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Theor. 40 (2007) 7193-7212] that it leads to the Berezin integral.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["math-ph"],"titles":[{"title":"Spherical harmonics and integration in superspace II"},{"source":"arXiv","title":"Spherical harmonics and integration in superspace II"}],"curated":true},"created":"2009-05-14T00:00:00+00:00","id":"820406","updated":"2023-03-06T14:40:54.641134+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/820406?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/820406?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/820406?format=latex-us","json":"https://inspirehep.net/api/literature/820406?format=json","json-expanded":"https://inspirehep.net/api/literature/820406?format=json-expanded","cv":"https://inspirehep.net/api/literature/820406?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A820406"}},{"metadata":{"citation_count_without_self_citations":0,"authors":[{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/00cv9y106"}],"full_name_unicode_normalized":"de bie, h.","full_name":"De Bie, H.","curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/authors/1048011"},"ids":[{"schema":"INSPIRE BAI","value":"H.De.Bie.1"}],"last_name":"De Bie","affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/902815"},"value":"Gent U."}],"signature_block":"BYh","uuid":"6e35a045-8f32-41cf-8694-dde02fd336e0","first_name":"H.","recid":1048011},{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/00cv9y106"}],"full_name_unicode_normalized":"sommen, f.","full_name":"Sommen, F.","curated_relation":true,"record":{"$ref":"https://inspirehep.net/api/authors/1048012"},"ids":[{"schema":"INSPIRE BAI","value":"F.Sommen.1"}],"last_name":"Sommen","affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/902815"},"value":"Gent U."}],"signature_block":"SANANf","uuid":"f7d59cc6-3039-4cb7-9a9f-5e70ec891eb2","first_name":"F.","recid":1048012}],"citation_count":0,"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","keywords":[{"source":"author","value":"Clifford analysis"},{"source":"author","value":"superspace"},{"source":"author","value":"Cauchy formula"},{"schema":"INSPIRE","value":"algebra: Clifford"},{"schema":"INSPIRE","value":"superspace"},{"schema":"INSPIRE","value":"boundary condition"},{"schema":"INSPIRE","value":"algebra: representation"}],"references":[{"reference":{"imprint":{"publisher":"Clarendon"},"label":"1","misc":["Polyharmonic functions, Oxford Mathematical Monographs. 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Sommen, H."}]}},{"reference":{"imprint":{"publisher":"Academic"},"label":"13","misc":["Clifford algebra and spinor-valued functions, vol. 53 of Mathematics and its Applications ( Publishers Group, Dordrecht, 1992)"],"authors":[{"full_name":"Delanghe, R."},{"full_name":"Souček, F. Sommen V."}]}},{"reference":{"label":"14","misc":["Supermanifolds, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 1984)"],"authors":[{"full_name":"DeWitt, B."}]}},{"reference":{"label":"15","misc":["Clifford algebras and Dirac operators in harmonic Analysis 26 of Cambridge Studies in Advanced Mathematics (Cambridge University Press, Cambridge, 1991)"],"authors":[{"full_name":"Murray, J.E. Gilbert M.A.M."}]}},{"reference":{"imprint":{"publisher":"Springer"},"label":"16","misc":["‘Graded manifolds, graded Lie theory, and prequantization’, Differential geometrical methods in mathematical Physics (Proc. Sympos., Univ. Bonn, Bonn, 1975). Lect.Notes Math. 570 ( , Berlin, 1977), pp. 177-306"],"authors":[{"full_name":"Kostant, B."}]}},{"reference":{"label":"17","publication_info":{"journal_volume":"35","artid":"3","page_start":"3","journal_title":"Usp.Mat.Nauk"},"misc":["D. A. Le˘ıtes, ‘Introduction to the theory of supermanifolds’"]}},{"reference":{"label":"18","misc":["‘Cogitations over Berezin’s integral’, Contemporary mathematical Physics 175 of Am.Math.Soc.Transl. (Amer. Math. Soc., Providence, RI, 1996), pp. 177-189"],"authors":[{"full_name":"Palamodov, V.P."}]}},{"reference":{"label":"19","publication_info":{"journal_volume":"21","artid":"1352","page_start":"1352","journal_title":"J.Math.Phys."},"misc":["‘A global theory of supermanifolds’"],"authors":[{"full_name":"Rogers, A."}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/140482"}},{"reference":{"label":"20","publication_info":{"journal_volume":"87","artid":"321","page_start":"321","journal_title":"J.Funct.Anal."},"misc":["‘Dirac operators, Schrödinger type operators in Cn and Huygens’ principle’"],"authors":[{"full_name":"Ryan, J."}]}},{"reference":{"label":"21","publication_info":{"journal_volume":"347","artid":"1331","page_start":"1331","journal_title":"Trans.Am.Math.Soc."},"misc":["‘Cauchy-Green type formulae in Clifford Analysis’"],"authors":[{"full_name":"Ryan, J."}]}},{"reference":{"label":"22","publication_info":{"journal_volume":"326","artid":"613","page_start":"613","journal_title":"Trans.Am.Math.Soc."},"misc":["‘Monogenic differential calculus’"],"authors":[{"full_name":"Sommen, F."}]}}],"number_of_pages":14,"referenced_authors_bais":["H.De.Bie.1","F.Sommen.1","Alice.Rogers.1"],"legacy_version":"20160326144736.0","inspire_categories":[{"term":"Math and Math Physics"}],"legacy_creation_date":"2009-05-14","preprint_date":"2009-05","author_count":2,"first_author":{"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/00cv9y106"}],"full_name":"De Bie, H.","last_name":"De Bie","first_name":"H.","recid":1048011},"control_number":820407,"earliest_date":"2009-05","document_type":["article"],"texkeys":["DeBie:2009gu"],"abstracts":[{"source":"arXiv","value":"In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. 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The en- tropy shows a sharp peak near the transition temperature and increases with the interquark distance. We use the gauge/gravity duality to repro- duce these lattice results holographically. We consider a phenomenological bottom–up Einstein–Maxwell-dilaton (EMD) gravity model and analyti- cally construct the gravity solutions, whose dual boundary theory satisfies the properties of confined/deconfined phases. We study the entropy of the q ̄ q pair and find that our holographic model qualitatively reproduces the corresponding lattice results. We further provide holographic results for the q ̄ q entropy with chemical potential."}],"titles":[{"source":"Jagiellonian University","title":"Thermal Entropy of a Quark--Antiquark Pair from a Dynamical Holographic EMD Model"}],"facet_author_name":["1026581_David H. 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Phys.: Conf. Ser. 888 012180\n\n \n\nView the article online for updates and enhancements.\n\nRelated content\nR2D2 — a symmetric measurement of\nreactor neutrinos free ofsystematical errors\nPatrick Huber, Manfred Lindner and\nThomas Schwetz\n\n-\n\nThe deployment of three prototype\ndetectors for reactor monitoring and\nsafeguards\nN S Bowden, A Bernstein, S Dazeley et al.