Covariant Helicity-Coupling Amplitudes: A New Formulation

TL;DR

This paper introduces a new covariant formulation for helicity-coupling amplitudes in two-body decays involving arbitrary spins, utilizing the Poincaré group generators and Lorentz factors for improved theoretical modeling.

Contribution

It presents a novel covariant amplitude construction method for resonances with arbitrary spins, incorporating the total intrinsic spin operator and Lorentz factors.

Findings

Derived covariant amplitudes for any two-body decay with arbitrary spins.

Connected the new formulation to Zemach amplitudes by adjusting Lorentz factors.

Provided a systematic approach for constructing decay amplitudes in relativistic frameworks.

Abstract

We have worked out covariant amplitudes for any two-body decay of a resonance with an arbitrary non-zero mass, which involves arbitrary integer spins in the initial and the final states. One key new ingredient for this work is the application of the total intrinsic spin operator $\vec S$ which is given directly in terms of the generators of the Poincar\'e group. Using the results of this study, we show how to explore the Lorentz factors which appear naturally, if the momentum-space wave functions are used to form the covariant decay amplitudes. We have devised a method of constructing our covariant decay amplitudes, such that they lead to the Zemach amplitudes when the Lorentz factors are set one.