On the line-shape and the experimental determination of the $J/\psi \to \gamma\eta_c$ branching fraction

We study the photon spectrum line-shape of the $J/\psi \to \gamma\eta_c\to \gamma X$ decay process in a nonrelativistic effective field theory (EFT) framework of quantum chromodynamics (QCD). We take into account the finite width of the $\eta_c$ and include $\mathcal{O}(v^2)$ corrections. We observe that the photon spectrum line-shape is divergent at large energies due to polynomially and logarithmically divergent terms, that upon integration over the photon energies in Dimensional Regularization (DR) produce no contribution or can be renormalized. We propose to subtract these divergences at the line-shape level in a manner consistent with the calculation of the width in DR and $\overline{\hbox{MS}}$ scheme. We analyze CLEO's data with the proposed subtracted line-shape and find good agreement between the theoretical prediction and the experimental result.