The role of charmed meson loops in charmonium decays

We investigate the effect of intermediate charmed meson loops on the M1 radiative decays J/ψ→η _cγ and ψ ^′→ηc(′)γ as well as the isospin [SU(3)] violating hadronic decays ψ ^′→J/ψπ0(η) using heavy hadron chiral perturbation theory. The calculations include tree level as well as one loop diagrams and are compared to the latest data from CLEO and BES-III. Our fit constrains the couplings of 1S and 2S charmonium multiplets to charmed mesons, denoted g ₂ and g2′, respectively. We find that there are two sets of solutions for g ₂ and g2′. One set, which agrees with previous values of the product g ₂g2′ extracted from analyses that consider only loop contributions to ψ ^′→ J/ψπ0(η), can only fit data on radiative decays with fine-tuned cancellations between tree level diagrams and loops in that process. The other solution for g ₂ and g2′ leads to couplings that are smaller by a factor of 2.3. In this case tree level and loop contributions are of comparable size and the numerical values of the tree level contributions to radiative decays are consistent with estimates based on the quark model as well as nonrelativistic QCD. This result shows that tree level heavy hadron chiral perturbation theory couplings are as important as the one loop graphs with charmed mesons in these charmonium decays. The couplings g ₂ and g2′ are also important for the calculations of the decays of charmed meson bound states, such as the X(3872), to conventional charmonia.