Towards quasi-transverse momentum dependent PDFs computable on the lattice
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 q...
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| Format: | Article |
| Language: | English |
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Springer Science and Business Media LLC
2020
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| Online Access: | https://hdl.handle.net/1721.1/126650 |
| _version_ | 1826205217877655552 |
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| author | Ebert, Markus Stewart, Iain W Zhao, Yong |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Ebert, Markus Stewart, Iain W Zhao, Yong |
| author_sort | Ebert, Markus |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:09:32Z |
| format | Article |
| id | mit-1721.1/126650 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:09:32Z |
| publishDate | 2020 |
| publisher | Springer Science and Business Media LLC |
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| spelling | mit-1721.1/1266502022-10-01T13:25:42Z Towards quasi-transverse momentum dependent PDFs computable on the lattice Ebert, Markus Stewart, Iain W Zhao, Yong Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Laboratory for Nuclear Science 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. 2020-08-18T17:25:28Z 2020-08-18T17:25:28Z 2019-09 2019-07 2020-03-03T18:43:41Z Article http://purl.org/eprint/type/JournalArticle 1029-8479 https://hdl.handle.net/1721.1/126650 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) en 10.1007/JHEP09(2019)037 Journal of High Energy Physics Creative Commons Attribution 4.0 International license https://creativecommons.org/licenses/by/4.0/ application/pdf Springer Science and Business Media LLC Springer |
| spellingShingle | Ebert, Markus Stewart, Iain W Zhao, Yong Towards quasi-transverse momentum dependent PDFs computable on the lattice |
| title | Towards quasi-transverse momentum dependent PDFs computable on the lattice |
| title_full | Towards quasi-transverse momentum dependent PDFs computable on the lattice |
| title_fullStr | Towards quasi-transverse momentum dependent PDFs computable on the lattice |
| title_full_unstemmed | Towards quasi-transverse momentum dependent PDFs computable on the lattice |
| title_short | Towards quasi-transverse momentum dependent PDFs computable on the lattice |
| title_sort | towards quasi transverse momentum dependent pdfs computable on the lattice |
| url | https://hdl.handle.net/1721.1/126650 |
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