skip to main content

Title: 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-ladder (RL) truncation of QCD’s Dyson–Schwinger equations and exemplified via the pion’s valence dressed-quark GPD, Hvπ(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 Hvπ(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 Hvπ(x, 0, t), expressed as the Radon transform of a single amplitude. Therewith we obtain results for Hvπ(x, 0, t) and the associated impact-parameter dependent distribution, qvπ(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 frommore » experiment or other nonperturbative methods.« less
 [1] ;  [2] ;  [1] ; ORCiD logo [3] ;  [4] ;  [1] ;  [5]
  1. Centre de Saclay, IRFU/Service de Physique Nucleaire, Gif-sur-Yvette (France)
  2. Univ. of Adelaide, Adelaide (Australia)
  3. Argonne National Lab. (ANL), Argonne, IL (United States)
  4. Univ. de Huelva, Huelva (Spain)
  5. Inst. for Advanced Simulation, Forschungszentrum Julich and JARA, Julich (Germany)
Publication Date:
OSTI Identifier:
Grant/Contract Number:
Published Article
Journal Name:
Physics Letters. Section B
Additional Journal Information:
Journal Volume: 741; Journal Issue: C; Journal ID: ISSN 0370-2693
Research Org:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; deeply virtual compton scattering; dynamical chiral symmetry breaking; Dyson-Schwinger equations; generalised parton distribution functions; π-meson