A simple grand unified relation between neutrino mixing and quark mixing

Abstract

It is proposed that all flavor mixing is caused by the mixing of the three quark and lepton families with vectorlike fermions in 5 + 5 multiplets of SU (5). This simple assumption implies that both V CKM and U MN S are generated by a single matrix. The entire 3 × 3 complex mass matrix of the neutrinos M ν is then found to have a simple expression in terms of two complex parameters and an overall scale. Thus, all the presently unknown neutrino parameters are predicted. The best fits are for θ atm < ∼ 40 • . The leptonic Dirac CP phase is found to be somewhat greater than π.It is a striking fact that the leptonic mixing angles of the MNS matrix [1] are much larger than the corresponding quark mixing angles of the CKM matrix [2]. Grand unification suggests a simple explanation for this. In SU (5), a family of quarks and leptons is contained in the multiplets 10 + 5, with the left-handed leptons contained in the 5 and the left-handed quarks contained in the 10. Thus, if there is more mixing among the 5 multiplets of different families than among the 10 multiplets, the disparity between leptonic and quark mixing angles would be explained. This idea can be implemented in models based on any grand unified group, since all such groups contain SU (5) as a subgroup. Several ways of implementing this basic idea have been proposed in the literature [3,4].Here we propose a model in which the three 10 + 5 families of fermions are supplemented by three 5 + 5 pairs. (The possible existence of such additional "vectorlike" fermions has been much discussed in the literature in a variety of contexts [3,5,6,7,8].) The central idea of the model proposed here is that all inter-family mixing is caused by the mixing between the 5 multiplets of the ordinary families and the 5 multiplets of the additional vectorlike pairs. As a consequence of having this common source, both quark mixing and lepton mixing are controlled in this model by a single matrix, which we call A. This matrix can be determined from the masses and mixing angles of the quarks alone, and this allows the entire 3 × 3 complex mass matrix M ν of the known neutrinos (which contains 9 real physical observables) to be predicted in terms of just two complex parameters and an overall mass scale. The resulting formula turns out to be quite simple. In the "flavor basis" of the neutrinos, i.e. the basis (ν e , ν µ , ν τ ), the neutrino mass matrix is given by

A single source for all flavor violation

“…The model of flavor symmetry and flavor violation proposed in [1] has the virtue that it is (a) conceptually simple, (b) explains some of the qualitative features of the quark and lepton spectrum (e.g. the MNS angles being much larger than the CKM angles), and (c) is highly predictive.…”

“…Therefore there are four predictions, which we may take to be (M ν ) ee (which comes into neutrino-less double beta decay), and the three CP-violating phases. In [1], it is found that the model's best-fit values are δ Dirac = 1.15π radians, and (M ν ) ee = 0.002 eV. But the model actually is considerably more predictive than counting parameters suggests, due to the fact that the expressions for observables in terms of model parameters are very non-linear.…”

“…another abelian symmetry that prevents the SU(5) adjoint Higgs field from coupling in these terms [1].…”

“…In a 2012 paper [1], we proposed a model in which all flavor changing effects, including CKM mixing [4,5] and MNS mixing [3], are controlled by a single "master matrix." In that paper, the model was shown to give several predictions for neutrino properties, including the Dirac neutrino CP phase, as well as post-dictions for quantities that are still not precisely known, such as the atmospheric and solar neutrino mixing angles, and m s /m d .…”

Anarchy with hierarchy: A probabilistic appraisal

“…Another interesting class of models proposed recently in Ref. [38,39] has a very similar structure for the mass matrices, which we shall not investigate here. We do analyze the flavor U (1) models as special cases of the general class of models described here, which are described next.…”