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

In this study, the non-trival effect of the selection of reference particles for decay angle definitions is demonstrated when constructing the partial-wave amplitude of multi-body decays using helicity formalism. This issue is often ignored in the standard use case of helicity formalism. A new technique is proposed to test the selection of the particle ordering, and it can also be used as a generalized method to calculate the rotation operators that are used for the final-state alignment between different decay chains. Moreover, numerical validations are performed to support the arguments and to verify the effectiveness of the proposed technique.

Automated summary

The study demonstrates the non-trivial effect of reference particle selection on decay angle definitions when constructing partial-wave amplitudes of multi-body decays using helicity formalism. A new technique is proposed to test particle ordering selection and can be used as a generalized method to calculate rotation operators for final-state alignment between different decay chains. Numerical validations are performed to support arguments and verify the proposed technique's effectiveness.