Abstract
We explore the concept of effective alignments: contractions of multiple flavour symmetry breaking flavon fields. These contractions give rise to directions that are hard or impossible to obtain directly by breaking the flavour symmetry. Within this context, and using $S_4$ as the flavour symmetry to exemplify, we perform a phenomenological check of lepton flavour models built from pairing any two effective alignments up to order 2 (in flavon contractions). The check is performed for each pair of effective alignments in a framework with models of constrained sequential dominance type, in a basis where the charged leptons are diagonal. We thus obtain an indication of which effective alignments are interesting for model building, within this so-called $S_4$ landscape. We find three types of viable topologies and provide examples of models realizing this strategy for each topology.
Highlights
The formulation of the Standard Model (SM) was one of the biggest successes of particle physics, accounting for most interactions of matter known to date
We explore the concept of effective alignments: contractions of multiple flavor symmetry breaking flavon fields
We briefly review the idea of effective alignments [20] in the flavor space
Summary
The formulation of the Standard Model (SM) was one of the biggest successes of particle physics, accounting for most interactions of matter known to date. These flavor symmetries do not affect the gauge structure of the model; rather they restrict the way the different particles are able to interact with each other in the Yukawa sector As such, this strategy has been widely used to predict the leptonic mixing structure, for which the flavor symmetries favored are typically non-Abelian discrete symmetries. Since in the indirect approach models the mixing structure is defined by the flavon VEVs, the problem trickles down to choosing appropriate VEVs to match the observed mixing pattern This is still a question that must be in accordance with the scalar potential of the chosen flavor model (both the flavor symmetry chosen and the number of flavons will influence the outcome).
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