Differential cross section analysis in kaon photoproduction using associated legendre polynomials

TL;DR

This paper analyzes angular distributions of kaon photoproduction cross sections using associated Legendre polynomials, determining that up to four polynomials suffice to model the CLAS data effectively.

Contribution

It introduces a method to describe kaon photoproduction data with associated Legendre polynomials and identifies the optimal number needed for accurate modeling.

Findings

CLAS data requires no more than four Legendre polynomials.

The best model's coefficients are extracted and presented.

Model comparison via posterior probabilities confirms the optimal polynomial count.

Abstract

Angular distributions of differential cross sections from the latest CLAS data sets \cite{bradford}, for the reaction ${\gamma}+p {\to} K^{+} + {\Lambda}$ have been analyzed using associated Legendre polynomials. This analysis is based upon theoretical calculations in Ref. \cite{fasano} where all sixteen observables in kaon photoproduction can be classified into four Legendre classes. Each observable can be described by an expansion of associated Legendre polynomial functions. One of the questions to be addressed is how many associated Legendre polynomials are required to describe the data. In this preliminary analysis, we used data models with different numbers of associated Legendre polynomials. We then compared these models by calculating posterior probabilities of the models. We found that the CLAS data set needs no more than four associated Legendre polynomials to describe the differential cross section data. In addition, we also show the extracted coefficients of the best model.