Feature extraction in partial wave analysis using $K$-matrix approach

Abstract

Structures in the invariant mass distribution are often linked to unstable intermediate states or resonances. In experiments, many signals are detected which have broad, overlapping or intricate profiles, which makes their characterization a formidable task. To ascertain whether or not these enhancements are resonances, and to determine their physical parameters, such as the resonance mass, coupling strength, resonance width, and quantum numbers, a tool known as partial wave analysis (PWA) is employed. To ensure unitarity, and to account for superposing states and non-resonant effects in modeling the scattering amplitude, $K$-matrix parametrization is utilized. To factor in the centrifugal effects on the decay rates arising from breakup processes in nonzero angular momenta, the Blatt-Weisskopf barrier factors are incorporated into the formulation. In this study, $K$-matrix parametrized differential cross sections were generated within near-threshold and resonance energy ranges, which served as the training and validation datasets for the Deep Neural Network (DNN). The Fully-Connected Neural Network (FCNN) architecture is applied to facilitate the classification task of this work, which is the discrimination of dominating partial waves in the scattering processes. The DNN model was designed to encompass various two-hadron scattering phenomena. As a stepping-off point, the values of the thresholds, coupling constants, resonance masses and widths, scattering energy ranges, and the decay channels used in this study found their physical inspiration from pion-nucleon ($\pi$$N$) scattering system in the $S$, $P$, $D$, $F$, and $G$ partial waves. The results of the model's performance showed that the DNN can distinguish the partial wave with resonances from the other partial waves with purely non-resonant contributions, at an accuracy of $69\%$.