Renormalization of the Neutrino Mass Operator

Abstract

A small neutrino Majorana mass can arise in the Standard Model as an effective dimension 5 operator. We calculate the renormalization of this operator in the minimal Standard Model and in its two-Higgs-doublet and supersymmetric extensions. Renormalization from the scale of lepton number violation (e.g., the Planck scale or a GUT scale) to the weak scale decreases the strength of this operator by an order of magnitude or more if the top quark and Higgs boson masses are large. Neutrino mixing angles also run with momentum. We show instances where small mixing at a high scale becomes large at the weak scale, and vice versa.