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

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 $J/ψ(1S)$ and $χ_{c1}(1P)$ are reproduced for $m_{c} \approx 1.1 GeV$. For $ψ(2S)$ we have three different sets of variational parameters and to choose the appropriate one we use the leptonic decay width of $ψ(2S)$ and $J/ψ(1S)$. Finally we use a spin-spin interaction to investigate the hyperfine splitting of Charmonium and use it to calculate the mass of $η_{c}(2S)$. Our theoretical results agree with the experimentally measured values of $η_{c}(2S)$ and thereby verifies the usefulness of non-relativistic quantum mechanics in the study of heavy quark meson.