Two classes of Majorana neutrinos in the seesaw model

Abstract

The commonly used pseudo-C symmetry $({\nu }_L{)}^c=C{\overline{{\nu }_L}}^T$ is not defined in Lagrangian field theory. In general, there exist two classes of Majorana fermions; the first is associated with the Dirac-type fermion with the conventional C and P symmetries, and the second is associated with the Weyl-type fermion defined by CP symmetry only and formally characterised by the pseudo-C symmetry. Taking the seesaw model as an example, it is shown that a generalized Pauli--Gürsey (or Bogoliubov-type) canonical transformation converts the neutrino defined by the Weyl-type fermion to the neutrino defined by the Dirac-type fermion and thus to the conventional Majorana fermion, while preserving the canonical anti-commutation relations. The mixing angles in the weak lepton sector are not modified by this generalized Pauli--Gürsey transformation.

Comments: 12 pages. Minor typographical corrections together with two additional footnotes and an additional reference. This version is to be published in Phys. Lett. B