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 construc...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-09-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2019)037 |
| _version_ | 1819052175418982400 |
|---|---|
| author | Markus A. Ebert Iain W. Stewart Yong Zhao |
| author_facet | Markus A. Ebert Iain W. Stewart Yong Zhao |
| author_sort | Markus A. Ebert |
| collection | DOAJ |
| description | 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 T ∼ 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 | 2024-12-21T12:15:39Z |
| format | Article |
| id | doaj.art-a59694d14699465c9db7218a52b120a3 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T12:15:39Z |
| publishDate | 2019-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-a59694d14699465c9db7218a52b120a32022-12-21T19:04:27ZengSpringerOpenJournal of High Energy Physics1029-84792019-09-012019917110.1007/JHEP09(2019)037Towards quasi-transverse momentum dependent PDFs computable on the latticeMarkus A. Ebert0Iain W. Stewart1Yong Zhao2Center for Theoretical Physics, Massachusetts Institute of TechnologyCenter for Theoretical Physics, Massachusetts Institute of TechnologyCenter for Theoretical Physics, Massachusetts Institute of TechnologyAbstract 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 ∼ 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.http://link.springer.com/article/10.1007/JHEP09(2019)037Lattice field theory simulationQCD Phenomenology |
| spellingShingle | Markus A. Ebert Iain W. Stewart Yong Zhao Towards quasi-transverse momentum dependent PDFs computable on the lattice Journal of High Energy Physics Lattice field theory simulation QCD Phenomenology |
| 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 |
| topic | Lattice field theory simulation QCD Phenomenology |
| url | http://link.springer.com/article/10.1007/JHEP09(2019)037 |
| work_keys_str_mv | AT markusaebert towardsquasitransversemomentumdependentpdfscomputableonthelattice AT iainwstewart towardsquasitransversemomentumdependentpdfscomputableonthelattice AT yongzhao towardsquasitransversemomentumdependentpdfscomputableonthelattice |