Bayesian analysis of kaon photoproduction with the Regge-plus-resonance model

Abstract

We address the issue of unbiased model selection and propose a methodology based on Bayesian inference to extract physical information from kaon photoproduction $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ data. We use the single-channel Regge-plus-resonance (RPR) framework for $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ to illustrate the proposed strategy. The Bayesian evidence $\mathcal{Z}$ is a quantitative measure for the model's fitness given the world's data. We present a numerical method for performing the multidimensional integrals in the expression for the Bayesian evidence. We use the $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ data with an invariant energy $W>2.6$ GeV in order to constrain the background contributions in the RPR framework with Bayesian inference. Next, the resonance information is extracted from the analysis of differential cross sections and single- and double-polarization observables. This background and resonance content constitutes the basis of a model, which is coined RPR-2011. It is shown that RPR-2011 yields a comprehensive account of the kaon photoproduction data and provides reasonable predictions for $e+p\ensuremath{\rightarrow}{e}^{\ensuremath{'}}+{K}^{+}+\ensuremath{\Lambda}$ observables.