Abstract
The large mixing in the lepton sector observed in the recent neutrino-oscillation experiments strongly suggests that nature of left-handed lepton doublets is very different from that of left-handed quark doublets. This means that there is a big disparity between the matter multiplets 5∗'s and 10's in the SU(5) unified theory. We show that this big difference can be explained in a six-dimensional spacetime compactified on the T2/Z3 orbifold. That is, we propose to put three families of 5∗'s on three equivalent fixed points of the orbifold and the three 10's in the two-dimensional bulk. We construct an explicit model realizing this situation and show that the democratic mass structure in the lepton sector is naturally obtained and hence the model explains the observed bi-large lepton mixing and simultaneously the required small mixing Ue3. The mass matrices and mixing in the quark sector are also briefly discussed.
Highlights
Bi-large mixing in the lepton sector [1, 2] is one of the most remarkable features in the standard model
Contrary to the quark sector, where the mass-diagonalization matrix of the left-handed up-type quarks almost coincides with that of the left-handed down-type quarks, there is a large discrepancy between the matrix of the left-handed charged leptons and that of the neutrinos
The Froggatt–Nielsen structure is able to explain the bi-large mixing assuming less hierarchy for the lepton doublets [4, 5], but an accidental cancellation is necessary between O(1) coefficients to explain the large mixing angle of the solar neutrino oscillation [4] or the small Ue3 [5]
Summary
Bi-large mixing in the lepton sector [1, 2] is one of the most remarkable features in the standard model. A number of tentative solutions are proposed within the framework of four-dimensional field theories, where one tries to understand the flavour structure as a result of some symmetries. Three N =1 SU(5)-10 chiral multiplets survive the orbifold projection, and three 5∗’s (and 1’s) are further introduced at the three fixed points of the T2/Z3 σ orbifold for theoretical consistency. These multiplets are identified with the three families of quarks, leptons (and right-handed neutrinos). The diagonal nature of the Majorana neutrino mass matrix is naturally explained, and the bi-large mixing and the smallness of the Ue3 follows in the lepton flavour mixing matrix [7]. The flavour structure of the quark sector is discussed
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