Transverse parton distribution and fragmentation functions at NNLO: the quark case

• Published in: The journal of high energy physics Vol. 2019; no. 10; pp. 1 - 39
• Main Authors: Luo, Ming-Xing, Wang, Xing, Xu, Xiaofeng, Yang, Li Lin, Yang, Tong-Zhi, Zhu, Hua Xing
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2019; Springer Nature B.V; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Distribution functions; Effective Field Theories; Elementary Particles; Fragmentation; High energy physics; Mathematical analysis; Partons; Perturbative QCD; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Regularization; Regulators; Relativity Theory; String Theory; Transverse momentum; Effective Field Theories; Perturbative QCD
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2019)083

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.