Revisiting on-shell renormalization conditions in theories with flavour mixing

TL;DR

This paper reviews the derivation of on-shell renormalization conditions for scalar and fermionic fields, including Majorana fermions, emphasizing a canonical propagator approach and clarifying their implementation in theories with flavor mixing.

Contribution

It provides a unified derivation of on-shell renormalization conditions applicable to scalar, fermionic, and Majorana fields, clarifying their implementation in flavor-mixing theories.

Findings

Derivation of on-shell conditions consistent with standard approaches

Application to theories with and without parity conservation

Clarification of implementation in renormalization procedures

Abstract

In this review, we present a derivation of the on-shell renormalization conditions for scalar and fermionic fields in theories with and without parity conservation. We also discuss the specifics of Majorana fermions. Our approach only assumes a canonical form for the renormalized propagators and exploits the fact that the inverse propagators are non-singular in $\varepsilon = p^2 - m_n^2$, where $p$ is the external four-momentum and $m_n$ is a pole mass. In this way, we obtain full agreement with commonly used on-shell conditions. We also discuss how they are implemented in renormalization.