Sketching the pion's valence-quark generalised parton distribution
Abstract
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.
- Publication:
-
Physics Letters B
- Pub Date:
- February 2015
- DOI:
- arXiv:
- arXiv:1411.6634
- Bibcode:
- 2015PhLB..741..190M
- Keywords:
-
- Deeply virtual Compton scattering;
- Dynamical chiral symmetry breaking;
- Dyson-Schwinger equations;
- Generalised parton distribution functions;
- π-meson;
- Nuclear Theory;
- High Energy Physics - Lattice;
- High Energy Physics - Phenomenology;
- Nuclear Experiment
- E-Print:
- 7 pages, 4 figures