Neutrino Seesaw Revelation

If it can be ascertained experimentally that the 3 × 3 Majorana neutrino mass matrix Mν has vanishing determinants for one or more of its 2 × 2 submatrices, the theoretically well-known canonical seesaw mechanism may be revealed as its progenitor. I show how these two things are connected and offer a realistic Mν with two zero subdeterminants as an example. It is a common theoretical belief in neutrino physics that the observed smallness of neutrino masses is due to the celebrated canonical seesaw mechanism [1], i.e. Mν = MDM N MD. (1) Here MD is the 3 × 3 Dirac mass matrix linking (νe, νμ, ντ ) to their right-handed singlet counterparts (Ne, Nμ, Nτ ), and MN is the 3×3 Majorana mass matrix of the latter. Assuming MD to be of order the electroweak breaking scale, a very large MN would then result in a very small Mν . However, it is impossible to verify this hypothesis without reaching energies of the scale of MN , or sensitivities of order Mν/MN in rare decay processes. Both are hopeless in the near future unless MN is of order a few TeV [2]. If MN is much greater than that, one may never know if Eq. (1) is really how neutrinos become massive. The form and texture of Mν have been under theoretical study for many years. Is it possible at all to discover from its structure that it actually comes from MN as given by Eq. (1)? The answer is “yes”, provided thatMN has one or more texture zeros. In that case, M N has one or more 2×2 submatrices with zero determinants. If MD is also diagonal, this property is preserved in Mν . Finding such a structure in the latter experimentally would be a strong hint that Eq. (1) is correct! In the basis where the charged-lepton mass matrix Ml is diagonal, the possible existence of texture zeros in Mν have been considered previously [3]. These zeros are derivable from Abelian discrete symmetries [4], and in the case of (Mν)μμ = (Mν)ττ = 0 also from the non-Abelian discrete groups Q8 [5] and D5 [6]. However, if MN is the progenitor of Mν , one should perhaps consider instead the texture zeros of the former [7]. For example, if (MN)μμ = (MN)ττ = 0, i.e. MN = 