AI 中文总结
该研究在扰动QCD中计算了$J/ψ$和$ψ(2S)$到$γη^{(′)}$的辐射衰变，考虑相对论修正，发现相对论修正显著提高了$J/ψ$分支比，但$ψ(2S)$的预测与数据存在不一致，通过引入$η_{c}$-混合贡献，干涉效应可使预测与数据一致。
AI 中文摘要
我们首次计算了$J/ψ$和$ψ(2S)$到$γη^{(′)}$的辐射衰变，在扰动QCD中包括所有三个短距离贡献中的$order-q^{2}$相对论修正，即夸克-反夸克、双胶子和QED贡献。振幅被发现对轻锥分布幅和轻夸克质量非常不敏感，这种稳健性持续到$order-q^{2}$，使预测相应可靠。相对论修正使$J/ψ$分支比增加约两倍，缩小了与实验的差距，而对于$ψ(2S)$则约为$J/ψ$的两倍，低阶展开收敛性较差。在两个代表性的$η$--$η'$混合方案中，比值$\mathcal{R}_{1S}=\mathcal{B}(\gamma\eta')/\mathcal{B}(\gamma\eta)$对混合角高度敏感，并倾向于较小的值。预测的$ψ(2S)$速率在两个通道中都高于数据，即使在Leading order也如此，最严重的对于异常小的$γη$通道。这种不一致表明，一个机制在硬扰动过程之外起作用。作为一种物理动机的尝试，我们探索了$η_{c}$-混合贡献，它在$γη$通道中与扰动过程相干地相加，并且与之相当，我们发现干涉可以将$ψ(2S)$速率与数据一致，尽管其提取受到对混合参数强敏感的限制。
英文摘要
We present the first calculation of the radiative decays $J/ψ,ψ(2S)\rightarrowγη^{(\prime)}$ in perturbative QCD that includes the order-$q^{2}$ 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 $q^{2}$ 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 $\mathcal{R}_{1S}=\mathcal{B}(γη')/\mathcal{B}(γη)$ 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 $η_{c}$-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.
Comments37 pages, 3 figures, 9 tables
