Prediction of mass of $\eta_{c}$ (2S) using variational method

Abstract

The suitability of using non-relativistic quantum mechanics to investigate heavy quark mesons is illustrated through a study of the charmonium meson. We consider a limiting form of the QCD potential which is a simple combination of the linear and Coulomb potential. The experimentally determined masses of $J/\psi (1S)$ and $\chi_{c1}(1P)$ are reproduced for $m_{c} \approx 1.1 GeV$. For $\psi(2S)$ we have three different sets of variational parameters and to choose the appropriate one we use the leptonic decay width of $\psi(2S)$ and $J/\psi(1S)$. Finally we use a spin-spin interaction to investigate the hyperfine splitting of Charmonium and use it to calculate the mass of $\eta_{c}(2S)$. Our theoretical results agree with the experimentally measured values of $\eta_{c}(2S)$ and thereby verifies the usefulness of non-relativistic quantum mechanics in the study of heavy quark meson.