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

Abstract

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.

48 pages, 2 figures. The section on threshold asymptotics of space-like quark bilinear coefficient functions rewritten thoroughly and moves to the second section, with formulas in the moment space added. Fully factorized asymptotic expansion in the moment space written down explicitly

References in corpus (6)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Quark and gluon form factors to three loops
• Soft Factor Subtraction and Transverse Momentum Dependent Parton Distributions on Lattice
• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
• Factorization connecting continuum and lattice TMDs
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• Bjorken and threshold asymptotics of a space-like structure function in the 2D $U(N)$ Gross-Neveu model
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Renormalon effect of quasi-PDF in gradient flow formalism
• Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses