2026/07/26 by Jun-Kang He, Chao-Jie Fan, Cong Wang
#hep-ph
We present the first calculation of the radiative decays J/ψ,ψ(2S)→γη(′) in perturbative QCD that includes the order-q2 relativistic corrections in all three short-distance contributions, namely the quark-antiquark, two-gluon, and QED contributions. The amplitudes are found to be remarkably insensitive to the light-cone distribution amplitude and to the light-quark mass, a robustness that persists through order q2 and makes the predictions correspondingly reliable. The relativistic correction enhances the J/ψ branching ratios by roughly a factor of two, narrowing their shortfall from experiment, whereas for the ψ(2S) it is about twice as large as for the J/ψ and the low-order expansion converges poorly. In two representative η--η' mixing schemes, the ratio R1S=B(γη')/B(γη) proves sharply sensitive to the mixing angle and favours the smaller of the two. The predicted ψ(2S) rates lie well above the data in both channels, already at leading order, and most severely for the anomalously small γη channel. Such a discrepancy suggests that a mechanism beyond the hard perturbative process is at work. As a physically motivated attempt, we explore the ηc-mixing contribution, which adds coherently to the perturbative one and is comparable to it in the γη channel, and find that the interference can bring the ψ(2S) rates into agreement with the data, although its extraction is limited by a strong sensitivity to the mixing parameters.