We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N3LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3LO. Our results are the last missing ingredient to extend the qT subtraction methods to N3LO and to obtain resummed qT spectra at N3LL′ accuracy both for gluon as well as for quark initiated processes.

中文翻译：

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N3LO 处的横向动量相关 PDF

我们在微扰 QCD 中以 next-to-next-to-next-to-lead 阶 (N3LO) 计算夸克和胶子横向动量相关的部分子分布函数。我们的计算基于差分 Drell-Yan 和胶子聚变希格斯产生截面围绕它们的共线极限的扩展。这种方法允许我们采用尖端的多回路技术来计算横截面，以提取 QCD 共线极限的这些通用构建块。所有通道的相应微扰匹配核都以权重为 5 的简谐多对数表示。作为副产品，我们确认了先前对 N3LO 横向动量分解的软函数的计算。