\n\n-\n\nReactor monitoring and safeguards using\nantineutrino detectors\nN S Bowden\n\n-\n\nThis content was downloaded from IP address 131.169.5.251 on 10/10/2017 at 08:28\n\nhttps://doi.org/10.1088/1742-6596/888/1/012180\nhttp://iopscience.iop.org/article/10.1088/1126-6708/2005/02/029\nhttp://iopscience.iop.org/article/10.1088/1126-6708/2005/02/029\nhttp://iopscience.iop.org/article/10.1088/1742-6596/136/4/042001\nhttp://iopscience.iop.org/article/10.1088/1742-6596/136/4/042001\nhttp://iopscience.iop.org/article/10.1088/1742-6596/136/4/042001\nhttp://iopscience.iop.org/article/10.1088/1742-6596/136/2/022008\nhttp://iopscience.iop.org/article/10.1088/1742-6596/136/2/022008\n\n\n1\n\nContent from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution\nof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.\n\nPublished under licence by IOP Publishing Ltd\n\n1234567890\n\nNeutrino2016 IOP Publishing\n\nIOP Conf. Series: Journal of Physics: Conf. Series 888 (2017) 012180  doi :10.1088/1742-6596/888/1/012180\n\nSoLid Detector Technology\n\nMathieu Labare 1\n\nDept. Physics and Astronomy, Ghent University, Belgium\n\nE-mail: mathieu.labare@ugent.be\n\nAbstract. SoLid is a reactor anti-neutrino experiment where a novel detector is deployed at\na minimum distance of 5.5 m from a nuclear reactor core. The purpose of the experiment is\nthree-fold: to search for neutrino oscillations at a very short baseline; to measure the pure\n235U neutrino energy spectrum; and to demonstrate the feasibility of neutrino detectors for\nreactor monitoring. This report presents the unique features of the SoLid detector technology.\nThe technology has been optimised for a high background environment resulting from low\noverburden and the vicinity of a nuclear reactor. The versatility of the detector technology is\ndemonstrated with a 288 kg detector prototype which was deployed at the BR2 nuclear reactor\nin 2015. The data presented includes both reactor on, reactor off and calibration measurements.\nThe measurement results are compared with Monte Carlo simulations. The 1.6t SoLid detector\nis currently under construction, with an optimised design and upgraded material technology to\nenhance the detector capabilities. Its deployement on site is planned for the begin of 2017 and\noffers the prospect to resolve the reactor anomaly within about two years.\n\n1. Introduction\nSoLid is a short baseline reactor anti-neutrino experiment using a novel detector technology\ndeployed at close distances, between 5.5 and 10 m from the BR2 nuclear reactor compact\ncore at SCK•CEN in Mol, Belgium. The physics goal of the SoLid experiment is to resolve\nthe reactor anti-neutrino anomaly [1] by searching for evidence of oscillation from the original\nelectron neutrino state to a non-standard “sterile” state [2]. The experiment will perform a\nprecise measurement of the anti-neutrino spectrum as a function of distance and energy thanks\nto a highly segmented, composite scintillator detector design (Sec.2). At the same time, it will\nprovide one of the most precise measurements of a pure 235U anti-neutrino spectrum, which is\nan essential ingredient for the improvement of the reactor flux calculation [3].\n\nThe BR2 reactor offers a compact core with diameter < 0.5 m while providing a high\nanti-neutrino flux (∼ 1019ν/s) . It usually runs ∼ 60 MW cycles lasting 3-4 weeks, running\napproximately 150 days per year. Although the BR2 reactor provides a relatively low background\ncompared to other facilities, the environment close to such a nuclear reactor raises a number\nof experimental challenges. From the physics side, low overburden and close proximity to\nthe reactor cause high rates of various background events. Cosmic ray muons can cause fast\nspallation neutrons which can mimic the signal produced by anti-neutrino events in the detector.\nHowever, the highly segmented detector allows most of these cosmic events to be reconstructed.\nThe muon energy deposition distribution provides also a standard candle that can be used\nfor channel and cube equalisation, and by comparison to simulation, the absolute energy scale\n\n1 On behalf of the SoLid Collaboration\n\nhttp://creativecommons.org/licenses/by/3.0\n\n\n2\n\n1234567890\n\nNeutrino2016 IOP Publishing\n\nIOP Conf. Series: Journal of Physics: Conf. Series 888 (2017) 012180  doi :10.1088/1742-6596/888/1/012180\n\ncan be extracted (Sec.3). These events can also be used to monitor the timing stability of the\ndetector. There are also backgrounds due to accidental time coincidences of randomly distributed\nbackground γ-rays with environmental neutrons. This background is increased by additional\nneutrons and γ-rays that can be emitted when the reactor is running. Technical constraints must\nalso be taken into account: the limited available space and strict security requirements around\na reactor core, impact on the size and admissible components of the detector, the accessibility\nand data handling infrastructure.\n\n2. Detection Principle\nThe detection of reactor anti-neutrinos is based on the inverse beta decay (IBD) ν̄e+p→ n+e+\n\nin which an anti-neutrino (Eν > 1.805 MeV) creates a positron and a neutron when interacting\nwith a proton of the fiducial volume (Fig.1). The active volume of the SoLid detector consists\nof highly segmented proton-rich 5 cm × 5 cm × 5 cm polyvinyl toluene (PVT) cubes coupled\nwith neutron-sensitive 6LiF:ZnS(Ag) tiles. The positron emitted from the IBD event causes the\nPVT to scintillate, before it annihilates with an electron in the detector, emitting a pair of 511\nkeV γ rays. The neutron from the IBD thermalises in the PVT and has approximately 50%\nprobability to be captured by a 6Li atom in the neutron-sensitive layer within ∼ 15 cm from the\ninteraction point, resulting in the interaction: n+6 Li→ α+3 H + 4.78 MeV.\n\nEach voxel is wrapped into a reflective Tyvek sheet to optically isolate the detector segments.\nThe scintillating light is guided out of the detection volume by a 2D orthogonal (horizontal\nand vertical) array of wavelength shifting (WLS) fibres, instrumented with a 3× 3 mm2 silicon\nphotomultiplier (SiPM) at one end. A mirror is coupled at the other end of each fibre to increase\nthe light collection.\n\nThe signal collected from an IBD event is a combination of two very different features. The\npositron yields a prompt and sharp pulse (Fig.2-top) while the neutron captured on 6Li induces\na slowly decaying pulse (Fig.2-bottom) in the ZnS(Ag) scintillator. The time delay between\nboth signals corresponds to the thermalisation time of the neutron.\n\nFigure 1. Detection of a IBD process in the\nSoLid detector.\n\nFigure 2. Typical IBD signal. Prompt\npositron pulse (top) followed by the slowly\ndecaying neutron pulse (bottom)\n\nBecause of the high level of segmentation, the positron pulse gives a good precision on the\nposition of the IBD interaction and the energy of the anti-neutrino. Moreover, the separation\nof true IBD events from background [7] not only benefits from the time information but, unlike\nconventional neutrino detectors, from the spacial configuration – e+ and n can possibly be\ndetected in neighbouring cubes – of the IBD event candidate as well, allowing some possible\ndirection reconstruction.