Effect of the neutrino magnetic moment on the properties of the muon

Abstract

The effect of the neutrino dipole magnetic moment on the properties of the muon is investigated within the standard model of electroweak interactions and a model based on the SU(2)L × SU(2)R × U(1)B-L gauge group (left-right model). In the case of the Dirac neutrino, muon decay through the channel µ− → e−γ is studied with allowance for the neutrino dipole magnetic moment. It is shown that, both in the standard model supplemented with an SU(2)L right-handed neutrino singlet and in the standard model featuring two doublets of Higgs fields, radiative muon decay is unobservable. In the left-right model, the contributions of diagrams associated with the neutrino dipole magnetic moment become significant only in the case of a mutual compensation of the contributions of diagrams involving the electromagnetic vertices of charged gauge bosons and singly charged Higgs bosons. At specific values of the parameters of the left-right model, one can then obtain an experimental upper limit on the branching fraction of this reaction. The contributions of the neutrino dipole magnetic moment to the muon anomalous magnetic moment are found for the Dirac and the Majorana neutrino. It is established that, both in the standard model and in the left-right model, values of the neutrino anomalous magnetic moment that are required for explaining the (g − 2)µ anomaly are in excess of the theoretical predictions for this moment.