On the polarization of fermion in an intermediate state

TL;DR

This paper introduces a covariant method for calculating fermion polarization, applicable to both final and intermediate states, using spectral representation of fermion propagators, with particular relevance to t-quark polarization.

Contribution

It presents a novel covariant approach for fermion polarization calculation using spectral representation, enabling consistent treatment of intermediate state fermions.

Findings

Provides a covariant separation of particle and antiparticle contributions.

Offers a natural definition for intermediate state fermion polarization.

Facilitates accurate description of t-quark polarization.

Abstract

We show that calculation of a final fermion polarization (for a pure initial state) is equivalent to the problem of looking for complete polarization axis of bispinor. This gives the method for calculation of polarization applicable both for final and intermediate state fermions. We suggest to use fermion propagator (bare or dressed) in form of spectral representation, which gives the orthogonal off-shell energy projectors. This representation leads to covariant separation of particle and antiparticle contributions and gives a natural definition for polarization of intermediate state fermion. The most evident application is related with consistent description of $t$-quark polarization.