\n\n3. Performances of the SM1 prototype\nA full-scale test module (Fig.3), named SubModule 1 (SM1), was constructed in 2014 and\ncommissioned in 2015. SM1 consists of 9 detector planes, each containing 16 by 16 PVT cubes,\n\n\n\n3\n\n1234567890\n\nNeutrino2016 IOP Publishing\n\nIOP Conf. Series: Journal of Physics: Conf. Series 888 (2017) 012180  doi :10.1088/1742-6596/888/1/012180\n\nFigure 3. The SM1 prototype.\n\nFigure 4. Prompt energy calibration\nwith AmBe source. Measurements are\ncompared with Geant4 simulations.\n\nresulting in a total of 2304 cubes weighing 288 kg. These cubes are read out by 288 WLS\nfibres coupled to as many SiPM sensors. The collected signal is amplified and digitised with\na 14 bit resolution at a sampling rate of 65 MHz using custom electronics. The module is\nsurrounded by a 9 cm thick polypropylene neutron shield, and 8 muon-veto scintillator panels\nused as active shielding. The SM1 prototype demonstrated the scalability of the detection\ntechnology and was used to test production methods and commissioning procedures[4]. From\nFebruary to August 2015, SM1 took data at the BR2 reactor site. The stability and performance\nof the SM1 prototype was monitored by detecting muons crossing or decaying in the fiducial\nvolume [5]. Calibration measurements were performed with several neutron and gamma sources\n(AmBe, 60Co, 252Cf) and validated with dedicated simulations (Fig.4). These measurements\ndemonstrated the high-quality background reduction of this novel neutrino-detector technology.\n\n4. Present and Future: SoLid phase 1\nThe phase 1 of SoLid has started during Summer 2016 with the development and gradual building\nof a 1.6 tonne detector. The system will be subdivided in 5 modules of 10 planes, holding\n12800 PVT cubes equipped with two neutron tiles. 3200 read-out channels will be equipped\nwith double-clad fibres, enhancing the light collection and therefore the energy resolution [6].\nThe installation of the first modules at BR2 is planned for February 2017. The full detector\nand readout electronics will be placed in a cooled container to reduce the SiPM dark count\nrate. The container will be surrounded with passive water shielding to diminish the rate of fast\nneutrons in the active detector volume. Based on the first IBD analysis performed with the SM1\nprototype [7], and the development of neutron identification methods on the full data stream\nand extended triggering, a detection efficiency of around 30% is expected, resulting in several\nhundreds of neutrinos that will be recorded every day. The combination of the detection rate\nand the excellent background rejection (∼ 100 for accidental and ∼10 for cosmic) will provide a\nstringent test of the reactor anti-neutrino anomaly within a few years of operation [8].\n\nReferences\n[1] Mention G et al 2011 Phys.Rev. D 83 073006\n[2] Kopp J et al 2013 JHEP 5 050\n[3] Mueller Th et al 2011 Phys.Rev. C 83 054615\n[4] Ryder N (SoLid Collaboration) 2015 PoS EPS -HEP2015 071\n[5] Saunders D (SoLid Collaboration) 2015 PoS EPS -HEP2015 086\n[6] Boursette D (SoLid Collaboration),these proceedings\n[7] Saunders D (SoLid Collaboration),these proceedings\n[8] Kalousis L (SoLid Collaboration),these proceedings"},"fulltext":true,"key":"c5a7c5ecd5ffee71dc0f9cdaadab6ec0","url":"https://inspirehep.net/files/c5a7c5ecd5ffee71dc0f9cdaadab6ec0"}],"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","keywords":[{"schema":"INSPIRE","value":"detector: technology"},{"schema":"INSPIRE","value":"neutrino: detector"},{"schema":"INSPIRE","value":"antineutrino: nuclear reactor"},{"schema":"INSPIRE","value":"neutrino: energy spectrum"},{"schema":"INSPIRE","value":"calibration"},{"schema":"INSPIRE","value":"numerical calculations: Monte Carlo"},{"schema":"INSPIRE","value":"monitoring"},{"schema":"INSPIRE","value":"background"}],"references":[{"reference":{"dois":["10.1103/PhysRevD.83.073006"],"label":"1","publication_info":{"journal_volume":"83","artid":"073006","year":2011,"journal_title":"Phys.Rev.D"},"misc":["Crossref:"],"authors":[{"full_name":"G, Mention"}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/884352"}},{"reference":{"dois":["10.1007/JHEP05(2013)050"],"label":"2","publication_info":{"journal_volume":"05","artid":"050","year":2013,"page_start":"050","journal_title":"JHEP"},"misc":["Crossref:"],"authors":[{"full_name":"J, Kopp"}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1223581"}},{"reference":{"imprint":{"publisher":"Mueller"},"dois":["10.1103/PhysRevC.83.054615"],"label":"3","publication_info":{"journal_volume":"83","artid":"054615","year":2011,"journal_title":"Phys.Rev.C"},"misc":["Th et al Crossref:"]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/884183"}},{"reference":{"label":"4","publication_info":{"journal_volume":"EPS-HEP2015","artid":"071","year":2015,"page_start":"071","journal_title":"PoS"},"misc":["and SoLid Collaboration"],"authors":[{"full_name":"N, Ryder"}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1401002"},"legacy_curated":true},{"reference":{"label":"5","publication_info":{"journal_volume":"EPS-HEP2015","artid":"086","year":2015,"page_start":"086","journal_title":"PoS"},"misc":["and SoLid Collaboration"],"authors":[{"full_name":"D, Saunders"}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1430508"},"legacy_curated":true},{"reference":{"label":"6","publication_info":{"journal_volume":"888","artid":"012090","journal_title":"J.Phys.Conf.Ser."},"misc":["(SoLid Collaboration), these proceedings"],"authors":[{"full_name":"D, Boursette"}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1625461"},"legacy_curated":true},{"reference":{"label":"7","publication_info":{"journal_volume":"888","artid":"012179","journal_title":"J.Phys.Conf.Ser."},"misc":["(SoLid Collaboration), these proceedings"],"authors":[{"full_name":"D, Saunders"}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1625511"},"legacy_curated":true},{"reference":{"label":"8","publication_info":{"journal_volume":"888","artid":"012181","journal_title":"J.Phys.Conf.Ser."},"misc":["(SoLid Collaboration), these proceedings"],"authors":[{"full_name":"L, Kalousis"}]},"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/1625624"},"legacy_curated":true}],"number_of_pages":3,"collaborations":[{"record":{"$ref":"https://inspirehep.net/api/experiments/1373184"},"value":"SoLid"}],"legacy_creation_date":"2017-09-26","author_count":1,"earliest_date":"2017-09-19","facet_author_name":["1046135_Mathieu Labare"],"core":true,"license":[{"license":"cc-by","imposing":"IOP","url":"http://creativecommons.org/licenses/by/3.0/"}],"_oai":{"sets":["Literature"],"id":"oai:inspirehep.net:1625512","updated":"2023-03-06T18:19:41.042670"},"journal_title_variants":["J. 