Note on recent measurements of theψ(1S)→γηC(1S)andψ(2S)→γηC(1S)branching ratios

Abstract

Recently published measurements of the branching ratios $\mathcal{B}(\ensuremath{\psi}(1S)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{C}(1S))$ and $\mathcal{B}(\ensuremath{\psi}(2S)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{C}(1S))$ by the CLEO Collaboration are examined in the context of a potential model that includes both relativistic and one-loop QCD corrections to the quark-antiquark interaction. The prediction for the width $\ensuremath{\Gamma}(\ensuremath{\psi}(1S)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{C}(1S))$ is in excellent agreement with the new data, but the prediction for $\ensuremath{\Gamma}(\ensuremath{\psi}(2S)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{C}(1S))$ is too small. In an effort to understand this discrepancy, we derive an upper bound on $\ensuremath{\Gamma}(\ensuremath{\psi}(2S)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\eta}}_{C}(1S))$ and point out its experimental value saturates this bound.