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 $m_c\approx 1.1GeV$. 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.

7 pages