Parity and CP operations for Majorana neutrinos

Abstract

The parity transformation law of the fermion field ψ(x) is usually defined by the "γ0 parity"ψp(t,-x→)=γ0ψ(t,-x→) with eigenvalues ±1, while the "iγ0 parity"ψp(t,-x→)=iγ0ψ(t,-x→) is required for the Majorana fermion. The compatibility issues of these two parity laws arise in generic fermion number violating theories where a general class of Majorana fermions appear. In the case of Majorana neutrinos constructed from chiral neutrinos in an extension of the Standard Model, the Majorana neutrinos can be characterized by CP symmetry although C and P are separately broken. It is then shown that either choice of the parity operation, γ0 or iγ0, in the level of the starting fermions gives rise to the consistent and physically equivalent descriptions of emergent Majorana neutrinos both for Weinberg's model of neutrinos and for a general class of seesaw models. The mechanism of this equivalence is that the Majorana neutrino constructed from a chiral neutrino, which satisfies the classical Majorana condition ψ(x)=Cψ(x)¯T, allows the phase freedom ψ(x)=eiανL(x)+e-iαCνL(x)¯T with α=0 or π/4. This accounts for the phase coming from the different definitions of parity for νL(x) and ensures the consistent definitions of CP symmetry (CP)ψ(x)(CP)†=±iγ0ψ(t,-x→).