= Orthogonal completion of mixed neutral lepton kinetic terms
{title2=$n_L=c_\alpha\nu_L+s_\alpha N_L,\quad n_L^\perp=-s_\alpha\nu_L+c_\alpha N_L$}
If a <chiral fermion> triplet uses one normalized linear combination of two neutral <leptons>, adding the perpendicular combination as a <gauge singlet> completes their canonical <kinetic terms>. The two combinations are related to the original fields by a real <orthogonal matrix>. Hence their summed kinetic quadratic form is exactly that of the two original fields, with no mixed terms. The singlet carries the same chirality; no right-handed component is created for a purely left-handed massless <neutrino>.
Back to article page
