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On the Role of Charmed Meson Loops in Charmonium Decays

We investigate the effect of intermediate charmed meson loops on the M1 radiative decays $J/ψ\to η_c γ$ and $ψ'\rightarrowη^{(\prime)}_cγ$ as well as the isospin violating hadronic decays $ψ'\rightarrow J/ψ\,π^0(η)$ using heavy hadron chiral perturbation theory (HH$χ$PT). 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 $g_2^\prime$, respectively. We find that there are two sets of solutions for $g_2$ and $g_2^\prime$. One set, which agrees with previous values of the product $g_2 g_2^\prime$ extracted from analyses that consider only loop contributions to $ψ'\rightarrow J/ψ\,π^0(η)$, 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 $g_2^\prime$ 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 non-relativistic QCD (NRQCD). This result shows that tree level HH$χ$PT couplings are as important as the one loop graphs with charmed mesons in these charmonium decays. The couplings $g_2$ and $g_2^\prime$ are also important for the calculations of the decays of charmed meson bound states, such as the X(3872), to conventional charmonia.