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Title: Towards quasi-transverse 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 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 b TQCD -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 matchedmore » 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.« less

Authors:
ORCiD logo [1];  [1];  [1]
  1. 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:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Volume: 2019; Journal Issue: 9; Journal ID: ISSN 1029-8479
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 quasi-transverse 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 quasi-transverse momentum dependent PDFs computable on the lattice. United States. https://doi.org/10.1007/jhep09(2019)037
Ebert, Markus A., Stewart, Iain W., and Zhao, Yong. Thu . "Towards quasi-transverse momentum dependent PDFs computable on the lattice". United States. https://doi.org/10.1007/jhep09(2019)037. https://www.osti.gov/servlets/purl/1611568.
@article{osti_1611568,
title = {Towards quasi-transverse 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 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.},
doi = {10.1007/jhep09(2019)037},
url = {https://www.osti.gov/biblio/1611568}, journal = {Journal of High Energy Physics (Online)},
issn = {1029-8479},
number = 9,
volume = 2019,
place = {United States},
year = {2019},
month = {9}
}

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Cited by: 8 works
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Works referenced in this record:

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    Works referencing / citing this record:

    Complete matching for quasidistribution functions in large momentum effective theory
    journal, October 2019