{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:42:54Z","timestamp":1760233374067,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T00:00:00Z","timestamp":1610409600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The transversity and the Sivers distribution functions of quarks incorporate important information about the transverse-spin and transverse-momentum structure of nucleons. We show how these distributions can be directly determined point by point from leptoproduction asymmetry data collected for various targets and produced hadrons by the COMPASS Collaboration. Only simple symmetry relations are used in the extraction.<\/jats:p>","DOI":"10.3390\/sym13010116","type":"journal-article","created":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T20:11:31Z","timestamp":1610482291000},"page":"116","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Transverse\u2013Spin Quark Distributions from Asymmetry Data and Symmetry Arguments"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4233-4784","authenticated-orcid":false,"given":"Vincenzo","family":"Barone","sequence":"first","affiliation":[{"name":"Dipartimento di Scienze e Innovazione Tecnologica, Universit\u00e0 del Piemonte Orientale, 15121 Alessandria, Italy"},{"name":"INFN, Sezione di Torino, 10125 Torino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-0143","authenticated-orcid":false,"given":"Anna","family":"Martin","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Trieste, 34127 Trieste, Italy"},{"name":"INFN, Sezione di Trieste, 34127 Trieste, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Franco","family":"Bradamante","sequence":"additional","affiliation":[{"name":"INFN, Sezione di Trieste, 34127 Trieste, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.ppnp.2010.07.003","article-title":"Transverse-spin and transverse-momentum effects in high-energy processes","volume":"65","author":"Barone","year":"2010","journal-title":"Prog. 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D"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s100529900196","article-title":"Global QCD analysis of parton structure of the nucleon: CTEQ5 parton distributions","volume":"12","author":"Lai","year":"2000","journal-title":"Eur. Phys. J. C"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.nuclphysb.2018.12.024","article-title":"Measurement of PT-weighted Sivers asymmetries in leptoproduction of hadrons","volume":"940","author":"Alexeev","year":"2019","journal-title":"Nucl. Phys. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"094025","DOI":"10.1103\/PhysRevD.73.094025","article-title":"Collins effect in semi-inclusive deeply inelastic scattering and in e+e\u2212 annihilation","volume":"73","author":"Efremov","year":"2006","journal-title":"Phys. Rev. D"},{"key":"ref_41","unstructured":"COMPASS Collaboration (2018). d-Quark Transversity and Proton Radius. Addendum to the COMPASS-II Proposal, European Organization for Nuclear Research. CERN\u2013SPSC\u20132017\u2013034, SPSC\u2013P\u2013340\u2013ADD\u20131."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/116\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:09:55Z","timestamp":1760159395000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/116"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,12]]},"references-count":41,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010116"],"URL":"https:\/\/doi.org\/10.3390\/sym13010116","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,1,12]]}}}