Artificial neural network approach for mass spectra of (ηc(nS),ψ(nS)) states and X(3940), X(4160), Y(4260), ψ(4415), Y(4660) charmonium-like resonances

Abstract

This work is devoted to the study of charmonium S-states by solving the Schrödinger equation with Cornell plus spin–spin interaction term via the artificial neural network (ANN) approach. From the solutions provided by ANN approach, we propose possible assignments for some of the recently discovered charmonium-like resonances. For simplicity purpose, we restricted the study to the ground and radially excited S-states of charmonium. The charmonium wave function is represented by the feed forward ANN and its inputs are assimilated to coordinate values. We calculated the masses, hyperfine splittings, spin-averaged mass spectrum and Regge trajectories of pseudoscalar and vector charmonium states. Overall, our results are in good accordance with the available experimental data and past studies of the mass spectrum of [Formula: see text] and [Formula: see text] charmonium states. Further, we propose a possible assignment for some of the recently discovered charmonium-like mesons. We concluded that [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] are, respectively, good candidates of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] charmonium-like resonances.