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

TL;DR

This paper uses a variational approach within non-relativistic quantum mechanics to accurately predict the mass of the excited charmonium state ηc(2S), confirming the method's effectiveness for heavy quark mesons.

Contribution

It demonstrates the successful application of a variational method with a simplified QCD potential to predict heavy meson masses, including hyperfine splitting effects.

Findings

Predicted ηc(2S) mass matches experimental data

Reproduced J/ψ and χc1 masses with chosen parameters

Validated non-relativistic quantum mechanics for heavy meson studies

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.