Lepton flavour symmetry and the neutrino magnetic moment

Abstract

With the standard model gauge group and the three standard left-handed Weyl neutrinos, two minimal scenarios are investigated where an arbitrary non-Abelian lepton flavour symmetry groupG H is responsible for a light neutrino with a large magnetic moment. In the first case, with scalar fields carrying lepton flavour, some finetuning is necessary to get a small enough neutrino mass for μ v =O(10)−11 B. In the second scenario, the introduction of heavy charged gauge singlet fermions with lepton flavour allows for a strictly massless neutrino to one-loop order. In both cases, the interference mechanism for smallm ν and large μ v is unique, independently ofG H . In explicit realizations of the two scenarios, the horizontal groups are found to be non-Abelian extensions of a Zeldovich-Konopinski-Mahmoud lepton number symmetry. Only a discrete part ofG H is spontaneously broken leading to a light Dirac neutrino with a large magnetic moment.