论文标题
重新访问$ p $ - 波式辐射衰减$ h_ {c} \rightArrowγη^{（\ prime）} $带相对论校正
Revisiting the $P$-wave charmonium radiative decays $h_{c}\rightarrowγη^{(\prime)}$ with relativistic corrections
论文作者
论文摘要
$ p $ - 波charmon衰减$ h_ {c} \rightarrowγη^{（\ prime）} $通过考虑相对论校正来重新审视。衰减幅度衍生在伯特盐钙板形式中，其中涉及的一环积分进行了分析评估。有趣的是，从Quark-Antiquark含量和$η^{（\ prime）} $的Gluonic内容中，相对论更正对$ h_ {c} \rightArrowγη^{（\ prime）} $的衰减率做出了重大贡献。通过与来自夸克 - 易夸克含量（一环级别）的领先贡献相比，Gluonic含量（树级）的贡献也很重要，这与没有相对论校正的结论兼容。通常，对于$η$生产过程，预测的分支比对$η-η^{\ prime} $混合的角度敏感。作为例证，使用Feldmann-Kroll-Stech结果进行混合角度$ ϕ = 39.3^{\ circ} \ pm1.0^{\ circ} $作为输入，我们发现预测的比率是$ r_ {h_ {c}} = \ Mathcal {b}（h_ {c} \rightarrowγη）/\ Mathcal {b}（h_ {c} \rightArrowγη^{\ prime}）$比实验测量小得多。而$ ϕ = 33.5^{\ circ} \ pm0.9^{\ circ} $从$γ^{\ ast}γ-η^{\ prime} $过渡形式提取的渐近极限提取，我们获得了$ r_ {h_ {c} = 30.3.3.3 \％$ $ $ $ $ $ $ $ $ $ $ $ r_ {h_ {c}}}^{exp} =（30.7 \ pm11.3 \ pm8.7）\％$。作为交叉检查，通过使用比率$ r_ {h_ {c}} $提取的混合角$ ϕ = 33.8^{\ circ} \ pm2.5^{\ circ} $，并简要讨论了$ ϕ $的确定差异。
The $P$-wave charmonium decays $h_{c}\rightarrowγη^{(\prime)}$ are revisited by taking into account relativistic corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, in which the involved one-loop integrals are evaluated analytically. Intriguingly, from both the quark-antiquark content and the gluonic content of $η^{(\prime)}$, the relativistic corrections make significant contributions to the decay rates of $h_{c}\rightarrowγη^{(\prime)}$. By comparison with the leading-order contributions from the quark-antiquark content (one-loop level), the ones from the gluonic content (tree level) are also important, which is compatible with the conclusion obtained without relativistic corrections. Usually, for $η$ production processes, the predicted branching ratios are sensitive to the angle of $η-η^{\prime}$ mixing. As an illustration, using the Feldmann-Kroll-Stech result about the mixing angle $ϕ=39.3^{\circ}\pm1.0^{\circ}$ as input, we find that the predicted ratio $R_{h_{c}}=\mathcal{B}(h_{c}\rightarrowγη)/\mathcal{B}(h_{c}\rightarrowγη^{\prime})$ is much smaller than the experiment measurement. While, with $ϕ=33.5^{\circ}\pm0.9^{\circ}$ extracted from the asymptotic limit of the $γ^{\ast}γ-η^{\prime}$ transition form factor, we obtain $R_{h_{c}}=30.3\%$ in consistent with $R_{h_{c}}^{exp}=(30.7\pm11.3\pm8.7)\%$. As a cross-check, the mixing angle $ϕ=33.8^{\circ}\pm2.5^{\circ}$ is extracted by employing the ratio $R_{h_{c}}$, and a brief discussion on the difference in the determinations of $ϕ$ is given.
