Understanding $J/\psi$ and $\psi '$ production using a modified version of Non-Relativistic Quantum Chromodynamics

There is serious disagreement between the predictions of Non-Relativistic Quantum Chromodynamics (NRQCD) and the data on $J/\psi$ polarisation which has persisted for almost a quarter of a century. We find that if we account for the effect of perturbative soft gluons on the intermediate charm-anticharm octet states in NRQCD then the polarisation problem can be resolved. In addition, this model, when used to fit the Run 1 data on $J/\psi$ and $\psi '$ production from the CDF experiment at Tevatron, gives good fits and yields values of (energy-independent) non-perturbative parameters. These, in turn, can be used to make parameter-free predictions for $J/\psi$ and $\psi '$ data from the CMS experiment at the Large Hadron Collider and the predictions are in excellent agreement with the CMS data.