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 $η_{c}^{} \to γγ$ and $χ_{c0,2}^{} \to γγ$ in good agreement with experimental data. The obtained transition form factor of $η_{c}^{} \to γγ^{\ast}$ 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 $η_{b}^{},χ_{b0,2}^{} \to γγ$ and the transition form factor of $η_{b}^{}, χ_{c0,b0}^{} \toγγ^{\ast}$ are predicted, which await for experimental test.