Family-separated seesaw relations of Majorana neutrinos

Abstract

Given the canonical seesaw mechanism as a most natural extension of the standard model in its neutrino sector, we find out a special but brand new solution to the exact seesaw equation: $m^{}_i/M^{}_i = - R^2_{αi}/U^2_{αi}$ for the masses and flavor mixing matrix elements of light and heavy Majorana neutrinos of the $i$-th family (for $i = 1, 2, 3$ and $α= e, μ, τ$). This family-separated seesaw scenario allows us to establish simple relations between the original seesaw parameters and the active degrees of freedom, and thus offers a number of testable predictions in neutrino phenomenology.