Radiative and leptonic decays of the pseudoscalar charmonium state $\eta_c$

Abstract

The radiative and leptonic decays of $\eta_c\to \gamma\gamma$ and $\eta_c\to l^+l^-$ are studied. For $\eta_c\to \gamma\gamma$ decay, the second-order electromagnetic tree-level diagram gives the leading contribution. The decay rate of $\eta_c\to \gamma\gamma$ is calculated, the prediction is in good agreement with the experimental data. For $\eta_c\to l^+\l^-$, both the tree and loop diagrams are calculated. The analysis shows that the loop contribution dominates, the contribution of tree diagram with $Z^0$ intermediate state can only modifies the decay rate by less than 1%. The prediction of the branching ratios of $\eta_c\to e^+e^-$ and $\mu^+\mu^-$ are very tiny within the standard model. The smallness of these predictions within the standard model makes the leptonic decays of $\eta_c$ sensitive to physics beyond the standard model. Measurement of the leptonic decay may give information of new physics.