Abstract
Parton distribution functions (PDFs) at large x are poorly constrained by high-energy experimental data, but extremely important for probing physics beyond standard model at colliders. We study the calculation of PDFs at large-x through large-momentum Pz expansion of the lattice quasi PDFs. Similar to deep-inelastic scattering, there are two distinct perturbative scales in the threshold limit where the matching coefficient can be factorized into a space-like jet function at scale Pz|1 − y| and a pair of heavy-light Sudakov form factors at scale Pz. The matching formula allows us to derive a full renormalization group resummation of large threshold logarithms, and the result is consistent with the known calculation to the next-to-next to leading order (NNLO). This paves the way for direct large-x PDFs calculations in lattice QCD. As by-products, we find that the space-like jet function is related to a time-like version calculated previously through analytic continuation, and the heavy-light Sudakov form factor, calculated here to NNLO, is a universal object appearing as well in the large momentum expansion of quasi transverse-momentum-dependent PDFs and quasi wave-function amplitudes.
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Acknowledgments
We thank Iain Stewart for pointing out possible connections between time-like and space-like heavy-quark jet functions, and the former has been computed in ref. [69]. This work is cross-checked, between Y. L and Y.S. This research is supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under contract number DE-SC0020682. 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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Ji, X., Liu, Y. & Su, Y. Threshold resummation for computing large-x parton distribution through large-momentum effective theory. J. High Energ. Phys. 2023, 37 (2023). https://doi.org/10.1007/JHEP08(2023)037
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DOI: https://doi.org/10.1007/JHEP08(2023)037