Towards quasi-transverse momentum dependent PDFs computable on the lattice
Name
Ebert2019_Article_TowardsQuasi-transverseMomentu.pdf
Description
Published version
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1.31 MB
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Adobe PDF
Checksum (MD5)
201513ef11b5a55abf06bd09848055ef
Author(s)
Ebert, Markus
Stewart, Iain W
Zhao, Yong
Date Issued
September 2019
Journal
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Citation
Ebert, Markus A., Iain W. Stewart and Yong Zhao. “Towards quasi-transverse momentum dependent PDFs computable on the lattice.” Journal of High Energy Physics, vol. 2019, article 37 © 2019 The Author(s)
Version
Final published version
Abstract
Transverse momentum dependent parton distributions (TMDPDFs) which appear in factorized cross sections involve infinite Wilson lines with edges on or close to the light-cone. Since these TMDPDFs are not directly calculable with a Euclidean path integral in lattice QCD, we study the construction of quasi-TMDPDFs with finite-length spacelike Wilson lines that are amenable to such calculations. We define an infrared consistency test to determine which quasi-TMDPDF definitions are related to the TMDPDF, by carrying out a one-loop study of infrared logarithms of transverse position bT ∼ ΛQCD−1, which must agree between them. This agreement is a necessary condition for the two quantities to be related by perturbative matching. TMDPDFs necessarily involve combining a hadron matrix element, which nominally depends on a single light-cone direction, with soft matrix elements that necessarily depend on two light-cone directions. We show at one loop that the simplest definitions of the quasi hadron matrix element, the quasi soft matrix element, and the resulting quasi-TMDPDF all fail the infrared consistency test. Ratios of impact parameter quasi-TMDPDFs still provide nontrivial information about the TMD-PDFs, and are more robust since the soft matrix elements cancel. We show at one loop that such quasi ratios can be matched to ratios of the corresponding TMDPDFs. We also introduce a modified “bent” quasi soft matrix element which yields a quasi-TMDPDF that passes the consistency test with the TMDPDF at one loop, and discuss potential issues at higher orders.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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Creative Commons Attribution 4.0 International license
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DOI of Published Version
https://doi.org/10.1007/JHEP09(2019)037
