Identifying a minimal flavor symmetry of the seesaw mechanism behind neutrino oscillations

Abstract

In the canonical seesaw framework flavor mixing and CP violation in weak charged-current interactions of light and heavy Majorana neutrinos are correlated with each other and described respectively by the 3 × 3 matrices U and R. We show that the very possibility of |Uμi| = |Uτi| (for i = 1, 2, 3), which is strongly indicated by current neutrino oscillation data, automatically leads to a novel prediction |Rμi| = |Rτi| (for i = 1, 2, 3). We prove that behind these two sets of equalities and the experimental evidence for leptonic CP violation lies a minimal flavor symmetry — the overall neutrino mass term keeps invariant when the left-handed neutrino fields transform as νeL→ (νeL)c, νμL→ (ντL)c, ντL→ (νμL)c and the right-handed neutrino fields undergo an arbitrary unitary CP transformation. Such a generalized μ-τ reflection symmetry may help constrain the flavor textures of active and sterile neutrinos to some extent in the seesaw mechanism.