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

Abstract

A simple extension of the standard model is to introduce $n$ heavy right-handed Majorana neutrinos and preserve its $\mathrm{SU}(2{)}_{\mathrm{L}}^{}\times \mathrm{U}(1{)}_{\mathrm{Y}}^{}$ gauge symmetry. Diagonalizing the $(3+n)\times (3+n)$ 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 $3\times 3$ neutrino mixing matrix $V$, 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.

Comments: RevTex 8 pages, no figures