Renormalization in general theories with inter-generation mixing

TL;DR

This paper derives explicit formulas for fermion propagators in theories with inter-generation mixing, addressing renormalization and physical property preservation in parity-nonconserving contexts.

Contribution

It provides general expressions for unrenormalized and renormalized fermion propagators with inter-generation mixing, including mass eigenvalues and counterterms, using matrix algebra and specific renormalization conditions.

Findings

Explicit formulas for dressed propagators derived

Mass eigenvalues and counterterms discussed

Renormalized propagators satisfy physical properties

Abstract

We derive general and explicit expressions for the unrenormalized and renormalized dressed propagators of fermions in parity-nonconserving theories with inter-generation mixing. The mass eigenvalues, the corresponding mass counterterms, and the effect of inter-generation mixing on their determination are discussed. Invoking the Aoki-Hioki-Kawabe-Konuma-Muta renormalization conditions and employing a number of very useful relations from Matrix Algebra, we show explicitly that the renormalized dressed propagators satisfy important physical properties.