A classical lower bound on the size of a massive neutrino

Abstract

In this paper, we calculate the size of a massive neutrino in the following approach. We perform our calculation using its mass, spin, and magnetic moment through the neutrino-electron interaction, $via$ the classical magnetic dipole-dipole interaction. Thus, our estimate is obtained by mimicking the low-energy electroweak scattering process $\nu_l$-$l^{\prime}$. This leads to surprisingly accurate result which differs in less than one order of magnitude of more detailed calculations with one-loop corrections based on the neutrino charge radius and the $\nu_l$-$l^{\prime}$ scattering process. The resulting estimates are flavour-blind and gauge independent by construction. We also find that our lower bound is below the reported experimental upper bound on the electron neutrino charged radius. So we obtained a constraining range for the neutrino size.