Towards quasi-transverse momentum dependent PDFs computable on the lattice

Ebert, Markus A.; Stewart, Iain W.; Zhao, Yong

doi:10.1007/jhep09(2019)037

Title: Towards quasi-transverse momentum dependent PDFs computable on the lattice

Journal Article · Thu Sep 05 00:00:00 EDT 2019 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep09(2019)037· OSTI ID:1611568

^[1]; Stewart, Iain W. ^[1]; Zhao, Yong ^[1]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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_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 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.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: SC0011090

OSTI ID:: 1611568

Journal Information:: Journal of High Energy Physics (Online), Vol. 2019, Issue 9; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 53 works

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Higgs-boson production at small transverse momentum Becher, Thomas; Neubert, Matthias; Wilhelm, Daniel Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)110	journal	May 2013
Soft-collinear factorization in effective field theory Bauer, Christian W.; Pirjol, Dan; Stewart, Iain W. Physical Review D, Vol. 65, Issue 5 https://doi.org/10.1103/PhysRevD.65.054022	journal	February 2002
Calculation of the transverse parton distribution functions at next-to-next-to-leading order Gehrmann, Thomas; Lübbert, Thomas; Yang, Li Lin Springer https://doi.org/10.5167/uzh-107413	text	January 2014
Structure of rapidity divergences in multi-parton scattering soft factors Vladimirov, Alexey Universität Regensburg https://doi.org/10.5283/epub.37184	text	January 2018
More on large-momentum effective theory approach to parton physics Ji, Xiangdong; Zhang, Jian-Hui; Zhao, Young Universität Regensburg https://doi.org/10.5283/epub.37215	text	January 2017
Transverse momentum in double parton scattering: factorisation, evolution and matching Buffing, Maarten G. A.; Diehl, Markus; Kasemets, Tomas Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-10376	text	January 2017
Matches and mismatches in the descriptions of semi-inclusive processes at low and high transverse momentum Bacchetta, Alessandro; Boer, Daniel; Diehl, Markus arXiv https://doi.org/10.48550/arxiv.0803.0227	text	January 2008
Electroweak Gauge-Boson Production at Small q_T: Infrared Safety from the Collinear Anomaly Becher, Thomas; Neubert, Matthias; Wilhelm, Daniel arXiv https://doi.org/10.48550/arxiv.1109.6027	text	January 2011
Factorization Theorem For Drell-Yan At Low q_T And Transverse-Momentum Distributions On-The-Light-Cone Echevarria, Miguel G.; Idilbi, Ahmad; Scimemi, Ignazio arXiv https://doi.org/10.48550/arxiv.1111.4996	text	January 2011
Analytic Regularization in Soft-Collinear Effective Theory Becher, Thomas; Bell, Guido arXiv https://doi.org/10.48550/arxiv.1112.3907	text	January 2011
A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory Chiu, Jui-yu; Jain, Ambar; Neill, Duff arXiv https://doi.org/10.48550/arxiv.1202.0814	text	January 2012
Higgs-Boson Production at Small Transverse Momentum Becher, Thomas; Neubert, Matthias; Wilhelm, Daniel arXiv https://doi.org/10.48550/arxiv.1212.2621	text	January 2012
Parton Physics on Euclidean Lattice Ji, Xiangdong arXiv https://doi.org/10.48550/arxiv.1305.1539	text	January 2013
Higher-twist corrections to gluon TMD factorization Balitsky, I.; Tarasov, A. arXiv https://doi.org/10.48550/arxiv.1706.01415	text	January 2017
Gluon quasidistribution function at one loop Wang, Wei; Zhao, Shuai; Zhu, Ruilin arXiv https://doi.org/10.48550/arxiv.1708.02458	text	January 2017
Transverse momentum in double parton scattering: factorisation, evolution and matching Buffing, Maarten G. A.; Diehl, Markus; Kasemets, Tomas arXiv https://doi.org/10.48550/arxiv.1708.03528	text	January 2017
Power corrections to TMD factorization for Z-boson production Balitsky, I.; Tarasov, A. arXiv https://doi.org/10.48550/arxiv.1712.09389	text	January 2017
Improved quasi parton distribution through Wilson line renormalization Chen, Jiunn-Wei; Ji, Xiangdong; Zhang, Jian-Hui Universität Regensburg https://doi.org/10.5283/epub.37217	text	January 2016
Transverse momentum dependent fragmentation function at next-to–next-to–leading order Echevarria, Miguel G.; Scimemi, Ignazio; Vladimirov, Alexey Physical Review D, Vol. 93, Issue 1 https://doi.org/10.1103/physrevd.93.011502	journal	January 2016
Renormalization of Wilson-line operators in the presence of nonzero quark masses Spanoudes, Gregoris; Panagopoulos, Haralambos Physical Review D, Vol. 98, Issue 1 https://doi.org/10.1103/physrevd.98.014509	journal	July 2018
Cancellation of Glauber gluon exchange in the double Drell-Yan process Diehl, Markus; Gaunt, Jonathan R.; Ostermeier, Daniel arXiv https://doi.org/10.48550/arxiv.1510.08696	text	January 2015
The Universal Transverse Momentum Dependent Soft Function at NNLO Echevarria, Miguel G.; Scimemi, Ignazio; Vladimirov, Alexey arXiv https://doi.org/10.48550/arxiv.1511.05590	text	January 2015
Lattice corrections to the quark quasidistribution at one-loop Carlson, Carl E.; Freid, Michael arXiv https://doi.org/10.48550/arxiv.1702.05775	text	January 2017
Factorization Theorem Relating Euclidean and Light-Cone Parton Distributions Izubuchi, Taku; Ji, Xiangdong; Jin, Luchang arXiv https://doi.org/10.48550/arxiv.1801.03917	text	January 2018

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Complete matching for quasidistribution functions in large momentum effective theory Wang, Wei; Zhang, Jian-Hui; Zhao, Shuai Universität Regensburg https://doi.org/10.5283/epub.45483	text	January 2019
Unpolarized isovector quark distribution function from lattice QCD: A systematic analysis of renormalization and matching Liu, Yu-Sheng; Chen, Jiunn-Wei; Huo, Yi-Kai Universität Regensburg https://doi.org/10.5283/epub.45463	text	January 2020
Unpolarized isovector quark distribution function from Lattice QCD: A systematic analysis of renormalization and matching Liu, Yu-Sheng; Chen, Jiunn-Wei; Huo, Yi-Kai arXiv https://doi.org/10.48550/arxiv.1807.06566	text	January 2018

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