Phenomenological Description of an Unstable Fermion

Abstract

We present a phenomenological description for an unstable fermion based upon one-loop renormalization of quantum field theory. It is emphasized that wave function renormalization can introduce important $CP$-conserving and $CP$-violating phases. Implications for the study of $CP$ violation are examined. Applications are given to $CP$-violating asymmetries in the $t$ decays: $t\to bW^+, bH^+$, in which we show that a naive calculation following the standard rule either is incomplete or violates $CPT$.