Legendre Analysis of Differential Distributions in Hadronic Reactions

TL;DR

This paper advocates for using Legendre series expansion to analyze differential distributions in hadronic reactions, enabling extraction of physical insights from experimental data without relying on model-dependent methods.

Contribution

It introduces a Legendre series approach to analyze hadronic reaction data, highlighting its advantages and properties in the helicity framework.

Findings

Legendre coefficients reveal physical information without model assumptions

The approach simplifies the analysis of complex angular distributions

Properties of coefficients relate to reaction dynamics

Abstract

Modern experimental facilities, such as CBELSA, ELPH, JLab, MAMI and SPring-8 have provided a tremendous volume of data, often with wide energy and angular coverage, and with increasing precision. For reactions with two hadrons in the final state, these data are often presented as multiple sets of panels, with angular distributions at numerous specific energies. Such presentations have limited visual appeal, and their physical content is typically extracted through some model- dependent treatment. Instead, we explore the use of a Legendre series expansion with a relatively small number of essential coefficients. This approach has been applied in several recent experimental investigations. We present some general properties of the Legendre coefficients in the helicity framework and consider what physical information can be extracted without any model-dependent assumptions.