Wigner rotations for cascade reactions

Parametrization of cascading 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 to match spin states of final-state particles, an operation known as the Wigner rotation. 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.