Tripartite Neutrino Mass Matrix

The 3 × 3 Majorana neutrino mass matrix is written as a sum of 3 terms, i.e. Mν = MA +MB +MC , where MA is proportional to the identity matrix and MB,C are invariant under different Z3 transformations. This Mν is very suitable for understanding atmospheric and solar neutrino oscillations, with sin 2θatm and tan 2 θsol fixed at 1 and 0.5 respectively, in excellent agreement with present data. It has in fact been proposed before, but only as an ansatz. This paper uncovers its underlying symmetry, thus allowing a complete theory of leptons and quarks to be constructed. With the recent experimental progress in measuring atmospheric [1] and solar [2] neutrino oscillations, the mass-squared differences of the 3 active neutrinos and their mixing angles are now known with some precision. Typical values at 90% confidence level are [3] (∆m2)atm ∼ (1.3− 3.0)× 10 eV, sin 2θatm ∼ 0.88− 1, (1) (∆m2)sol ∼ (6− 9)× 10 eV, tan θsol ∼ 0.33− 0.76. (2) These few numbers have inspired the writing of hundreds of papers on the structure of the resulting 3× 3 Majorana neutrino mass matrix Mν . Is the problem that complicated? Perhaps not, if it is looked at with the proper perspective. Motivated by the idea that Mν should satisfy [4, 5] UMνU = Mν , (3) where U is a specific unitary matrix, a very simple form of Mν is here proposed: Mν = MA +MB +MC , (4) where MA = A 