Why is the $3\times 3$ neutrino mixing matrix almost unitary in realistic seesaw models?

A simple extension of the standard model is to introduce $n$ heavy right-handed Majorana neutrinos and preserve its $\rm SU(2)^{}_L \times U(1)^{}_Y$gaugesymmetry\mathrm{.}Diagonalizingthe$(3+n) \times (3+n)$ neutrino mass matrix, we obtain an exact analytical expression for the effective mass matrix of ${\nu }_e^{}$, ${\nu }_{\mu }^{}$ and ${\nu }_{\tau }^{}$. It turns out that the $3\times 3$neutrinomixingmatrix$V$, which appears in the leptonic charged-current weak interactions, must not be exactly unitary. The unitarity violation of $V$ is negligibly tiny, however, if the canonical seesaw mechanism works to reproduce the correct mass scale of light Majorana neutrinos. A similar conclusion can be drawn in the realistic Type-II seesaw models.