2025/10/15 by Fujikawa, Kazuo
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)
paper · doi:10.48550/arxiv.2510.14998
It is customary to identify ψ+=νR + CνRT with a Majorana fermion on the basis of chirality changing charge conjugation C: νR→ CνRT and parity P: νR→ iγ0νR. The theorem on the absence of a Majorana-Weyl fermion in d=4 states Cγ5C-1= -γ5 with C=Cγ4T, and thus the charge conjugation of the equivalent Majorana ψ+=(\frac1+γ52)νR + (\frac1-γ52)CνRT vanishes without subsidiary γ5→ - γ5, namely, not defined in field theory. To be consistent with the theorem, it is common to use a doublet representation of chirality preserving charge conjugation C:νR,L→ CνL,RT and parity P: νR,L→ iγ0νL,R in theory containing both νR,L. In the type I seesaw model, the latter formulation is applicable but ψ+=νR + CνRT is not a Majorana fermion. An analogue of the Bogoliubov transformation converts ψ±=νR, L ± CνR, LT, which are obtained by a precise diagonalization of the seesaw model, to Majorana fermions ψ_M1,2=(ψ± CψT)/√(2) with a Dirac-type fermion ψ, as originally defined by Majorana. A chiral projection [(1+γ5)/2] ψ_M1 of a Majorana fermion is not a chiral fermion, which ensures the presence of the neutrino-less double beta decay.