Understanding small neutrino mass and its implication

Abstract

We have derived previously the relations between the neutrino masses and mixing angles in a dispersive analysis on the mixing of neutral leptonic states. The only involved assumption is that the electroweak symmetry of the Standard Model (SM) is restored at a high energy scale in some new physics scenario, which diminishes the box diagrams responsible for the mixing. Here we include corrections to the analysis up to three loops, arising from exchanges of additional neutral and charged scalars in the electroweak symmetric phase. The solution to the dispersion relation for the ${\mu }^{-}{e}^{+}$-${\mu }^{+}{e}^{-}$ mixing generates a typical neutrino mass $m_{\nu }\sim O\left(1\right)\mathrm{eV}$ in the SM unambiguously. The solution also favors the normal ordering of the neutrino masses over the inverted one, and links the large electroweak symmetry restoration, i.e., new physics scale to the small neutrino mass.