Di-electron and two-photon widths in charmonium

Abstract

The vector and pseudoscalar decay constants are calculated in the framework of the Field Correlator Method. Di-electron widths: $Γ_{ee}(J/ψ)=5.41$ keV, $Γ_{ee}(ψ'(3686))=2.47$ keV, $Γ_{ee}(ψ''(3770))=0.248$ keV, in good agreement with experiment, are obtained with the same coupling, $α_s=0.165$, in QCD radiative corrections. We show that the larger $α_s=0.191\pm 0.004$ is needed to reach agreement with experiment for $Γ_{γγ}(η_c)=7.22$ keV, $Γ_{γγ} (χ(^3P_0))=3.3$ keV, $Γ_{γγ}(χ(^3P_2))= 0.54$ keV, and also for $Γ(J/ψ\to 3g)=59.5$ keV, $Γ(J/ψ\to γ2g)=5.7$ keV. Meanwhile even larger $α_s=0.238$ gives rise to good description of $Γ(ψ'\to 3g)=52.7$ keV, $Γ(ψ'\to γ2g)= 3.5$ keV, and provides correct ratio of the branching fractions: $\frac{\mathcal{B}(J/ψ\to light hadrons)}{\mathcal{B}(ψ'\to light hadrons)}=0.24.$