The $p(\gamma,K^+)\Lambda$ reaction: consistent high-spin interactions and Bayesian inference of its resonance content

Abstract

A Bayesian analysis of the world's $p(\gamma,K^+)\Lambda$ data is presented. We adopt a Regge-plus-resonance framework featuring consistent interactions for nucleon resonances up to spin $J = 5/2$. The power of the momentum dependence of the consistent interaction structure rises with the spin of the resonance. This leads to unphysical structures in the energy dependence of the computed cross sections when the short-distance physics is cut off with standard hadronic form factors. A plausible, spin-dependent modification of the hadronic form factor is proposed which suppresses the unphysical artifacts. Next, we evaluate all possible combinations of 11 candidate resonances. The best model is selected from the 2048 model variants by calculating the Bayesian evidence values against the world's $p(\gamma,K^+)\Lambda$ data. From the proposed selection of 11 resonances, we find that the following nucleon resonances have the highest probability of contributing to the reaction: $S_{11}(1535)$, $S_{11}(1650)$, $F_{15}(1680)$, $P_{13}(1720)$, $D_{13}(1900)$, $P_{13}(1900)$, $P_{11}(1900)$, and $F_{15}(2000)$.