Inclusive radiative ψ(2S) decays

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/{psi}(1S){yields}{gamma}gg, via the ''tagged'' process: e{sup +}e{sup -}{yields}{psi}(2S); {psi}(2S){yields}J/{psi}{pi}{sup +}{pi}{sup -}; J/{psi}{yields}{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{sub {gamma}}=B(gg{gamma})/B(ggg)] to be R{sub {gamma}}=0.137{+-}0.001{+-}0.016{+-}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/{psi}{yields}gg{gamma} is observed to be very similar to that of {upsilon}{yields}gg{gamma}. The R{sub {gamma}} value obtained is roughly consistent with that expected by a simple quark-charge scaling [R{sub {gamma}}{approx}(q{sub c}/q{sub b}){sup 2}] of the value determined at the {upsilon}(1S), but somewhat higher than the value expected from the running of the strong coupling constant.