Bayesian Analysis of $C_{x'}$ and $C_{z'}$ Double Polarizations in Kaon Photoproduction

TL;DR

This paper applies Bayesian model selection to analyze experimental data on double polarization observables in kaon photoproduction, determining the polynomial order needed to accurately describe the data and revealing insights into baryon resonance structures.

Contribution

It introduces a Bayesian approach using nested sampling to identify the optimal Legendre polynomial order for modeling polarization data in kaon photoproduction.

Findings

$C_{x'}$ polarization best described by second-order Legendre polynomial.

$C_{z'}$ polarization best described by third-order Legendre polynomial.

The analysis provides coefficients that qualitatively reveal baryon resonance structures.

Abstract

Have been analyzed the latest experimental data for $\gamma + p \to K^{+} + \Lambda$ reaction of $C_{x'}$ and $C_{z'}$ double polarizations. In theoretical calculation, all of these observables can be classified into four Legendre classes and represented by associated Legendre polynomial function itself \cite{fasano92}. In this analysis we attempt to determine the best data model for both observables. We use the bayesian technique to select the best model by calculating the posterior probabilities and comparing the posterior among the models. The posteriors probabilities for each data model are computed using a Nested sampling integration. From this analysis we concluded that $C_{x'}$ and $C_{z'}$ double polarizations require two and three order of associated Legendre polynomials respectively to describe the data well. The extracted coefficients of each observable will also be presented. It shows the structure of baryon resonances qualitatively