The Relativistic Correction To Charmonium Production In Electron Positron Annihilation

In recent years a lot of attention has been focused on Heavy quarkonium, and a lot of experimental and theoretical studies also have been done. The issue electron-positron annihilation produce charmonium is also a very hot topic.The process electron-positron annihilation produce heavy charmonium was factor into two part：The short coefficient section which can be calculated perturbative and the long distance matrix which was fix with the experiment data. And the short coefficient can be in the color octet state and emit a soft gluon to form the meson in the final state.The theory of color octet has obtain a lot of success and consistent with the experimental results with many process. However the theory also has some problems, for example in the process electron-positron annihilation produce heavy charmonium the long distance matrix cannot consistent with that fixed with the hadron collider process. Do not support the nature that long-distance matrix universality.We calculated the relativistic correction of cross section of the electron-positron annihilation production of ηc and J/ψ at10.6GeV based on the NRQCD factortion theroy. Re-estimate the range of long-distance matrix combinations by considering the QCD and relativistic correction. We compared the theoretical results with the hadron collider process. We found that the relativistic correction reduce the cross section about30%to40%.We also predicted that the observed event and the cross-section at Belle and BESIII of ηc produce, and gave the figure of cross-section with the center of mass energy.We hope that this picture will be helpful to measure the cross section in the experiment.