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The purpose of the experiment is three-fold: to search for neutrino oscillations at a very short baseline, to measure the pure (235)U neutrino energy spectrum, and to demonstrate the feasibility of neutrino detectors for reactor monitoring. This report presents the unique features of the SoLid detector technology. The technology has been optimised for a high background environment resulting from low overburden and the vicinity of a nuclear reactor. The versatility of the detector technology is demonstrated with a 288 kg detector prototype which was deployed at the BR2 nuclear reactor in 2015. The data presented includes both reactor on, reactor off and calibration measurements. The measurement results are compared with Monte Carlo simulations. The 1.6t SoLid detector is currently under construction, with an optimised design and upgraded material technology to enhance the detector capabilities. 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Furthermore, the K\\\"all\\'en-Lehmann representation is inverted and the corresponding spectral density evaluated using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are discussed.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["hep-lat"],"titles":[{"source":"arXiv","title":"Lattice Landau gauge gluon propagator at finite temperature: non-zero Matsubara frequencies and spectral densities"}],"imprints":[{"date":"2017"}],"curated":true},"created":"2017-10-04T00:00:00+00:00","id":"1628414","updated":"2023-03-06T15:30:03.427621+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1628414?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1628414?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1628414?format=latex-us","json":"https://inspirehep.net/api/literature/1628414?format=json","json-expanded":"https://inspirehep.net/api/literature/1628414?format=json-expanded","cv":"https://inspirehep.net/api/literature/1628414?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1628414"}},{"metadata":{"citation_count_without_self_citations":0,"authors":[{"raw_affiliations":[{"value":"Ghent University"}],"full_name_unicode_normalized":"cosyn, w.","full_name":"Cosyn, W.","record":{"$ref":"https://inspirehep.net/api/authors/1024722"},"affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/902815"},"value":"Gent U."}],"last_name":"Cosyn","ids":[{"schema":"INSPIRE BAI","value":"W.Cosyn.1"}],"signature_block":"CASANw","uuid":"ec428082-4742-4007-adaf-1eec8a39efc9","first_name":"W.","recid":1024722},{"raw_affiliations":[{"value":"IHEP (Beijing)"}],"full_name_unicode_normalized":"dong, yu-bing","full_name":"Dong, Yu-Bing","record":{"$ref":"https://inspirehep.net/api/authors/1011560"},"affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/903123"},"value":"Beijing, Inst. 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Studies"}],"last_name":"Kumano","ids":[{"schema":"INSPIRE BAI","value":"S.Kumano.2"}],"signature_block":"CANANs","uuid":"2eed5c4f-7859-4ff6-b4e6-9c076c72e75d","first_name":"S.","recid":1001577},{"raw_affiliations":[{"value":"Florida International University, Miami, FL 33199, USA"}],"full_name_unicode_normalized":"sargsian, m.","full_name":"Sargsian, M.","record":{"$ref":"https://inspirehep.net/api/authors/1042073"},"affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/902802"},"value":"Florida Intl. U."}],"last_name":"Sargsian","ids":[{"schema":"INSPIRE BAI","value":"M.M.Sargsian.1"}],"signature_block":"SARGSANm","uuid":"e4520dfc-b405-4885-8436-64f69e2a9d3c","first_name":"M.","recid":1042073}],"citation_count":0,"publication_info":[{"journal_volume":"DIS2017","artid":"113","conference_record":{"$ref":"https://inspirehep.net/api/conferences/1496074"},"year":2018,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1213080"},"page_start":"113","journal_title":"PoS","parent_record":{"$ref":"https://inspirehep.net/api/literature/1647747"},"cnum":"C17-04-03.1"}],"documents":[{"filename":"PoS(DIS2017)113.pdf","attachment":{"content":"P\no\nS\n(\nD\nI\nS\n2\n0\n1\n7\n)\n1\n1\n3\n\nStandard convolution description of deuteron tensor\nspin structure\n\nW. Cosyn∗\n\nDepartment of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B9000 Ghent,\nBelgium\nE-mail: wim.cosyn@ugent.be\n\nYu-Bing Dong\nInstitute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China\nTheoretical Physics Center for Science Facilities (TPCSF), CAS, Beijing 100049, China\n\nS. Kumano\nKEK Theory Center, Institute of Particle and Nuclear Studies, High Energy Accelerator\nResearch Organization (KEK), 1-1, Ooho, Tsukuba, Ibaraki, 305-0801, Japan\nJ-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK, and Theory\nGroup, Particle and Nuclear Physics Division, J-PARC Center, 203-1, Shirakata, Tokai, Ibaraki,\n319-1106, Japan\n\nM. Sargsian\n\nDepartment of Physics, Florida International University, Miami, Florida 33199, USA\n\nSpin-1 hadrons have additional structure functions not present for spin 1/2 hadrons. These could\nprobe novel aspects of hadron structure and QCD dynamics. For the deuteron, the tensor structure\nfunction b1 inherently mixes quark and nuclear degrees of freedom. These proceedings discuss\ntwo standard convolution models applied to calculations of the deuteron b1 structure functions.\nWe find large differences with the existing HERMES data and other convolution model calcula-\ntions. This leaves room for non-standard contributions to b1 in the deuteron. We also discuss the\ninfluence of higher twist nuclear effects in the model calculations and data extraction at kinemat-\nics covered in HERMES and Jefferson Lab.\n\nXXV International Workshop on Deep-Inelastic Scattering and Related Subjects\n3-7 April 2017\nUniversity of Birmingham, UK\n\n∗Speaker.\n\nc© Copyright owned by the author(s) under the terms of the Creative Commons\nAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/\n\nmailto:wim.cosyn@ugent.be\n\n\nP\no\nS\n(\nD\nI\nS\n2\n0\n1\n7\n)\n1\n1\n3\n\nStandard convolution description of deuteron tensor spin structure W. Cosyn\n\n1. Introduction\n\nIn addition to vector spin observables familiar from the spin 1/2 case, a spin 1 hadron also\ngives access to additional tensor spin observables. In inclusive deep inelastic scattering (DIS) these\ngive rise to four additional structure functions, called b1−4 [1]. Two (b1,b2) of these are leading\ntwist and obey a Callan-Gross like relation b2 = 2xT b1, where xT = Q2/2Pq is the Bjorken scaling\nvariable for the spin 1 hadron. In the parton model, b1 obeys a sum rule\n\n∫\ndxb1(x) = 0 [2] when\n\nconsidering only the valence quark sector and b1 has an explicit interpretation as a function of\nunpolarized quark distributions in a polarized hadron\n\nb1 =\n1\n2 ∑\n\nq\ne2\n\nq(q\n0−q1) , (1.1)\n\nwhere the sum runs over all (anti)quark flavors, eq is the fractional quark charge and qi represents\nthe unpolarized quark distribution function in a hadron with polarization i.