Two classes of Majorana neutrinos in the seesaw model

TL;DR

This paper clarifies the classification of Majorana neutrinos within the seesaw model, showing how a generalized transformation relates Weyl-type and Dirac-type Majorana fermions without altering mixing angles.

Contribution

It introduces a generalized Pauli–Gürsey transformation that connects different classes of Majorana neutrinos in the seesaw model, preserving canonical relations and mixing angles.

Findings

Weyl-type Majorana neutrinos can be transformed into Dirac-type Majorana neutrinos.

The transformation preserves the canonical anti-commutation relations.

Neutrino mixing angles remain unaffected by this transformation.

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--G\"{u}rsey (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--G\"{u}rsey transformation.