Canonical normalisation and Yukawa matrices

Abstract

We highlight the important role that canonical normalisation of kinetic terms in flavour models based on family symmetries can play in determining the Yukawa matrices. Even though the kinetic terms may be correctly canonically normalised to begin with, they will inevitably be driven into a non-canonical form by a similar operator expansion to that which determines the Yukawa operators. Therefore in models based on family symmetry canonical re-normalisation is mandatory before the physical Yukawa matrices can be extracted. In nearly all examples in the literature this is not done. As an example we perform an explicit calculation of such mixing associated with canonical normalisation of the Kahler metric in a supersymmetric model based on SU(3) family symmetry, where we show that such effects can significantly change the form of the Yukawa matrix. In principle quark mixing could originate entirely from canonical normalisation, with only diagonal Yukawa couplings before canonical normalisation.