Constraining flavour symmetries at the EW scale II: the fermion processes

Abstract

Abstract:We study the set of models in which the Standard Model symmetry is extended with the flavour group A 4 and there are three copies of the Standard Model Higgs that transform as a triplet under this group. In this setup, new channels for flavour violating processes can be studied once the A 4 representations of the fermions in the theory are given. We show that it is of great importance to take these constraints into account as they can put severe constraints on the viability of flavour models.

S4flavoredCPsymmetry for neutrinos

“…• The Higgs potential for doublet fields in our model is the same as in the A 4 models discussed in [23] and it is easy to see from there that there is a range of parameters in the scalar self couplings where the vacuum alignment of the doublet fields in our model is justified.…”

“…The potential for φ i is in fact the same as the general A 4 invariant potential [11], implying that A 4 invariance leads automatically toS 4 invariance for the potential of three Higgs doublets. For that potential, it has been shown that (7) is a possible minimum [23].…”

Revisiting Minimal Lepton Flavour Violation in the light of leptonic CP violation

“…The use of flavour symmetries turned out to be useful also with this respect: a very well-known example is the MFV setup, as previously discussed, whose construction was originally meant exactly to solve this aspect of the Flavour Problem. Promising results have been obtained also with smaller symmetries than the MFV ones, both continuous [110][111][112][113][114][115] and discrete [116][117][118][119][120][121][122][123].…”

The minimal flavour violating axion

“…The first class of theories exhibited very predictive mass textures [8][9][10][11][12][13][14][15][16][16][17][18][19][20][21][22][23][24][25] and provided a certain protection from flavour violating processes [26][27][28][29][30][31][32][33][34]. However, the 2011 discovery of a nonvanishing, and relatively large, leptonic reactor angle [35][36][37][38][39] has raised strong doubts on the use of non-Abelian discrete models, whose most common prediction was a vanishing reactor angle.…”