CKM mixing matrix and, simultaneously, non-degenerate and non-zero quark masses is requiring the vacuum expectation values of the Higgs fields to break completely the full flavour group, except possibly for some symmetry belonging to baryon number.