\n\nExperimentally, b1 can be extracted in polarized inclusive DIS from measuring the tensor\nasymmetry\n\nAzz =\nσ++σ−−2σ0\n\nσ++σ−+σ0 , (1.2)\n\nwhere σ i is the cross section for a target with polarization i along a chosen direction. For the\ndeuteron, Hermes measured Azz [3] and found a sizeable asymmetry and hence also extracted b1 in\nits covered kinematics. In the near future, the 12 GeV upgrade of Jefferson Lab will probe tensor\npolarization in the deuteron in two experiments [4], one in the DIS regime that will improve experi-\nmental knowledge of Azz and b1, the second in the quasi-elastic regime. Additionally, opportunities\nto access tensor polarization in the deuteron exist at Fermilab in Drell-Yan reactions [5] and at the\nJefferson Lab implementation of a future electron ion collider (JLEIC), also allowing for spectator\nnucleon tagging capabilities [6, 7].\n\nIn standard calculations of the deuteron, considering only the pn-component, b1 is only non-\nzero because of the D-wave component in the nuclear wave function. Due to the small size of\nthe D-wave component, the obtained b1 is very small and cannot explain the size of the HER-\nMES data. This suggests the need to consider more advanced or exotic mechanisms, such as\nshadowing [8, 9, 10, 11], eikonal final-state interactions [12], and pionic and hidden color contri-\nbutions [13], where inclusion of the latter can explain the HERMES data. Model calculations for\nb1 considering the pn component [1, 14] are scarce in the literature but are essential to constrain\nthe baseline calculation. Recently, we calculated b1 in two standard convolution models [15], and\nfound significant deviation from the previous model calculations. The formalism and results of\nthese calculations are summarized in the following sections, for more details we refer to Ref. [15].\n\n2. Standard convolution formalism for b1 in two approaches\n\nFor nuclear DIS in a standard convolution formulation, separation of scales between nuclear\nand partonic structure is used to write the nuclear hadronic tensor W A\n\nµν as a convolution of a nuclear\nspectral function S(p) and the hadronic tensor of the nucleon W N\n\nµν :\n\nW A\nµν(PA,q) =\n\n∫\nd4 pS(p)W N\n\nµν(p,q) . (2.1)\n\n1\n\n\n\nP\no\nS\n(\nD\nI\nS\n2\n0\n1\n7\n)\n1\n1\n3\n\nStandard convolution description of deuteron tensor spin structure W. Cosyn\n\nIn a first approach (Theory 1), scaling limit relations between virtual photon-hadron helicity am-\nplitudes and structure functions of the deuteron and nucleon are used to obtain the expression\n\nb1(x,Q2) =\n∫ dy\n\ny\n\n[\nf 0(y)− f+(y)+ f−(y)\n\n2\n\n]\nFN\n\n1 (x/y,Q2) , (2.2)\n\nwhere FN\n1 = (F p\n\n1 +Fn\n1 )/2 is the average of proton and neutron structure functions, and\n\nf H(y) =\n∫\n\nd3 pppy |φ H(ppp)|2δ\n\ny−\n\n√\nm2\n\nN + ppp2− pz\n\nmN\n\n , (2.3)\n\nwith φ H(ppp) the deuteron wave function for polarization H, normalized as\n∫\n\nd3 pppy |φ H(ppp)|2 = 1.\nFor the nucleon FN\n\n1 , the leading order expression, taking into account the finite ratio of transverse\nto longitudinal cross sections R = σL/σT is used\n\nFN\n1 (x,Q2) =\n\n1+4m2\nNx2/Q2\n\n2x[1+R(x,Q2]\nx∑\n\nf\ne2\n\nf\n[\nq f (x,Q2)+ q̄ f (x,Q2)\n\n]\nLO . (2.4)\n\nA second approach (Theory 2) is based on the virtual nucleon approximation (VNA) frame-\nwork, which has been applied previously to unpolarized deuteron DIS [16, 17] and can be gener-\nalized to polarized reactions. In the VNA approach, no scaling limit relations are assumed, hence\nhigher twist nuclear effects are automatically included. The VNA expression for b1 is given by\n\nb1(x,Q2) =\n3\n\n4(1+Q2/ν2)\n\n∫ k2\n\nαi\ndk d(cosθk)\n\n[\nFN\n\n1 (xi,Q2)\n(\n6cos2\n\nθk−2\n)\n\n+\nppp⊥2\n\ni\n\n2 piq\nFN\n\n2 (xi,Q2)\n(\n5cos2\n\nθk−1\n)][U(k)W (k)√\n\n2\n+\n\nW (k)2\n\n4\n\n]\n. (2.5)\n\nHere ν is the virtual photon energy in the deuteron rest frame, pi, xi = Q2/2piq and αi = 2p−i /P−\n\nare respectively the four-momentum, Bjorken variable and lightcone momentum fraction of the\nstruck nucleon, k is the dynamical variable appearing in the light-front deuteron wave function\nrelated to the deuteron and nucleon momenta by [18]\n\nk3 = (1−αi)Ek E2\nk =\n\nm2\nN +\n\n(\nppp⊥i + αi\n\n2 PPP⊥\n)\n\nαi(2−αi)\n. (2.6)\n\nU(k), W (k) are the radial S- and D-wave components of the light-front deuteron wave function\nobeying the baryon and momentum sum rules\n\n∫ dkkk\nEk\n\n[\nU(k)2 +W (k)2]= 1\n\n∫ dkkk\nEk\n\nαi\n[\nU(k)2 +W (k)2]= 1 , (2.7)\n\nand are here approximated by their non-relativistic counterparts. Comparing Eq. (2.5) with Eq. (2.2),\nthe presence of the additional FN\n\n2 term reflects the inclusion of higher twist nuclear effects.\n\n2\n\n\n\nP\no\nS\n(\nD\nI\nS\n2\n0\n1\n7\n)\n1\n1\n3\n\nStandard convolution description of deuteron tensor spin structure W. Cosyn\n\n-0.002\n\n-0.001\n\n0\n\n0.001\n\n0.002\n\n0.003\n\n0.004\n\n0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6\n\nx\n\nxb\n1\n\nSD+DD\n\nTheory 1\n\nTheory 2\n\nQ2 =1.0 GeV2\n\nQ2 =2.5 GeV2\n\nQ2 =5.0 GeV2\n\n-0.003\n\n-0.002\n\n-0.001\n\n0\n\n0.001\n\n0.002\n\n0.003\n\n0.004\n\n0 0.2 0.4 0.6 0.8 1 1.2 1.4\n\nx\n\nxb\n1\n\nHERMES\n\nTheory 1\n\nTheory 2\n\nQ2 =2.5 GeV2\n\nFigure 1: Calculations of deuteron structure function b1 by the two convolution descriptions of Theory 1\n[Eq. (2.2)] and Theory 2 [Eq. (2.5)]. (Left panel) Q2 dependence of xb1 at Q2 1.0, 2.5, and 5.0 GeV2. (Right\npanel) Comparison with the HERMES data [3]. Calculations are for Q2 = 2.5 GeV2, representative for the\naverage Q2 value of the HERMES data. Figure adapted from Ref. [15]\n\n3. Results\n\nFig. 1 shows the Q2-dependence of the deuteron b1 for the two different calculations and\ncompares the calculations to the HERMES data. In these calculations, we used the MSTW2008\n(Martin-Stirling-Thorne-Watt, 2008) leading-order (LO) parametrization for F2\n\nN , the SLAC- R1998\nparametrization for the ratio R, and the CD-Bonn deuteron wave function. We observe that both\ncalculations exhibit a similar oscillating x-dependence. Compared to the calculations of Ref. [1, 14]\n(denoted KH from now on) two differences are worth noting: (i) the dominant term originating\nfrom the deuteron SD-wave interference (not shown separately here, see Fig. 4 of Ref. [15] ) has\nan opposite sign in our calculations compared to the KH calculations, (ii) we find a non-zero b1\n\nfor x > 1, whereas it is identically zero in the KH results. The left panel of Fig. 1 shows that the\ndifference in size between the two calculations becomes larger for smaller Q2 values. The main\norigin of this is the inclusion of higher twist effects in Theory 2. Another origin is the different\nway deuteron nuclear structure is considered (wave function normalization, instant form versus\nlight-front form wave function). The variation of the deuteron b1 with Q2 shows its sensitivity to\ndynamical aspects of hadron structure. When comparing our calculations with the HERMES data\nin the right panel of Fig. 1, we see that both calculations fail to accurately describe the data, though\nit has to be noted the error bars are quite large. The upcoming Jefferson Lab data should improve\nthat in the future. Nevertheless, this current comparison certainly does not rule out the possibility\nof additional mechanisms (possibly of exotic nature) playing an important role in the b1 of the\ndeuteron.