Renormalization and matching for the Collins-Soper kernel from lattice QCD

• Published in: The journal of high energy physics Vol. 2020; no. 3; pp. 1 - 40
• Main Authors: Ebert, Markus A., Stewart, Iain W., Zhao, Yong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2020; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Collaboration; correlation function; Correlators; distribution function; Distribution functions; Drell-Yan process; Elementary Particles; Euclidean; High energy physics; Kernels; lattice; Lattice field theory simulation; Mathematical analysis; NUCLEAR PHYSICS AND RADIATION PHYSICS; Operators (mathematics); parton; Partons; Physics; Physics and Astronomy; QCD Phenomenology; Quantum chromodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Regularization; Relativity Theory; renormalization; String Theory; Subtraction; Transverse momentum; transverse momentum dependence; Wilson loop; Lattice field theory simulation; QCD Phenomenology
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP03(2020)099

A bstract The Collins-Soper kernel, which governs the energy evolution of transverse- momentum dependent parton distribution functions (TMDPDFs), is required to accurately predict Drell-Yan like processes at small transverse momentum, and is a key ingredient for extracting TMDPDFs from experiment. Earlier we proposed a method to calculate this kernel from ratios of the so-called quasi-TMDPDFs determined with lattice QCD, which are defined as hadronic matrix elements of staple-shaped Euclidean Wilson line operators. Here we provide the one-loop renormalization of these operators in a regularization-independent momentum subtraction (RI′/MOM) scheme, as well as the conversion factor from the RI′/MOM-renormalized quasi-TMDPDF to the MS ¯ scheme. We also propose a procedure for calculating the Collins-Soper kernel directly from position space correlators, which simplifies the lattice determination.