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 the QCD radiative corrections. We show that the larger α s = 0.191 ± 0.004 is needed to reach agreement with experiment for Γ γγ (χ c ) = 7.22 keV, Γ γγ (χ c (3 P0)) = 3.3 keV, Γ γγ χ c (3 P 2)) = 0.54 keV, and also for Γ(J/ψ → 3g) = 59.5 keV, Γ(J/ψ → γ2g) = 5.7 keV. Meanwhile, even larger α s = 0.238 gives rise to good description of Γ(ψ′ → 3g) = 52.7 keV, Γ(ψ′ → γ2g) = 3.5 keV, and provides correct ratio of the branching fractions: \( \frac{{\mathcal{B}({J \mathord{\left/ {\vphantom {J \psi }} \right. \kern-\nulldelimiterspace} \psi } \to light hadrons)}} {{\mathcal{B}(\psi ' \to light hadrons)}} = 0.24 \).