The role of flavon cross couplings in leptonic flavour mixing

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.

Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes

“…These models, which have been constructed in ref. [51], are very economical and consistent with current oscillation data.…”

“…The latter may be directly from higher-dimensional operators in the couplings between flavons and leptons [21,54,55]. In our recent paper [51], we observe that cross coupling between neutrino and charged lepton flavons can shift the VEVs from their original Z 3 and Z 2 symmetric values. In the models based on A 4 , we studied in detail the modification to the TBM flavour mixing pattern, in particular conserving the origin of non-zero θ 13 and Dirac-type CP violation.…”

“…At least two flavon multiplets, one for charged leptons and the other for neutrinos, have to be introduced to guarantee different residual symmetries in the two sectors. The well-known and simplest case is the realisation of TBM in A 4 models [26][27][28][29][30][31][32]51]. In models with larger symmetry groups, more flavon multiplets may be needed for model constructions [18, 19, 34-38, 41-45, 47-49, 52, 53].…”

Theoretical motivations for the precision measurement of the oscillation parameters

“…is found [15]. The mixing angles θ 12 and θ 23 also gain small corrections from their leading order values.…”

“…In Ref. [15], we find that such simple vacuum alignments may be a result of the spontaneous breaking of the flavour symmetry. For example, in A 4 models, the VEVs of ϕ and χ in Eq.…”