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arXiv 2201.07237hep-ph
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动量空间 TMD 中长程与短程距离的分离

Disentangling Long and Short Distances in Momentum-Space TMDs

Markus A. Ebert, Johannes K. L. Michel, Iain W. Stewart, Zhiquan Sun

备注：
39 pages + appendices and references, 15 figures; v2: journal version
发表信息：
JHEP 07 (2022) 129
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AI总结：

提出一种与模型无关的积分泛函方法，将动量空间观测量限制在微扰域，从而分离 TMD 中的长程与短程贡献，实现对累积积分的精确计算及对非微扰 OPE 贡献的独立约束。

摘要：

屏蔽 Landau 极点的处理方案使得动量空间中的长程与短程贡献相互纠缠，导致提取非微扰 TMD 物理面临挑战。使用不同处理方案使得对底层非微扰贡献的拟合结果比较失去独立意义。我们提出一种与模型无关的方法，将动量空间观测量限制在微扰区域内。该方法基于一组积分泛函，它们对传统位置空间算符乘积展开（OPE）中的各项线性作用。积分截断产生的伪影可被系统性地推至 $Λ_{\rm QCD}/k_T$ 的高次项。我们证明，该方法可用于计算 TMD PDF 在 $k_T \le k_T^\mathrm{cut}$ 范围内的累积积分，且同时考虑了辐射修正与演化效应。这提供了一种系统性的方式来修正 TMD PDF 积分为共线 PDF 的朴素图像；对于非极化夸克分布，我们发现当重整化标度选择在 $k_T^\mathrm{cut}$ 附近时，此类修正是百分比量级的效应。我们还表明，结合实验数据与改进的微扰输入，我们的积分泛函将能够对 Collins-Soper kernel 和内禀 TMD 分布的非微扰 OPE 贡献设定与模型无关的界限。

英文摘要：

The extraction of nonperturbative TMD physics is made challenging by prescriptions that shield the Landau pole, which entangle long- and short-distance contributions in momentum space. The use of different prescriptions then makes the comparison of fit results for underlying nonperturbative contributions not meaningful on their own. We propose a model-independent method to restrict momentum-space observables to the perturbative domain. This method is based on a set of integral functionals that act linearly on terms in the conventional position-space operator product expansion (OPE). Artifacts from the truncation of the integral can be systematically pushed to higher powers in $Λ_{\rm QCD}/k_T$. We demonstrate that this method can be used to compute the cumulative integral of TMD PDFs over $k_T \le k_T^\mathrm{cut}$ in terms of collinear PDFs, accounting for both radiative corrections and evolution effects. This yields a systematic way of correcting the naive picture where the TMD PDF integrates to a collinear PDF, and for unpolarized quark distributions we find that when renormalization scales are chosen near $k_T^\mathrm{cut}$, such corrections are a percent-level effect. We also show that, when supplemented with experimental data and improved perturbative inputs, our integral functionals will enable model-independent limits to be put on the nonperturbative OPE contributions to the Collins-Soper kernel and intrinsic TMD distributions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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