On kinematical constraints in fermion-antifermion systems

TL;DR

This paper develops a method to eliminate kinematical constraints in fermion-antifermion scattering amplitudes, facilitating better data analysis and effective field theory construction.

Contribution

It introduces transformations that remove kinematical constraints from helicity partial-wave amplitudes for fermion-antifermion scattering.

Findings

Derived transformations eliminate all kinematical constraints.

Provides a basis for partial-wave dispersion relations.

Applicable to fermions with spin 1/2 and 3/2.

Abstract

We consider the scattering of fermions off antifermions with spin 1/2 and 3/2. Starting from helicity partial-wave scattering amplitudes we derive transformations that eliminate all kinematical constraints. Such amplitudes are expected to satisfy partial-wave dispersion relations and therefore provide a suitable basis for data analysis and the construction of effective field theories. Our derivation relies on a decomposition of the various scattering amplitudes into suitable sets of invariant functions.