On kinematical constraints in boson-boson systems

TL;DR

This paper develops a method to eliminate kinematical constraints in boson-boson scattering amplitudes, enabling more effective data analysis and theoretical modeling in particle physics.

Contribution

It introduces a transformation framework for helicity partial-wave amplitudes that removes kinematical constraints, facilitating the use of dispersion relations and effective field theories.

Findings

Derived transformations for kinematical constraint elimination

Developed a novel algebra for invariant function computation

Provided a basis for improved data analysis in boson-boson scattering

Abstract

We consider the scattering of two-bosons with negative parity and spin 0 or 1. 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. A novel algebra was developed that permits the efficient computation of such functions in terms of computer algebra codes.