Sketching the pion's valence-quark generalised parton distribution
In order to learn effectively from measurements of generalised parton distributions (GPDs), it is desirable to compute them using a framework that can potentially connect empirical information with basic features of the Standard Model. We sketch an approach to such computations, based upon a rainbow...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2015-02-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269314008983 |
| _version_ | 1819112745987997696 |
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| author | C. Mezrag L. Chang H. Moutarde C.D. Roberts J. Rodríguez-Quintero F. Sabatié S.M. Schmidt |
| author_facet | C. Mezrag L. Chang H. Moutarde C.D. Roberts J. Rodríguez-Quintero F. Sabatié S.M. Schmidt |
| author_sort | C. Mezrag |
| collection | DOAJ |
| description | In order to learn effectively from measurements of generalised parton distributions (GPDs), it is desirable to compute them using a framework that can potentially connect empirical information with basic features of the Standard Model. We sketch an approach to such computations, based upon a rainbow-ladder (RL) truncation of QCD's Dyson–Schwinger equations and exemplified via the pion's valence dressed-quark GPD, Hπv(x,ξ,t). Our analysis focuses primarily on ξ=0, although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting Hπv(x,ξ=±1,t) with the pion's valence-quark parton distribution amplitude. We explain that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for Hπv(x,0,t), expressed as the Radon transform of a single amplitude. Therewith we obtain results for Hπv(x,0,t) and the associated impact-parameter dependent distribution, qπv(x,|b→⊥|), which provide a qualitatively sound picture of the pion's dressed-quark structure at a hadronic scale. We evolve the distributions to a scale ζ=2 GeV, so as to facilitate comparisons in future with results from experiment or other nonperturbative methods. Keywords: Deeply virtual Compton scattering, Dynamical chiral symmetry breaking, Dyson–Schwinger equations, Generalised parton distribution functions, π-meson |
| first_indexed | 2024-12-22T04:18:24Z |
| format | Article |
| id | doaj.art-a52c9aa49def46249751d6e773004767 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-12-22T04:18:24Z |
| publishDate | 2015-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-a52c9aa49def46249751d6e7730047672022-12-21T18:39:21ZengElsevierPhysics Letters B0370-26932015-02-01741190196Sketching the pion's valence-quark generalised parton distributionC. Mezrag0L. Chang1H. Moutarde2C.D. Roberts3J. Rodríguez-Quintero4F. Sabatié5S.M. Schmidt6Centre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, FranceCSSM, School of Chemistry and Physics, University of Adelaide, Adelaide SA 5005, AustraliaCentre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, FrancePhysics Division, Argonne National Laboratory, Argonne, IL 60439, USADepartamento de Física Aplicada, Facultad de Ciencias Experimentales, Universidad de Huelva, Huelva E-21071, SpainCentre de Saclay, IRFU/Service de Physique Nucléaire, F-91191 Gif-sur-Yvette, FranceInstitute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, GermanyIn order to learn effectively from measurements of generalised parton distributions (GPDs), it is desirable to compute them using a framework that can potentially connect empirical information with basic features of the Standard Model. We sketch an approach to such computations, based upon a rainbow-ladder (RL) truncation of QCD's Dyson–Schwinger equations and exemplified via the pion's valence dressed-quark GPD, Hπv(x,ξ,t). Our analysis focuses primarily on ξ=0, although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting Hπv(x,ξ=±1,t) with the pion's valence-quark parton distribution amplitude. We explain that the impulse-approximation used hitherto to define the pion's valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for Hπv(x,0,t), expressed as the Radon transform of a single amplitude. Therewith we obtain results for Hπv(x,0,t) and the associated impact-parameter dependent distribution, qπv(x,|b→⊥|), which provide a qualitatively sound picture of the pion's dressed-quark structure at a hadronic scale. We evolve the distributions to a scale ζ=2 GeV, so as to facilitate comparisons in future with results from experiment or other nonperturbative methods. Keywords: Deeply virtual Compton scattering, Dynamical chiral symmetry breaking, Dyson–Schwinger equations, Generalised parton distribution functions, π-mesonhttp://www.sciencedirect.com/science/article/pii/S0370269314008983 |
| spellingShingle | C. Mezrag L. Chang H. Moutarde C.D. Roberts J. Rodríguez-Quintero F. Sabatié S.M. Schmidt Sketching the pion's valence-quark generalised parton distribution Physics Letters B |
| title | Sketching the pion's valence-quark generalised parton distribution |
| title_full | Sketching the pion's valence-quark generalised parton distribution |
| title_fullStr | Sketching the pion's valence-quark generalised parton distribution |
| title_full_unstemmed | Sketching the pion's valence-quark generalised parton distribution |
| title_short | Sketching the pion's valence-quark generalised parton distribution |
| title_sort | sketching the pion s valence quark generalised parton distribution |
| url | http://www.sciencedirect.com/science/article/pii/S0370269314008983 |
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