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

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.