LSZ-reduction, resonances and non-diagonal propagators: fermions and scalars

TL;DR

This paper provides a detailed analysis of fermionic and scalar field mixing, offering a proof of residue factorization at complex poles and a systematic method for calculating residues in various renormalization schemes.

Contribution

It introduces a general proof of residue factorization for non-diagonal propagators and a prescription for computing residues to all orders in perturbation theory for fermions and scalars.

Findings

Residues of non-diagonal propagators factorize at complex poles.

A systematic method for calculating residues in arbitrary renormalization schemes.

Applicable to systems with multiple Majorana or Dirac particles.

Abstract

We analyze in details the effects associated with mixing of fermionic fields. In a system with an arbitrary number of Majorana or Dirac particles, a simple proof of factorizability of residues of non-diagonal propagators at the complex poles is given, together with a prescription for finding the "square-rooted" residues to all orders of perturbation theory, in an arbitrary renormalization scheme. Corresponding prescription for the scalar case is provided as well.