Sketching the pion's valence-quark generalised parton distribution

C. Mezrag; L. Chang; H. Moutarde; C. D. Roberts; J. Rodriguez-Quintero; F. Sabatie; S. M. Schmidt

doi:10.1016/j.physletb.2014.12.027

paper

Sketching the pion's valence-quark generalised parton distribution

arXiv:1411.6634 · doi:10.1016/j.physletb.2014.12.027

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, $H_{π}^{v} (x, ξ, t)$ . Our analysis focuses primarily on $ξ = 0$ , although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting $H_{π}^{v} (x, ξ = \pm 1, t)$ 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 $H_{π}^{v} (x, 0, t)$ , expressed as the Radon transform of a single amplitude. Therewith we obtain results for $H_{π}^{v} (x, 0, t)$ and the associated impact-parameter dependent distribution, $q_{π}^{v} (x, ∣ b_{⊥} ∣)$ , which provide a qualitatively sound picture of the pion's dressed-quark structure at an 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.

arXiv comment7 pages, 4 figures

Sketching the pion's valence-quark generalised parton distribution

Abstract

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