\n\nAnother point worth of scrutiny is the way b1 is extracted from the Azz observable. For the\nHERMES experiment, this was done using formulas that include Bjorken scaling limit relations\nand neglect the higher twist b3,b4. Our analysis (see Ref. [15]) shows that this is not necessarily\nthe case for the kinematics of HERMES and Jefferson Lab, with the Callan-Gross like relation\nviolated and the higher twist b3,4 of similar magnitude as the leading twist structure functions.\nConsequently, inclusion of higher twist effects in the extraction procedure might be warranted at\nthese kinematics to accurately extract b1.\n\n3\n\n\n\nP\no\nS\n(\nD\nI\nS\n2\n0\n1\n7\n)\n1\n1\n3\n\nStandard convolution description of deuteron tensor spin structure W. Cosyn\n\n4. Conclusion\n\nWe have summarized calculations of the b1 deuteron structure function in two models based\non the standard convolution approach of nuclear DIS. We find significant differences with older\ncalculations and our calculations cannot reproduce the size or trend of the HERMES data, leaving\nroom for more advanced or exotic mechanisms playing an important role. An upcoming experiment\nat Jefferson Lab and additional opportunities at Fermilab and a future JLEIC could shed more light\non these issues and motivate additional theoretical work.\n\nAcknowledgments\n\nThis work was supported by Japan Society for the Promotion of Science (JSPS) Grants-in-\nAid for Scientific Research (KAKENHI) Grant No. JP25105010. It is also partly supported by\nthe National Natural Science Foundation of China (No. 11475192) and by the fund of the Sino-\nGerman CRC 110 “Symmetries and the Emergence of Structure in QCD project” (NSFC Grant No.\n11621131001). Y.-B. D. thanks the warm hospitality of the KEK theory center during his visit.\n\nReferences\n\n[1] P. Hoodbhoy, R. Jaffe and A. 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Sargsian, Final-state interactions in inclusive deep-inelastic\nscattering from the deuteron, Phys.Rev. C89 (2014) 014612, [1311.3550].\n\n[18] L. L. Frankfurt and M. I. Strikman, High-Energy Phenomena, Short Range Nuclear Structure and\nQCD, Phys. Rept. 76 (1981) 215–347.\n\n5\n\nhttp://dx.doi.org/10.1142/S0218301317300041\nhttp://arxiv.org/abs/1704.06117\nhttp://dx.doi.org/10.1103/PhysRevC.89.045203\nhttp://arxiv.org/abs/1311.4561\nhttp://dx.doi.org/10.1103/PhysRevC.44.1219\nhttp://dx.doi.org/10.1103/PhysRevD.95.074036\nhttp://arxiv.org/abs/1702.05337\nhttp://dx.doi.org/10.1103/PhysRevC.84.014601\nhttp://arxiv.org/abs/1012.0293\nhttp://dx.doi.org/10.1103/PhysRevC.89.014612\nhttp://arxiv.org/abs/1311.3550\nhttp://dx.doi.org/10.1016/0370-1573(81)90129-0"},"fulltext":true,"source":"PoS","key":"ee7f622d13564b68714f621262e44854","url":"https://inspirehep.net/files/ee7f622d13564b68714f621262e44854"}],"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","keywords":[{"schema":"INSPIRE","value":"structure function: tensor"},{"schema":"INSPIRE","value":"spin: 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(Left panel) $Q^2$ dependence of $xb_1$ at $Q_2$ 1.0, 2.5, and 5.0 GeV$^2$. (Right panel) Comparison with the HERMES data~\\cite{Airapetian:2005cb}. Calculations are for $Q^2=2.5~\\text{GeV}^2$, representative for the average $Q^2$ value of the HERMES data. Figure adapted from Ref.~\\cite{Cosyn:2017fbo}","source":"arxiv","key":"d634a0d9dbedff93225664f6fc040dab","url":"https://inspirehep.net/files/d634a0d9dbedff93225664f6fc040dab"},{"filename":"xb1-comp-hermes.png","caption":"Calculations of deuteron structure function $b_1$ by the two convolution descriptions of Theory 1 [Eq.~(\\ref{eq:b1conv})] and Theory 2 [Eq.~(\\ref{eq:b1vna})]. (Left panel) $Q^2$ dependence of $xb_1$ at $Q_2$ 1.0, 2.5, and 5.0 GeV$^2$. (Right panel) Comparison with the HERMES data~\\cite{Airapetian:2005cb}. Calculations are for $Q^2=2.5~\\text{GeV}^2$, representative for the average $Q^2$ value of the HERMES data. Figure adapted from Ref.~\\cite{Cosyn:2017fbo}","source":"arxiv","key":"8aeac3b5c08c1c44c662bc4c177e3a85","url":"https://inspirehep.net/files/8aeac3b5c08c1c44c662bc4c177e3a85"}],"legacy_version":"20210607084901.0","inspire_categories":[{"term":"Phenomenology-HEP"},{"term":"Theory-Nucl"}],"urls":[{"description":"PoS server","value":"https://pos.sissa.it/297/113/pdf"}],"first_author":{"emails":["wim.cosyn@ugent.be"],"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/00cv9y106"}],"full_name":"Cosyn, W.","last_name":"Cosyn","first_name":"W.","recid":1024722},"control_number":1625320,"dois":[{"value":"10.22323/1.297.0113"}],"document_type":["conference paper"],"texkeys":["Cosyn:2017gfc"],"abstracts":[{"source":"arXiv","value":"Spin-1 hadrons have additional structure functions not present for spin 1/2 hadrons. These could probe novel aspects of hadron structure and QCD dynamics. For the deuteron, the tensor structure function $b_1$ inherently mixes quark and nuclear degrees of freedom. These proceedings discuss two standard convolution models applied to calculations of the deuteron $b_1$ structure functions. We find large differences with the existing HERMES data and other convolution model calculations. This leaves room for non-standard contributions to $b_1$ in the deuteron. We also discuss the influence of higher twist nuclear effects in the model calculations and data extraction at kinematics covered in HERMES and Jefferson Lab.","abstract_source_suggest":{"input":"arXiv"}}],"primary_arxiv_category":["hep-ph"],"titles":[{"source":"arXiv","title":"Standard convolution description of deuteron tensor spin structure"}],"imprints":[{"date":"2017-09-01","publisher":"SISSA"}],"curated":true},"created":"2017-09-26T00:00:00+00:00","id":"1625320","updated":"2023-03-06T15:51:31.555432+00:00","links":{"bibtex":"https://inspirehep.net/api/literature/1625320?format=bibtex","latex-eu":"https://inspirehep.net/api/literature/1625320?format=latex-eu","latex-us":"https://inspirehep.net/api/literature/1625320?format=latex-us","json":"https://inspirehep.net/api/literature/1625320?format=json","json-expanded":"https://inspirehep.net/api/literature/1625320?format=json-expanded","cv":"https://inspirehep.net/api/literature/1625320?format=cv","citations":"https://inspirehep.net/api/literature/?q=refersto%3Arecid%3A1625320"}},{"metadata":{"citation_count_without_self_citations":1,"authors":[{"raw_affiliations":[{"value":"Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B9000 Ghent, Belgium"}],"full_name_unicode_normalized":"cosyn, w.","last_name":"Cosyn","affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/902815"},"value":"Gent U."