Towards quasitransverse momentum dependent PDFs computable on the lattice
Abstract
Transverse momentum dependent parton distributions (TMDPDFs) which appear in factorized cross sections involve infinite Wilson lines with edges on or close to the lightcone. Since these TMDPDFs are not directly calculable with a Euclidean path integral in lattice QCD, we study the construction of quasiTMDPDFs with finitelength spacelike Wilson lines that are amenable to such calculations. We define an infrared consistency test to determine which quasiTMDPDF definitions are related to the TMDPDF, by carrying out a oneloop study of infrared logarithms of transverse position b_{T}~Λ^{QCD}_{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 lightcone direction, with soft matrix elements that necessarily depend on two lightcone directions. We show at one loop that the simplest definitions of the quasi hadron matrix element, the quasi soft matrix element, and the resulting quasiTMDPDF all fail the infrared consistency test. Ratios of impact parameter quasiTMDPDFs still provide nontrivial information about the TMDPDFs, and are more robust since the soft matrix elements cancel. We show at one loop that such quasi ratios can be matched to ratios ofmore »
 Authors:

 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Publication Date:
 Research Org.:
 Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Nuclear Physics (NP)
 OSTI Identifier:
 1611568
 Grant/Contract Number:
 SC0011090
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 9; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; physics; lattice field theory simulation; QCD phenomenology
Citation Formats
Ebert, Markus A., Stewart, Iain W., and Zhao, Yong. Towards quasitransverse momentum dependent PDFs computable on the lattice. United States: N. p., 2019.
Web. doi:10.1007/jhep09(2019)037.
Ebert, Markus A., Stewart, Iain W., & Zhao, Yong. Towards quasitransverse momentum dependent PDFs computable on the lattice. United States. doi:https://doi.org/10.1007/jhep09(2019)037
Ebert, Markus A., Stewart, Iain W., and Zhao, Yong. Thu .
"Towards quasitransverse momentum dependent PDFs computable on the lattice". United States. doi:https://doi.org/10.1007/jhep09(2019)037. https://www.osti.gov/servlets/purl/1611568.
@article{osti_1611568,
title = {Towards quasitransverse momentum dependent PDFs computable on the lattice},
author = {Ebert, Markus A. and Stewart, Iain W. and Zhao, Yong},
abstractNote = {Transverse momentum dependent parton distributions (TMDPDFs) which appear in factorized cross sections involve infinite Wilson lines with edges on or close to the lightcone. Since these TMDPDFs are not directly calculable with a Euclidean path integral in lattice QCD, we study the construction of quasiTMDPDFs with finitelength spacelike Wilson lines that are amenable to such calculations. We define an infrared consistency test to determine which quasiTMDPDF definitions are related to the TMDPDF, by carrying out a oneloop study of infrared logarithms of transverse position bT~ΛQCD1, 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 lightcone direction, with soft matrix elements that necessarily depend on two lightcone directions. We show at one loop that the simplest definitions of the quasi hadron matrix element, the quasi soft matrix element, and the resulting quasiTMDPDF all fail the infrared consistency test. Ratios of impact parameter quasiTMDPDFs still provide nontrivial information about the TMDPDFs, 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 quasiTMDPDF that passes the consistency test with the TMDPDF at one loop, and discuss potential issues at higher orders.},
doi = {10.1007/jhep09(2019)037},
journal = {Journal of High Energy Physics (Online)},
number = 9,
volume = 2019,
place = {United States},
year = {2019},
month = {9}
}
Web of Science
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