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

TL;DR

This paper calculates the radiative and leptonic decay rates of the $ ext{eta}_c$ meson, showing good agreement with experimental data for the radiative decay and highlighting the potential of leptonic decays to probe new physics beyond the standard model.

Contribution

It provides detailed theoretical calculations of $ ext{eta}_c$ decay rates, including loop and tree diagrams, and emphasizes the sensitivity of leptonic decays to new physics beyond the standard model.

Findings

Decay rate of $ ext{eta}_c o ext{gamma} ext{gamma}$ matches experimental data.

Loop diagrams dominate the leptonic decay contributions.

Leptonic decay branching ratios are extremely small within the standard model.

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.