}],"uuid":"909527bc-6eca-4e6b-8275-7ed14fbe9a4b","affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/00cv9y106"}],"full_name":"Cosyn, W.","record":{"$ref":"https://inspirehep.net/api/authors/1024722"},"ids":[{"schema":"INSPIRE BAI","value":"W.Cosyn.1"}],"signature_block":"CASANw","first_name":"W.","recid":1024722},{"raw_affiliations":[{"value":"Centre de Physique Théorique, École Polytechnique, CNRS, 91128 Palaiseau, France"}],"affiliations_identifiers":[{"schema":"ROR","value":"https://ror.org/02bsd9p69"}],"full_name_unicode_normalized":"pire, b.","full_name":"Pire, B.","record":{"$ref":"https://inspirehep.net/api/authors/993281"},"ids":[{"schema":"INSPIRE BAI","value":"B.Pire.2"}],"last_name":"Pire","affiliations":[{"record":{"$ref":"https://inspirehep.net/api/institutions/909206"},"value":"Ecole Polytechnique, CPHT"}],"signature_block":"PARb","first_name":"B.","uuid":"46c39a98-72c6-45e5-ac15-e0c60f285214","recid":993281}],"citation_count":1,"publication_info":[{"journal_volume":"26","artid":"021005","conference_record":{"$ref":"https://inspirehep.net/api/conferences/1622346"},"year":2019,"journal_record":{"$ref":"https://inspirehep.net/api/journals/1289282"},"journal_title":"JPS Conf.Proc.","parent_record":{"$ref":"https://inspirehep.net/api/literature/1764476"},"cnum":"C18-11-13"}],"report_numbers":[{"source":"arXiv","value":"CPHT-PC003.022019"}],"documents":[{"filename":"fulltext1719331.pdf","attachment":{"content":"Deuteron Helicity Flip Generalized Parton Distributions in\na Convolution Model\nWim Cosyn1 and Bernard Pire2\n\n1Department of Physics and Astronomy, Ghent University, Proeftuinstraat 86, B9000 Ghent,\nBelgium\n2Centre de Physique Théorique,École Polytechnique, CNRS, 91128 Palaiseau, France\n\nE-mail: wim.cosyn@ugent.be\n\n(Received February 1, 2019)\n\nWe discuss the general properties of generalized parton distributions with helicity flip (transversity)\nfor spin-1 hadrons in the leading twist case. Using a basic light cone convolution model, we show the\ndeuteron helicity amplitudes containing quark helicity flip GPDs and comment on the role deuteron\nangular momentum plays in these.\n\nKEYWORDS: generalized parton distributions, deuteron, transversity\n\n1. Helicity flip GPDs for spin 1 hadrons\n\nGeneralized parton distributions (GPDs) appear as scalar functions in the decomposition of off-\nforward quark and gluon correlators in hadrons. Through QCD factorization theorems they parametrize\nthe non-perturbative part of the amplitude in processes such as deeply virtual Compton scattering\n(DVCS) and deep exclusive meson production (DEMP) [1]. While a rich phenomenology exists for\nthe nucleon, there is comparatively less material available concerning nuclear GPDs, which enter\nin coherent exclusive processes on nuclei. In this proceedings, we report on recent work on quark\nhelicity flip GPDs for the deuteron. More details can be found in Refs. [2,3].\n\nAs the deuteron is a spin 1 object, it admits more GPDs than the spin 1/2 case. In the leading\ntwist case, both for quark and gluons there are 9 helicity conserving GPDs and 9 helicity flip or\ntransversity ones. The helicity conserving ones were introduced in Ref. [4], while the helicity flip\nones were recently introduced in Ref. [2]. Both sectors evolve separately under QCD evolution, and\nfor the helicity flip sector quarks and gluon operators do not mix.\n\nFor the helicity flip sector, the decomposition of the quark correlator for a spin-1 hadron takes\nthe following form [2]\n\nTq i\nλ′λ =\n\n1\n2\n\n∫\ndκ\n2π\n\neixκ(Pn)⟨p′ λ′|ψ̄(− κ\n2\n\nn)(inµσ\nµi)ψ(\n\nκ\n\n2\nn)|pλ⟩ = M\n\n(ϵ′∗n)ϵi − ϵ′∗i(ϵn)\n\n2\n√\n\n2(Pn)\nHqT\n\n1 (x, ξ, t)\n\n+ M\n\n[\n2Pi(ϵn)(ϵ′∗n)\n\n2\n√\n\n2(Pn)2\n− (ϵn)ϵ′i∗ + ϵ i(ϵ′∗n)\n\n2\n√\n\n2(Pn)\n\n]\nHqT\n\n2 (x, ξ, t)\n\n+\n\n[\n(ϵ′∗n)∆i − ϵ′i∗(∆n)\n\n2M(Pn)\n(ϵ∆) +\n\n(ϵn)∆i − ϵ i(∆n)\n2M(Pn)\n\n(ϵ′∗∆)\n\n]\nHqT\n\n3 (x, ξ, t)\n\n+\n\n[\n(ϵ′∗n)∆i − ϵ′i∗(∆n)\n\n2M(Pn)\n(ϵ∆) − (ϵn)∆i − ϵ i(∆n)\n\n2M(Pn)\n(ϵ′∗∆)\n\n]\nHqT\n\n4 (x, ξ, t)\n\n+ M\n\n[\n(ϵ′∗n)∆i − ϵ′i∗(∆n)\n\n2\n√\n\n2(Pn)2\n(ϵn) +\n\n(ϵn)∆i − ϵ i(∆n)\n\n2\n√\n\n2(Pn)2\n(ϵ′∗n)\n\n]\nHqT\n\n5 (x, ξ, t)\n\n1■■■\n\nJPS Conf. Proc. , 021005 (2019)\n\n©2019 The Author(s)\n\nhttps://doi.org/10.7566/JPSCP.26.021005\n26\n\nmust maintain attribution to the author(s) and the title of the article, journal citation, and DOI.\n\nProc. 8th Int. Conf. Quarks and Nuclear Physics (QNP2018)\n\n021005-1\n\nThis article is published by the Physical Society of Japan under the terms of the Creative Commons Attribution 4.0 License. Any further distribution of this work\n\nProceedings of the 8th International Conference on Quarks and Nuclear Physics (QNP2018)\nDownloaded from journals.jps.jp by Deutsches Elek Synchrotron on 11/24/19\n\nhttp://creativecommons.org/licenses/by/4.0/\nhttp://crossmark.crossref.org/dialog/?doi=10.7566%2FJPSCP.26.021005&domain=pdf&date_stamp=2019-11-07\n\n\n+\n(∆i + 2ξPi)\n\nM\n(ϵ′∗ϵ)HqT\n\n6 (x, ξ, t) − (∆i + 2ξPi)\nM\n\n(ϵ′∗∆)(ϵ∆)\n4M2\n\nHqT\n7 (x, ξ, t)\n\n+\n\n[\n(ϵ′∗n)Pi − ϵ′i∗(Pn)\n\nM(Pn)\n(ϵ∆) − (ϵn)Pi − ϵ i(Pn)\n\n2M(Pn)\n(ϵ′∗∆)\n\n]\nHqT\n\n8 (x, ξ, t)\n\n+\n\n[\n(ϵ′∗n)Pi − ϵ′i∗(Pn)\n\nM(Pn)\n(ϵ∆) +\n\n(ϵn)Pi − ϵ i(Pn)\n2M(Pn)\n\n(ϵ′∗∆)\n\n]\nHqT\n\n9 (x, ξ, t) . (1)\n\nHere,n is a light-like fourvector andi a transverse index. The initial spin-1 hadron (massM) has\nfourvectorp, polarization vectorϵ and light-front helicityλ, with the equivalent primed variables for\nthe final hadron. Kinematic variables are defined as follows\n\nP =\np′ + p\n\n2\n, ∆ = p′ − p, t = ∆2, ξ = − (∆n)\n\n2(Pn)\n. (2)\n\nThe9 real GPDs have the following properties:\n\n(1) 6 GPDs are even functions in skewnessξ (HqT\ni , i ∈ {1,4,5,6,7,9}), the other 3 are odd inξ.\n\n(2) Only one GPD does not decouple in the forward limit and can be linked to the collinear transver-\nsity distribution:HqT\n\n1 (x, 0,0) = h1(x).\n\n(3) General Mellin moments of the GPDs [where then-th moment corresponds to an integral over∫\ndx xn−1HTq\n\ni (x, ξ, t) ] obey polynomiality sum rules, where the moments can be written as a\npolynomial inξ with generalized form factors in their coefficients. For then-th moment, there\nare 5+ 3\n\n(\n⌊n2⌋\n)\n\nindependentgeneralized form factors in the quark helicity flip sector [3]. Four\ntransversity GPDs (i ∈ {2,3,5,8}) have zero sum rules for the first Mellin moment.\n\n2. Deuteron convolution model\n\nTo compute the quark transversity GPDs for the deuteron, we consider a basic convolution model.\nWe only consider the dominantnp component of the deuteron wave function and consider the lead-\ning order impulse approximation, where one of the nucleons acts as a so-called “spectator”. Using\nmethods of light-front perturbation theory, nuclear and nucleon structure can be separated and we can\nwrite the correlator of Eq. (1) as a convolution of two light-front deuteron wave functions and a quark\nhelicity flip correlator for the nucleon [2, 5]. The nucleon correlators are then decomposed through\ntheir corresponding spin 1/2 GPDs.\n\nOne disadvantage of only considering the lowest Fock state in the deuteron (np component) is\nthat this truncation breaks Lorentz covariance and consequently also the polynomiality requirements\nof the deuteron GPDs [2]. Extensions including additional contributions to restore the polynomiality\ncondition will be the topic of a future study.