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

TL;DR

This paper uses a covariant QCD approach to accurately compute the two-photon transition form factors and decay widths of charmonium and bottomonium states, aligning well with experimental data and providing predictions for unmeasured quantities.

Contribution

It introduces a covariant method based on Dyson-Schwinger and Bethe--Salpeter equations to calculate transition form factors and decay widths of heavy quarkonia, with results consistent with experiments.

Findings

Decay widths of $ ext{η}_c o ext{γγ}$ and $ ext{χ}_{c0,2} o ext{γγ}$ match experimental data.

Transition form factor of $ ext{η}_c o ext{γγ}^*$ agrees with BABAR measurements.

Predictions for decay widths of bottomonium states await experimental verification.

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.