When the Standard Model first emerged, there was no evidence of neutrino mass. Since only left-chiral neutrino fields are coupled to the gauge bosons, the simplest way to accommodate the lack of a neutrino mass was to omit any right-handed counterparts to the neutrino field, in which case masslessness is automatic. Because of the degeneracy of the three massless neutrinos, the charged weak leptonic current can be made diagonal and there exists no lepton analog to the CKM matrix.

In light of evidence for neutrino mass, the most conservative response is to postulate the existence of right-handed neutrinos, similar to the right-handed partners of the other fields. Because the right-handed neutrino carries no gauge charge, its mass may be Dirac or Majorana (or both), and it may be heavy or light. Whether one considers this modification to be an extension beyond the Standard Model or not is largely a matter of semantics. In this chapter, we will describe the rich physics induced by the inclusion of a right-handed neutrino. We note in passing that all fermion fields appearing here will be described as four-component spinors.

Neutrino mass

A right-handed neutrino νR has no couplings to any of the gauge fields because its Standard Model charges are zero. Nonetheless, it can enter the lagrangian in two ways: there can be a Yukawa coupling to lepton doublet lL plus a Higgs and there can be a Majorana mass term involving νR.