AI 中文总结
该研究在自洽光前夸克模型中，利用CLEO、BABAR等实验数据约束$η$-$η^{\text{'}}$混合角，计算其非微扰性质，验证了跃迁形状因子数据的强约束作用。
AI 中文摘要
我们在自洽光前夸克模型（LFQM）中研究$η$-$η^{\text{'}}$介子系统，采用夸克味混合方案，其中单一混合角由跃迁形状因子（TFFs）$F_{η^{(\text{'})}γ}(Q^2)$约束。对CLEO和BABAR数据的联合$χ^2$扫描得到最佳拟合值$θ=41.5^\text{°}$，与最近LHCb的结果$(41.6^{+1.0}_{-1.2})^\text{°}$吻合良好。利用该混合角，我们计算了$η$和$η^{\text{'}}$介子的衰变常数、光前分布振幅（LCDAs）、盖根鲍尔矩、$ξ$矩、横动量矩、电磁相互作用半径及双光子衰变宽度。预测的$a_2^η$和$\text{〈}ξ^2\text{〉}_η$与最新BABAR结果一致，电磁相互作用半径也与A2和BESIII的测量结果吻合良好。这些结果表明，TFFs数据为$η$-$η^{\text{'}}$介子系统非微扰性质的光前描述提供了强约束。由于缺乏对实光子值$F_{η^{(\text{'})}γ}(0)$的直接实验约束，预测的衰变宽度略低于实验数据，可通过未来测量进一步检验。
英文摘要
We study the $η$-$η^{\prime}$ system in the self-consistent light-front quark model (LFQM) with the quark flavor mixing scheme, where the single mixing angle is constrained by the transition form factors (TFFs) $F_{η^{(\prime)}γ}(Q^2)$. A combined $χ^2$ scan of the CLEO and BABAR data yields the best fit value $θ=41.5^\circ$, in close agreement with the recent LHCb result $(41.6^{+1.0}_{-1.2})^\circ$. Using this mixing angle, we calculate the decay constants, light-cone distribution amplitudes (LCDAs), Gegenbauer moments, $ξ$-moments, transverse momentum moments, electromagnetic interaction radii and two photon decay widths of the $η$ and $η^{\prime}$ mesons. The predicted $a_2^η$ and $\langleξ^2\rangle_η$ are consistent with the latest BABAR results, and the electromagnetic interaction radii also agreeing well with the A2 and BESIII measurements. These results demonstrate that TFFs data provide strong constraints on the light-front description for the nonperturbative properties of the $η$-$η^{\prime}$ system. Owing to the lack of direct experimental constraints on the real photon value $F_{η^{(\prime)}γ}(0)$, the predicted decay widths are somewhat lower than the experimental data, which can be further examined with future measurements.
Comments14 pages, 4 figures
