Wigner rotations for cascade reactions

Cascade parameterization of hadronic reactions is a central tool in hadron spectroscopy for modeling matrix elements and extracting parameters of hadronic states. Implementing the helicity formalism consistently presents challenges, particularly for particles with spin, due to the need for matching spin states of final-state particles, known as the Wigner rotations. This paper discusses these challenges in detail and offers solutions, including a practical method for implementation. Equipped with a general algorithm for computing Wigner rotations, we extend the studies to alternative amplitude formulations, the minus-phi and canonical conventions.