Note on recent measurements of the $ψ(1S)\to\ga η_C(1S)$ and $ψ(2S)\to\ga η_C(1S)$ branching ratios

Stanley F. Radford, Wayne W. Repko

Published 2008-05-25, updated 2008-05-30Version 2

Recently published measurements of the branching ratios ${\cal B}(\psi(1S)\to\ga \eta_C(1S))$ and ${\cal B}(\psi(2S)\to\ga \eta_C(1S))$ 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 $\Gamma(\psi(1S)\to\ga \eta_C(1S))$ is in excellent agreement with the new data but the prediction for $\Gamma(\psi(2S)\to\ga \eta_C(1S))$ is too small. In an effort to understand this discrepancy, we derive an upper bound on $\Gamma(\psi(2S)\to\ga \eta_C(1S))$ and point out its experimental value saturates this bound.