The transverse-momentum-dependent distributions (TMDs), which are defined by gauge-invariant 3D parton correlators with staple-shaped lightlike Wilson lines, can be calculated from quark and gluon correlators fixed in the Coulomb gauge on a Euclidean lattice. These quantities can be expressed gauge invariantly as the correlators of Coulomb-gauge-dressed fields, which reduce to the standard TMD correlators under principal-value prescription in the infinite boost limit. In the framework of large-momentum effective theory, a quasi-TMD defined from such correlators in a large-momentum hadron state can be matched to the TMD via a factorization formula, whose exact form is derived using soft collinear effective theory and verified at one-loop order. Compared to the currently used gauge-invariant correlators, this new method can substantially improve statistical precision and simplify renormalization for the time-reversal-even TMDs, which will greatly enhance the predicative power of lattice QCD in the nonperturbative region. Published by the American Physical Society 2024

中文翻译：

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无威尔逊线的晶格 QCD 的横向动量分布


横向动量依赖性分布 （TMD） 由规范不变的 3D parton 相关器与订书钉形轻线性 Wilson 线定义，可以根据固定在欧几里得晶格上库仑规范中的夸克和胶子相关器计算。这些量可以不变地表示为库仑规修饰场的相关器，在无限升压极限的本值规定下，这些量减少到标准 TMD 相关器。在大动量有效理论的框架中，由大动量强子状态下的此类相关器定义的准 TMD 可以通过因式分解公式与 TMD 匹配，其确切形式是使用软共线有效理论推导的，并在单环阶上验证。与目前使用的规范不变相关器相比，这种新方法可以大大提高统计精度并简化时间反转偶数 TMD 的重整化，这将大大增强晶格 QCD 在非扰动区域中的预测能力。 美国物理学会 2024 年出版