Sphalerons of a new gauge interaction can convert a primordial asymmetry in B or L into a dark matter asymmetry. From the equilibrium conditions for the sphalerons of both the electroweak and the new interactions, one can compute the ratios of B, L, and X, where X is the dark matter number, thus determining the mass of the dark matter particle fairly precisely. Such a scenario can arise naturally in the context of unification with larger groups. An illustrative model embeddable in SU (6)× SU (2) ⊂ E 6 is described in detail as well as an equally simple model based on SU (7).
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
It is shown that an idea proposed in 1996 that relates in a qualitatively correct way the interfamily mass hierarchies of the up quarks, down quarks, charged leptons, and neutrinos, can be combined with a predictive scheme recently proposed for relating quark mixing and neutrino mixing. In the resulting model, the entire flavor structure of the quarks and leptons is expressible in terms of two "master matrices": a diagonal matrix that gives the inter-family mass ratios, and an offdiagonal matrix that controls all flavor mixing.
It was recently proposed that all flavor mixing has a single source, namely the mixing of the three quark and lepton families with "extra" vectorlike fermions in 5 + 5 multiplets of SU (5). This was shown to lead to several testable predictions including neutrino masses and CP-violating phases. Here it is shown that the mixing angles within grand unified fermion multiplets are also predicted. Proton decay branching ratios would thus give several independent tests of the model. Certain model parameters could be determined independently from the quark and lepton spectrum and from proton decay.
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.
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