Finite family groups for fermionic and leptoquark mixing patterns

Abstract

We employ a bottom-up and model-independent technique to search for non-Abelian discrete flavour symmetries capable of predicting viable CKM and PMNS matrices alongside of special patterns of leptoquark couplings. In particular, we analyze patterns derived when an ultra-violet flavour theory is assumed to break to global Abelian symmetries in Standard Model fermion masses and new Yukawa-like terms sourced by the leptoquark representation. The phenomenology of different classes of these 'simplified models' can be explored without reference to explicit model-building assumptions, e.g. the nature of flavour symmetry breaking or any additional field content associated to it, and are also capable of explaining hints of lepton non-universality in R K (⋆) . Assuming experimentally interesting CKM and PMNS matrix elements, our algorithm finds an abundance of predictive non-Abelian flavour groups and therefore provides promising directions for future model building in the flavoured leptoquark space, regardless of whether the anomalous R K (⋆) measurements withstand further experimental scrutiny.

Reconstructing effective Lagrangians embedding residual family symmetries

“…RFS therefore provide a powerful, bottom-up means of understanding observed patterns of flavour mixing in a rather modelindependent way, as the only assumption made thus far is that the accidental flavour symmetries of the SM mass sector encoded in (4) are in fact the global RFS of a complete flavour theory broken as in (1) or its analogues. 2 In this way the RFS formalism defines a set of 'simplified flavour models,' which can easily be extended to BSM constructions as well -see [35] for a recent application of RFS to the Yukawa sector of multi-Higgs doublet models, where they were shown to be capable of controlling dangerous flavour-changing neutral currents alongside of fermionic mixing, and [31,32] where it is demonstrated that they can also structure the flavour patterns of leptoquark couplings (we also address some of these models in Sect. 4 below).…”

“…In what follows we will use the bottom-up approach to 'reconstructing' NADS first discussed in [20,23], but recently applied to a class of BSM leptoquark models in [31,32]. Here one assumes that the RFS generators form the complete generating set for G F ,L,Q , such that the latter are recovered upon using GAP to close all elements of the former:…”

“…Of course, when searching for NADS in the bottom-up approach one must also apply a discretization scheme to all of these mixing parameters, and details on this procedure and other cuts made regarding group order, etc., can be found on case-by-case bases in [20,23,32]. However, it does not matter how one finds the parent symmetry with associated RFS for our present purposes.…”

“…As a particularly relevant extension of the field content of the SM, we now apply our algorithm to a class of flavoured leptoquark models defined in [31,32], which we will briefly review for completeness. Leptoquarks have been become popular in the recent literature due to their ability to resolve (potential) anomalies in heavy meson decay observables like R K observed by LHCb [45,46], as well as other potentially anomalous measurements sensitive to muon physics (see e.g.…”

“…We first apply this method to models addressing SM mixing structures alone, i.e. the U P M N S or U C K M matrices, and then also to a class of 'Simplified Models of Flavourful Leptoquarks' developed in [31,32]. These models include a new Yukawa-like coupling between the leptoquark and SM quark and lepton doublets which is, in addition to the SM mixing, controlled by RFS.…”