Third Family Corrections to Quark and Lepton Mixing in SUSY Models with non-Abelian Family Symmetry

TL;DR

This paper examines how canonical normalisation corrections in SUSY models with non-Abelian family symmetry can significantly alter quark and lepton mixing angles, especially affecting the CKM matrix and neutrino mixing patterns.

Contribution

It highlights the importance of canonical normalisation effects in flavour models with non-Abelian symmetries and analyzes conditions under which these effects are large or negligible.

Findings

Canonical normalisation can cause significant corrections to fermion mixing angles.

Third family operators in Kahler potential can lead to sizeable effects.

Explicit examples show impact on |V_{cb}| and neutrino mixing patterns.

Abstract

We re-analyse the effect of corrections from canonical normalisation of kinetic terms on the quark and lepton mixing angles. This type of corrections emerges, for example, from effective higher-dimensional Kahler potential operators in the context of locally supersymmetric models of flavour. In contrast to previous studies we find that the necessary procedure of redefining the fields in order to restore canonically normalised kinetic terms, i.e. canonical normalisation, can lead to significant corrections to the fermion mixing angles (as determined from the superpotential). Such potentially large effects are characteristic of flavour models based on non-Abelian family symmetries, where some of the possible Kahler potential (and superpotential) operators, in particular those associated with the third family, are only mildly suppressed. We investigate under which conditions the messenger sector of such flavour models generates such Kahler potential operators for which the canonical normalisation effects are sizeable, and under which conditions these operators may be absent and canonical normalisation effects are small. As explicit examples for potentially relevant CN effects, we will discuss the corrections to the CKM matrix element |V_{cb}| as well as corrections to tri-bimaximal neutrino mixing.