Gauge-invariant right-handed neutrino Majorana mass ($-\frac{1}{2}M\overline{{\nu }_R^c}{\nu }_R+\text{Hermitian conjugate}$)

A right-handed neutrino is a singlet of the entire Standard Model gauge group. Its same-chirality bilinear with the field obtained by charge conjugation therefore admits the displayed renormalizable Majorana mass term, in addition to a Higgs-induced Dirac mass term. It violates lepton number by two units. Analogous terms for electrically charged Standard Model fermions carry nonzero electric charge; quarks also have nontrivial color charge. The presence of a right-handed field permits mass but does not force a nonzero mass parameter.