Reexamining radiative decays of 1−−1^{--} quarkonium into η′\eta' and η\eta

Recently CLEO has studied the radiative decay of $\Upsilon$ into $\eta'$ and an upper limit for the decay has been determined. Confronting with this upper limit,most of theoretical predictions for the decay fails. After briefly reviewing these predictions we re-examine the decay by separating nonperturbative effect related to the quarkonium and that related to $\eta'$ or $\eta$, in which the later is parameterized by distribution amplitudes of gluons in $\eta'$. With this factorization approach we obtain theoretical predictions which are in agreement with experiment. Uncertainties in our predictions are discussed. The possibly largest uncertainties are from relativistic corrections for $J/\Psi$ and the value of the charm quark mass. We argue that the effect of these uncertainties can be reduced by using quarkonium masses instead of using quark masses. An example of the reduction is shown with an attempt to explain the violation of the famous 14% rule in radiative decays of charmonia.Comment: 9 Pages, Latex fil

Further Experimental Studies of Two-Body Radiative \Upsilon Decays

Continuing our studies of radiative Upsilon(1S) decays, we report on a search for Upsilon to gamma eta and Upsilon to gamma f_{J}(2220) in 61.3 pb^{-1} of e^{+}e^{-} data taken with the CLEO II detector at the Cornell Electron Storage Ring. For the gamma eta search the three decays of the eta meson to pi^{+}pi^{-}pi^{0}, pi^{0}pi^{0}pi^{0}, and gamma gamma were investigated. We found no candidate events in the two (3\pi)^{0} modes and no significant excess over expected backgrounds in the gamma gamma mode to set a limit on the branching fraction of B(Upsilon to gamma eta) < 2.1 x 10^{-5} at 90% C.L. The three charged two-body final states h h-bar (h = pi^{+}, K^{+}, p) were investigated for f_{J}(2220) production, with one, one, and two events found, respectively. Limits at 90% C.L. of B(\Upsilon to gamma f_{J}) x B(f_{J} to h h-bar) ~ 1.5 x 10^{-5} have been set for each of these modes. We compare our results to measurements of other radiative Upsilon decays, to measurements of radiative J/psi decays, and to theoretical predictions.Comment: 19 pages postscript, also available through http://w4.lns.cornell.edu/public/CLNS, submitted to Physical Review