A novel method to test particle ordering and final state alignment in helicity formalism

TL;DR

This paper introduces a new technique for selecting reference particles in helicity formalism to improve decay angle definitions and final-state alignment, supported by numerical validation.

Contribution

A novel method for determining particle ordering and calculating rotation operators in helicity formalism, enhancing decay analysis accuracy.

Findings

The new technique improves decay angle definitions.

Numerical validations confirm the effectiveness of the method.

The approach generalizes rotation operator calculations.

Abstract

In this article, the importance is demonstrated of a proper choice of reference particles for decay angle definitions, when constructing partial-wave amplitude of multi-body decays using helicity formalism. This issue is often ignored in the standard use case of the helicity formalism. A new technique is proposed to determine the correct particle ordering, and can also be used as a generalized method to calculate the rotation operators used for the final-state alignment between different decay chains. Numerical validations are also performed to support the arguments and new technique proposed in this article.