\n\nIn Figs. 1 and 2 we show results in this convolution model for the helicity amplitudesAλ′+;λ−,\nwhere the plus and minus refer to the helicities of the outgoing and incoming quark in the correlator.\nThese helicity amplitudes form linear combinations of the transversity GPDs through the relation\n\nAλ′+;λd− =\n1\n2\n\n(\nTq1\nλ′λ + i Tq2\n\nλ′λ\n\n)\n, (3)\n\nand exhibit the role deuteron angular momentum in a more transparent way than the corresponding\nGPDs. For plots of the GPDs, we refer to Ref. [2]. For the calculations in the convolution model, we\nuse the nucleon transversity GPDs of Ref. [6], and the AV18 deuteron wave function parametriza-\ntion [7].\n\nFigure 1 shows the different contributions from the deuteron S- and D-wave components to the\ntotal result. The difference between the first two and the latter originates from S-D interference con-\ntributions. Considering the top row of Fig. 1, which correspond to the deuteron helicity conserving\n\n2■■■\n\n021005-2JPS Conf. Proc. , 021005 (2019)26\n\nProceedings of the 8th International Conference on Quarks and Nuclear Physics (QNP2018)\nDownloaded from journals.jps.jp by Deutsches Elek Synchrotron on 11/24/19\n\n\n\namplitudes,it is clear that these are dominated by the pure S-wave contribution, whereas the other\namplitudes that admit a change in deuteron helicity receive major contributions from the S-D inter-\nference terms. The two amplitudes with two units of deuteron helicity flip (bottom row, right two\npanels) are identically zero when only including the deuteron S-wave as in that case there is no or-\nbital angular momentum available in the deuteron to compensate the change in helicities (two units\nfor the deuteron, one for the quark).\n\n−0.2 0.0 0.2 0.4 0.6\n\n0.0\n\n0.5\n\n1.0\n\n1.5\n\n×10−1\n\nA++;+−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0\n\n1\n\n2\n\n×10−1\n\nA−+;−−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0\n\n1\n\n2\n\n×10−1\n\nA0+;0−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0.00\n\n0.25\n\n0.50\n\n0.75\n×10−1\n\nA0+;+−\n\n−0.2 0.0 0.2 0.4 0.6\n\n−0.75\n\n−0.50\n\n−0.25\n\n0.00\n\n×10−1\n\nA−+;0−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0.0\n\n0.5\n\n1.0\n\n×10−1\n\nA++;0−\n\n−0.2 0.0 0.2 0.4 0.6\n\n−0.5\n\n0.0\n\n0.5\n\n1.0\n×10−1\n\nA0+;−−\n\n−0.2 0.0 0.2 0.4 0.6\n\n−4\n\n−2\n\n0\n\n×10−2\n\nA−+;+−\n\n−0.2 0.0 0.2 0.4 0.6\n\nx\n\n−4\n\n−2\n\n0\n\n×10−2\n\nA++;−−\n\nS+D\n\nS\n\nD\n\nFig. 1. Deuteron quark helicity amplitudes computed in the convolution formalism, atξ = 0.1,t =\n−0.25 GeV2. Full blue curve includes the full deuteron wave function, and dotted orange (dashed green) only\nincludes the deuteron radialS-(D-)wave.\n\nFigure 2 shows the helicity amplitudes at two values of momentum transfert. Helicity amplitudes\nwith different units of deuteron helicity change show different behavior with increasing momentum\ntransfer: for no helicity flip the amplitude shrinks with largert, the amplitudes with a single unit of\nhelicity change increase a little bit in size at the largert value, and the amplitudes with a complete\ndeuteron helicity flip grow significantly larger. This again reflects the role deuteron angular momen-\ntum plays, supplied through the momentum transfer.\n\nTo conclude, the role of these GPDs for the deuteron could be explored in the phenomenology\nof coherent DVCS (where gluon transversity enters at NLO) on the deuteron, double vector meson\nproduction (See Refs. [8, 9] for the nucleon case) and DEMP (in combination with a higher twist\ndistribution amplitude) [6,10] on deuteron targets.\n\nReferences\n\n[1] M. Diehl, Phys. Rept.388, 41 (2003)\n[2] W. Cosyn, and B. Pire, Phys. Rev.D98, 074020 (2018).\n\n3■■■\n\n021005-3JPS Conf. Proc. , 021005 (2019)26\n\nProceedings of the 8th International Conference on Quarks and Nuclear Physics (QNP2018)\nDownloaded from journals.jps.jp by Deutsches Elek Synchrotron on 11/24/19\n\n\n\n−0.2 0.0 0.2 0.4 0.6\n\n0.0\n\n0.5\n\n1.0\n\n1.5\n\n×10−1\n\nA++;+−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0\n\n1\n\n2\n\n×10−1\n\nA−+;−−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0\n\n1\n\n2\n\n×10−1\n\nA0+;0−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0.00\n\n0.25\n\n0.50\n\n0.75\n×10−1\n\nA0+;+−\n\n−0.2 0.0 0.2 0.4 0.6\n\n−0.75\n\n−0.50\n\n−0.25\n\n0.00\n×10−1\n\nA−+;0−\n\n−0.2 0.0 0.2 0.4 0.6\n\n0.0\n\n0.5\n\n1.0\n\n×10−1\n\nA++;0−\n\n−0.2 0.0 0.2 0.4 0.6\n−1.0\n\n−0.5\n\n0.0\n\n0.5\n\n×10−1\n\nA0+;−−\n\n−0.2 0.0 0.2 0.4 0.6\n\n−0.75\n\n−0.50\n\n−0.25\n\n0.00\n×10−1\n\nA−+;+−\n\n−0.2 0.0 0.2 0.4 0.6\n\nx\n\n−0.5\n\n0.0\n×10−1\n\nA++;−−\n\nt = −0.25 GeV2\n\nt = −0.50 GeV2\n\nFig. 2. Deuteron quark helicity amplitudes computed in the convolution formalism, atξ = 0.1 and two values\nof momentum transfert.\n\n[3] W. Cosyn, A. Freese and B. Pire, arXiv:1812.01511 (2018)\n[4] E. R. Berger, F. Cano, M. Diehl and B. Pire, Phys. Rev. Lett.87, 142302 (2001)\n[5] F. Cano, B. Pire, Eur. Phys. J.A19, 423 (2004)\n[6] S. V. Goloskokov and P. Kroll, Eur. Phys. J.A47, 112 (2011)\n[7] R. B. Wiringa, V. G. J. Stoks and R. Schiavilla, Phys. Rev.C51, 38 (1995)\n[8] R. Enberg, B. Pire, L. Szymanowski, Eur. Phys. J.C4787-94, (2006)\n[9] D. Yu. Ivanov, B. Pire, L. Szymanowski, O. V. Teryaev, Phys. Lett.B550, 65-76 (2002)\n\n[10] S. Ahmad, G. R. Goldstein and S Liuti, Phys. Rev.D79054014, (2009)\n\n4■■■\n\n021005-4JPS Conf. Proc. , 021005 (2019)26\n\nProceedings of the 8th International Conference on Quarks and Nuclear Physics (QNP2018)\nDownloaded from journals.jps.jp by Deutsches Elek Synchrotron on 11/24/19"},"fulltext":true,"key":"9882fd74f48a6c98254287b33cea5ab7","url":"https://inspirehep.net/files/9882fd74f48a6c98254287b33cea5ab7"}],"citeable":true,"$schema":"https://inspirehep.net/schemas/records/hep.json","keywords":[{"schema":"INSPIRE","value":"helicity: amplitude analysis"},{"schema":"INSPIRE","value":"quark: helicity"},{"schema":"INSPIRE","value":"generalized parton distribution"},{"schema":"INSPIRE","value":"deuteron"},{"schema":"INSPIRE","value":"angular momentum"},{"schema":"INSPIRE","value":"transversity"},{"schema":"INSPIRE","value":"light cone"},{"schema":"INSPIRE","value":"twist"}],"references":[{"reference":{"dois":["10.1016/j.physrep.2003.08.002"],"label":"1","publication_info":{"journal_volume":"388","artid":"41","year":2003,"page_start":"41","journal_title":"Phys.Rept."},"authors":[{"full_name":"M.Diehl"}]},"raw_refs":[{"schema":"text","value":"1) M.Diehl, Phys. 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A 47, 112 (2011). 10.1140/epja/i2011-11112-6"}],"curated_relation":false,"record":{"$ref":"https://inspirehep.net/api/literature/915867"}},{"reference":{"dois":["10.1103/PhysRevC.51.38"],"label":"7","publication_info":{"journal_volume":"51","artid":"38","year":1995,"page_start":"38","journal_title":"Phys.Rev.C"},"authors":[{"full_name":"B.Wiringa, R."},{"full_name":"J.Stoks, V.G."},{"full_name":"R.Schiavilla"}]},"raw_refs":[{"schema":"text","value":"7) R. B.Wiringa, V. G. J.Stoks, and R.Schiavilla, Phys. Rev. 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