Partial wave analysis of two-body decay with helicity formalism

TL;DR

This paper develops a helicity formalism for analyzing two-body decay and scattering processes, focusing on angular distributions, symmetries, and polarization, with implications for extracting coupling constants from experimental data.

Contribution

It introduces a helicity-based approach to study angular distributions, symmetries, and polarization in two-body decays, facilitating the extraction of coupling constants from experimental data.

Findings

Angular distribution depends only on helicity amplitudes along the Z axis.

Symmetries like parity and time reversal affect helicity and canonical states.

Density matrix properties help analyze polarization and simplify calculations.

Abstract

In this paper, We find that the angular distribution of two-body decay and scattering process that can be studied by introducing the helicity method.It has been argued that the angular distribution only depends on magnitude of the decaying amplitude which final particle momentum is along the $Z$ axis. Therefore, when calculating the angular distribution,we only need to know the helicity amplitude in the $Z$ direction. At the same time, we also discuss the symmetry of physical processes, such as parity and time inversion transformation and so on. The effects of these symmetric transformations on the helicity state and the canonical states are studied in this paper. When it is applied to two body decay process, the symmetry of the amplitude can be obtained by helicity method. In addition, we also introduce the density matrix to study the polarization of the final state particles, and discuss some inherent symmetries of the density matrix. When we study the polarization and angular distribution of final state particles, we can use these properties to simplify density matrix without knowing all the elements of the density matrix.Then we find that there is a close relationship between the partial wave\cite{2003Tree}coupling constants and the angular distribution parameters, indicating that these coupling constants can be obtained by experimental fitting to data.In a word, the properties of two body decay and two body cascade decay process can be analyzed by helicity method, which has a very good application .