Extended scaling and residual flavor symmetry in the neutrino Majorana mass matrix

Abstract

The residual symmetry approach, along with a complex extension for some flavor invariance, is a powerful tool to uncover the flavor structure of the $3\times3$ neutrino Majorana mass matrix $M_ν$ towards gaining insights into neutrino mixing. We utilize this to propose a complex extension of the real scaling ansatz for $M_ν$ which was introduced some years ago. Unlike the latter, our proposal allows a nonzero mass for each of the three light neutrinos as well as a nonvanishing $θ_{13}$. A major result of this scheme is that leptonic Dirac CP-violation must be maximal while atmospheric neutrino mixing need not be exactly maximal. Moreover, each of the two allowed Majorana phases, to be probed by the search for nuclear $0νββ$ decay, has to be at one of its two CP-conserving values. There are other interesting consequences such as the allowed occurrence of a normal mass ordering which is not favored by the real scaling ansatz. Our predictions will be tested in ongoing and future neutrino oscillation experiments at T2K, NO$ν$A and DUNE.

24 pages, 4 figures, 6 tables; accepted for publication in European Physical Journal C