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.
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Acknowledgments
We thank Prof. Xiangdong Ji for discussion. Y. Liu thanks Prof. Vladimir M. Braun for helpful discussion. Calculations in the work are cross-checked between two authors. Y. L. is supported by the Priority Research Area SciMat and DigiWorlds under the program Excellence Initiative - Research University at the Jagiellonian University in Kraków. Y.S. is partially supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, contract no. DE-AC02-06CH11357.
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Liu, Y., Su, Y. Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators. J. High Energ. Phys. 2024, 204 (2024). https://doi.org/10.1007/JHEP02(2024)204
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DOI: https://doi.org/10.1007/JHEP02(2024)204