Di-electron and two-photon widths in charmonium

TL;DR

This paper calculates di-electron and two-photon decay widths of charmonium states using the Field Correlator Method, achieving good agreement with experimental data by adjusting the strong coupling constant.

Contribution

It introduces a consistent calculation framework for charmonium decay widths using the Field Correlator Method with specific QCD corrections and coupling constants.

Findings

Calculated di-electron widths agree with experiment using α_s=0.165.

Larger α_s=0.191 improves agreement for two-photon widths.

Different α_s values are needed for various decay processes.

Abstract

The vector and pseudoscalar decay constants are calculated in the framework of the Field Correlator Method. Di-electron widths: $\Gamma_{ee}(J/\psi)=5.41$ keV, $\Gamma_{ee}(\psi'(3686))=2.47$ keV, $\Gamma_{ee}(\psi''(3770))=0.248$ keV, in good agreement with experiment, are obtained with the same coupling, $\alpha_s=0.165$, in QCD radiative corrections. We show that the larger $\alpha_s=0.191\pm 0.004$ is needed to reach agreement with experiment for $\Gamma_{\gamma\gamma}(\eta_c)=7.22$ keV, $\Gamma_{\gamma\gamma} (\chi(^3P_0))=3.3$ keV, $\Gamma_{\gamma\gamma}(\chi(^3P_2))= 0.54$ keV, and also for $\Gamma(J/\psi\to 3g)=59.5$ keV, $\Gamma(J/\psi\to \gamma 2g)=5.7$ keV. Meanwhile even larger $\alpha_s=0.238$ gives rise to good description of $\Gamma(\psi'\to 3g)=52.7$ keV, $\Gamma(\psi'\to \gamma 2g)= 3.5$ keV, and provides correct ratio of the branching fractions: $\frac{\mathcal{B}(J/\psi\to light hadrons)}{\mathcal{B}(\psi'\to light hadrons)}=0.24.$