Family-separated seesaw relations of Majorana neutrinos

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: $m_i^{}\mathrm{/}{M}_i^{}=-R_{\alpha i}^2\mathrm{/}{U}_{\alpha i}^2$ 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 $\alpha =e,\mu ,\tau$). 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.