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

Abstract

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