The role of flavon cross couplings in leptonic flavour mixing

TL;DR

This paper demonstrates that flavon cross couplings, often neglected, are crucial for correcting leptonic flavour mixing patterns, enabling realistic reactor angles and CP violation in models based on discrete symmetries like A4.

Contribution

It introduces the novel idea that flavon cross couplings can generate necessary corrections to leptonic mixing, providing explicit models with predictive sum rules for CP phases.

Findings

Achieved sizable reactor angle with nearly maximal CP violation.

Derived a sum rule linking CP phase to flavon cross couplings.

Presented models with minimal degrees of freedom, compatible with supersymmetry.

Abstract

In models with discrete flavour symmetries, flavons are critical to realise specific flavour structures. Leptonic flavour mixing originates from the misalignment of flavon vacuum expectation values which respect different residual symmetries in the charged lepton and neutrino sectors. Flavon cross couplings are usually forbidden, in order to protect these symmetries. Contrary to this approach, we show that cross couplings can play a key role and give raise to necessary corrections to flavour-mixing patterns, including a non-zero value for the reactor angle and CP violation. For definiteness, we present two models based on $A_4$. In the first model, all flavons are assumed to be real or pseudo-real, with 7 real degrees of freedom in the flavon sector in total. A sizable reactor angle associated with nearly maximal CP violation is achieved, and, as both originate from the same cross coupling, a sum rule results with a precise prediction for the value of the Dirac CP-violating phase. In the second model, the flavons are taken to be complex scalars, which can be connected with supersymmetric models and multi-Higgs models. The complexity properties of flavons provide new sources for generating the reactor angle. Models in this new approach introduce very few degrees of freedom beyond the Standard Model and can be more economical than those in the framework of extra dimension or supersymmetry.