$\Sigma$ Resonances from a Neural Network-based Partial Wave Analysis on $K^-p$ Scattering

Abstract

We implement a convolutional neural network to study the $\Sigma$ hyperons using experimental data of the $K^-p\to\pi^0\Lambda$ reaction. The averaged accuracy of the NN models in resolving resonances on the test data sets is ${\rm 98.5\%}$, ${\rm 94.8\%}$ and ${\rm 82.5\%}$ for one-, two- and three-additional-resonance case. We find that the three most significant resonances are $1/2^+$, $3/2^+$ and $3/2^-$ states with mass being ${\rm 1.62(11)~GeV}$, ${\rm 1.72(6)~GeV}$ and ${\rm 1.61(9)~GeV}$, and probability being $\rm 100(3)\%$, $\rm 72(24)\%$ and $\rm 98(52)\%$, respectively, where the errors mostly come from the uncertainties of the experimental data. Our results support the three-star $\Sigma(1660)1/2^+$, the one-star $\Sigma(1780)3/2^+$ and the one-star $\Sigma(1580)3/2^-$ in PDG. The ability of giving quantitative probabilities in resonance resolving and numerical stability make NN potentially a life-changing tool in baryon partial wave analysis, and this approach can be easily extended to accommodate other theoretical models and/or to include more experimental data.