Families from supergroups and predictions for leptonic CP violation

S M Barr,Heng-Yu Chen

doi:10.1007/jhep10(2017)128

Abstract

As was shown in 1984 by Caneschi, Farrar, and Schwimmer, decomposing representations of the supergroup SU(M |N ), can give interesting anomaly-free sets of fermion representations of SU(M ) × SU(N ) × U(1). It is shown here that such groups can be used to construct realistic grand unified models with non-abelian gauged family symmetries. A particularly simple three-family example based on SU(5) × SU(2) × U(1) is studied. The forms of the mass matrices, including that of the right-handed neutrinos, are determined in terms of SU(2) Clebsch coefficients; and the model is able to fit the lepton sector and predict the Dirac CP-violating phase of the neutrinos. Models of this type would have a rich phenomenology if part of the family symmetry is broken near the electroweak scale.

Highlights

The anomaly-free sets constructed in [1] are interesting from the point of view of gauged family symmetry
As we shall see in detail, the forms of mass matrices of the quarks and leptons that arise from the Yukawa terms in eq (2.2) are determined by the SU(2) family symmetry, and the Clebsch coefficients of SU(2)
By decomposition of multiplets of the supergroups SU(M |N ), anomaly-free sets of fermion multiplets of the bosonic groups SU(M ) × SU(N ) × U(1) can be found, as was shown in [1]. Models based on such groups and multiplets can give both grand unification of the Standard Model gauge interactions and gauged non-abelian family groups

Summary

Predictions of neutrino properties

Let us see whether the simple model we have presented can fit the lepton sector, i.e. For Case I, we have done a numerical search of parameter space and found that there are values of the parameters that give excellent fits to the three PMNS angles, but none of them gives a small enough value for the ratio of mass splittings ∆m212/∆m223. In table 1, we present the fits to the neutrino mixing angles and the predictions of δCP for the two solutions These were found in the following way. We searched over the three complex parameters z1, z2, y and kept only those points which yielded values for the three PMNS angles and for the ratio of neutrino mass splittings that were each within one-sigma of the experimental value. Can be modified to allow a realistic quark sector, without affecting the predictions for the lepton sector

Making the quark sector realistic

The Higgs sector

Conclusions