Transverse parton distribution and fragmentation functions at NNLO: the quark case - Luo, Ming-Xing; Wang, Xing; Xu, Xiaofeng; Yang, Li Lin; Yang, Tong-Zhi; Zhu, Hua Xing (The journal of high energy physics, 2019)
A bstract We revisit the calculation of perturbative quark transverse momentum de- pendent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consistent framework for the calculation of various ingredients in transverse momentum dependent factorization. Compared to existing regulators in the literature, the exponential regulator has a couple of advantages which we explain in detail. As a result, the calcula- tion is greatly simplified and we are able to obtain the next-to-next-to-leading order results up to O ( E 2 ) in dimensional regularization. These terms are necessary for a higher order calculation which is made possible with the simplification brought by the new regulator. As a by-product, we have obtained the two-loop quark jet function for the Energy-Energy Correlator in the back-to-back limit, which is the last missing ingredient for its N 3 LL resummation.