Two Photon Transition Form Factor of $\bar{c}c$ Quarkonia

Abstract

The two photon transition of $\bar{c}c$ quarkonia are studied within a covariant approach based on the consistent truncation scheme of the quantum chromodynamics Dyson-Schwinger equation for the quark propagator and the Bethe--Salpeter equation for the mesons. We find the decay widths of ${\eta }_c^{}\to \gamma \gamma$ and ${\chi }_{c0,2}^{}\to \gamma \gamma$ in good agreement with experimental data. The obtained transition form factor of ${\eta }_c^{}\to \gamma {\gamma }^{\ast }$ for a wide range of space-like photon momentum transfer squared is also in agreement with the experimental findings of the BABAR experiment. As a by-product, the decay widths of ${\eta }_b^{},{\chi }_{b0,2}^{}\to \gamma \gamma$ and the transition form factor of ${\eta }_b^{},{\chi }_{c0,b0}^{}\to \gamma {\gamma }^{\ast }$ are predicted, which await for experimental test.