Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators

• Published in: The journal of high energy physics Vol. 2024; no. 2; pp. 204 - 46
• Main Authors: Liu, Yizhuang, Su, Yushan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2024; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: Asymptotic series; Classical and Quantum Gravitation; Correlation; Elementary Particles; Factorization; Higher-Order Perturbative Calculations; Large-Order Behaviour of Perturbation Theory; Light; Operators (mathematics); Parton Distributions; Partons; Physics; Physics and Astronomy; Prime numbers; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; Renormalization Group; Renormalons; String Theory; Thermal expansion; Transverse momentum; Wave functions; Renormalization Group; Parton Distributions; Large-Order Behaviour of Perturbation Theory; Factorization; Higher-Order Perturbative Calculations; Renormalons
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2024)204

A bstract In this paper, we show that the common hard kernel of double-log-type or threshold-type factorization for certain space-like parton correlators that arise in the context of lattice parton distributions, the heavy-light Sudakov hard kernel , has linear infrared (IR) renormalon. We explicitly demonstrate how this IR renormalon correlates with ultraviolet (UV) renormalons of next-to-leading power operators in two explicit examples: threshold asymptotics of space-like quark-bilinear coefficient functions and transverse momentum dependent (TMD) factorization of quasi wave function amplitude. Theoretically, the pattern of renormalon cancellation complies with general expectations to marginal asymptotics in the UV limit. Practically, this linear renormalon explains the slow convergence of imaginary parts observed in lattice extraction of the Collins-Soper kernel and signals the relevance of next-to-leading power contributions. Fully factorized, fully controlled threshold asymptotic expansion for space-like quark-bilinear coefficient functions in coordinate and moment space has also been proposed.