ar X iv : h ep - p h / 05 12 25 2 v 1 2 0 D ec 2 00 5 Universal 2 - 3 Symmetry Anjan

Possible maximal mixing seen in the oscillations of the atmospheric neutrinos has led to postulate of a μ-τ symmetry which interchanges νμ and ντ . We argue that such symmetry need not be special to neutrinos but can be extended to all fermions. The assumption that all fermion mass matrices are approximately invariant under interchange of the second and the third generation fields is shown to be phenomenologically viable and has interesting consequences. In the quark sector, the smallness of Vub and Vcb can be a consequences of this approximate 2-3 symmetry. The same approximate symmetry can simultaneously lead to large atmospheric mixing angle and can describe the leptonic mixing quite well provided the neutrino spectrum is quasi degenerate. We present this scenario, elaborate on its consequences and discuss its realization. E-mail address: [email protected] The vastly different mixing patterns [1] of quarks and leptons have been used as an argument in favour of special leptonic symmetries such as μ-τ interchange [2, 3, 4], Le − Lμ − Lτ [5] , D4 [6] , A4 [7] etc.. These symmetries lead to large or maximal mixing angles seen in the leptonic sector. Logically, such symmetries would then not be present in the quark sector which exhibits small mixing angles. This need not be so and it is possible to describe both the quark and leptonic mixing as a consequence of an approximately broken 2-3 symmetry which exchanges the second and the third generation fermionic fields. We argue that this symmetry manifests itself more forcefully in the quark sector than in the leptonic sector and results in the understanding of small values of Vub and Vcb when it is broken at few percent level. The leptonic mass matrices can also be thought to be nearly invariant under the 2-3 symmetry if the neutrino mass spectrum is quasi degenerate. Let us first elaborate on the well-known [2, 3] consequences of the μ-τ symmetry. The light neutrino mass matrix Mν is restricted to have the following form in the presence of this symmetry: Mν = 