$\Sigma$ 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 $98.5\%$, $94.8\%$ and $82.5\%$ 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 $1.62(11)\mathrm{GeV}$, $1.72(6)\mathrm{GeV}$ and $1.61(9)\mathrm{GeV}$, and probability being $100(3)\%$, $72(24)\%$ and $98(52)\%$, 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.

Comments: 6 pages, 6 figures with supplemental materials