Extraction of charmonium branching fractions from $J/\psi\to\gamma\eta_c$ radiative decays
We assess the tension between theoretical predictions and the values quoted by the Particle Data Group (PDG) for the partial decay width and branching fraction associated with the radiative charmonium decay $J/\psi\to\gamma\eta_c$. A profile scan over the most recent PDG data depending on the branching fraction $\mathcal{B}(J/\psi\to\gamma\eta_c)$ suggests that the correlation between measured branching fractions is compatible with lattice QCD determinations of the partial decay widths $\Gamma(J/\psi\to\gamma\eta_c)$ and $\Gamma(\eta_c\to\gamma\gamma)$. We propose a theoretically grounded photon line shape for the radiative decay spectrum and a prescription for the extraction of (product) branching fractions involving the magnetic dipole (M1) transition $J/\psi\to\gamma\eta_c$. This approach obviates the need to modify the photon energy spectrum line shape using empirical damping functions, as done in the most recent experimental extractions of $\mathcal{B}(J/\psi\to\gamma\eta_c)$ from the photon line shape, thereby eliminating an inherent ambiguity in the determination of the derived observables.