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

  • Ming-Xing Luo
  • Xing Wang
  • Xiaofeng Xu
  • Li Lin YangEmail author
  • Tong-Zhi Yang
  • Hua Xing Zhu
Open Access
Regular Article - Theoretical Physics


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(E2) 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 N3LL resummation.


Effective Field Theories Perturbative QCD 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Ming-Xing Luo
    • 1
  • Xing Wang
    • 2
  • Xiaofeng Xu
    • 2
  • Li Lin Yang
    • 2
    • 3
    Email author
  • Tong-Zhi Yang
    • 1
  • Hua Xing Zhu
    • 1
  1. 1.Zhejiang Institute of Modern Physics, Department of PhysicsZhejiang UniversityHangzhouChina
  2. 2.School of Physics and State Key Laboratory of Nuclear Physics and TechnologyPeking UniversityBeijingChina
  3. 3.Center for High Energy PhysicsPeking UniversityBeijingChina

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