We obtain the leading-twist valence quark transverse-momentum-dependent parton distribution functions (TMD PDFs) for the proton within the basis light-front quantization (BLFQ) framework. Our results are consistent with lattice QCD calculations and our previous results for the collinear limit. We also obtain consistency with the Soffer-type bounds. Within our approach, we find that six T-even TMDs in the leading twist are all independent of each other, and previously found model-dependent relations do not hold. This is a promising sign that our results are representative of future, more extensive treatments of QCD. Furthermore, we obtain a non-trivial x-dependence of the $〈{(p^{\perp })}^2〉$ and some consistency with the Gaussian ansatz but only in the small ${(p^{\perp })}^2$ region. Those features suggest our results may be a useful alternative in future experimental extractions.

我们在基础光前量化（BLFQ）框架内获得了质子的前捻价夸克横向动量相关部分分布函数（TMD PDF）。我们的结果与晶格 QCD 计算和我们之前的共线极限结果一致。我们还获得了与 Soffer 类型边界的一致性。在我们的方法中，我们发现领先扭曲中的六个 T 偶数 TMD 都是相互独立的，并且之前发现的模型相关关系不成立。这是一个有希望的迹象，表明我们的结果代表了未来更广泛的 QCD 治疗。此外，我们获得了一个非平凡的x依赖性$〈{(p^{\perp })}^2〉$并且与高斯 ansatz 有一些一致性，但仅在小范围内${(p^{\perp })}^2$地区。这些特征表明我们的结果可能是未来实验提取的有用替代方案。