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

TL;DR

This paper analyzes recent experimental measurements of specific charmonium radiative decay branching ratios within a potential model, finding good agreement for one but a discrepancy for the other, and deriving an upper bound for the latter.

Contribution

The study provides a detailed theoretical analysis of recent measurements, including relativistic and QCD corrections, and establishes an upper bound on the $ o o$ decay width.

Findings

Prediction for $ o o$ width matches data for $ o$

Prediction for $ o$ width is too small compared to data

Experimental value saturates the derived upper bound

Abstract

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.