Predictivity of models with spontaneously broken non-Abelian discrete flavor symmetries

Abstract

In a class of supersymmetric flavor models predictions are based on residual symmetries of some subsectors of the theory such as those of the charged leptons and neutrinos. However, the vacuum expectation values of the so-called flavon fields generally modify the Kähler potential of the setting, thus changing the predictions. We derive simple analytic formulae that allow us to understand the impact of these corrections on the predictions for the masses and mixing parameters. Furthermore, we discuss the effects on the vacuum alignment and on flavor changing neutral currents. Our results can also be applied to non-supersymmetric flavor models. 1

Flavon alignments from orbifolding: SU(5) × SU(3) model with 𝕋6/∆(54)

“…for all point group elements θ ∈ ∆ (54). Importantly, one can show that in this case the (gauge) embeddings of the translations have to be trivial, i.e.…”

“…We want to enlarge the orbifolding symmetry once again, to allow a place to locate the fermions consistently but keep the alignments we have achieved. We can note that S 4 ∆(24) so that we can continue in the ∆(6n 2 ) discrete group series by choosing the next one, ∆ (54).…”

“…We assume a standard Kähler potential with canonical normalized fields (and without Field Representation Localization extra dim. Zero mode SU(3) fl SU(5) GUT U(1) large corrections [54]). Then, the Yukawa sector after compactification reads…”

“…We find that the boundary conditions must exhibit some non-Abelian structure so that we can have non-trivial VEV alignments. Hence, we are led to consider 10d non-Abelian orbifolds [31][32][33], where the torus is modded out, for example, by S 4 or ∆ (54). The latter case is an example where we can locate the SM fermions on fixed points in extra dimensions.…”

Lepton flavor violation and neutrino masses from A5 and CP in the non-universal MSSM

“…Finally, we notice that, for some configurations, significant corrections from the Kähler potential emerge that break the residual symmetries and could modify the LO predictions. This fact is independent of SUSY and it actually corresponds to the usual wave-function renormalization that should always be taken into account [24,[41][42][43][44].…”