Propagator mixing renormalization for Majorana fermions

We consider a mixed system of unstable Majorana fermions in a general parity-nonconserving theory and renormalize its propagator matrix to all orders in the pole scheme, in which the squares of the renormalized masses are identified with the complex pole positions and the wave-function renormalization (WFR) matrices are adjusted in compliance with the Lehmann-Symanzik-Zimmermann reduction formalism. In contrast to the case of unstable Dirac fermions, the WFR matrices of the in and out states are uniquely fixed, while they again bifurcate in the sense that they are no longer related by pseudo-Hermitian conjugation. We present closed analytic expressions for the renormalization constants in terms of the scalar, pseudoscalar, vector, and pseudovector parts of the unrenormalized self-energy matrix, which is computable from the one-particle-irreducible Feynman diagrams of the flavor transitions, as well as their expansions through two loops. In the case of stable Majorana fermions, the well-known one-loop results are recovered.