Inclusive radiativeJ/ψdecays

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Abstract

Using data taken with the CLEO-c detector at the Cornell Electron Storage Ring, we have investigated the direct-photon momentum spectrum in the decay $J/\ensuremath{\psi}(1\mathrm{S})\ensuremath{\rightarrow}\ensuremath{\gamma}gg$, via the ``tagged'' process: ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\psi}(2\mathrm{S})$; $\ensuremath{\psi}(2\mathrm{S})\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$; $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}+X$. Including contributions from two-body radiative decay processes, we find the ratio of the inclusive direct-photon branching fraction to that of the dominant three-gluon branching fraction [${R}_{\ensuremath{\gamma}}=B(gg\ensuremath{\gamma})/B(ggg)$] to be ${R}_{\ensuremath{\gamma}}=0.137\ifmmode\pm\else\textpm\fi{}0.001\ifmmode\pm\else\textpm\fi{}0.016\ifmmode\pm\else\textpm\fi{}0.004$, where the errors shown are statistical, systematic, and the model-dependent uncertainty related to the extrapolation to zero photon energy. The shape of the scaled photon energy spectrum in $J/\ensuremath{\psi}\ensuremath{\rightarrow}gg\ensuremath{\gamma}$ is observed to be very similar to that of $\ensuremath{\Upsilon}\ensuremath{\rightarrow}gg\ensuremath{\gamma}$. The ${R}_{\ensuremath{\gamma}}$ value obtained is roughly consistent with that expected by a simple quark-charge scaling [${R}_{\ensuremath{\gamma}}\ensuremath{\sim}({q}_{c}/{q}_{b}{)}^{2}$] of the value determined at the $\ensuremath{\Upsilon}(1\mathrm{S})$, but somewhat higher than the value expected from the running of the strong coupling constant.

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