Nucleon quark distribution functions from the Dyson–Schwinger equations

Abstract

We present results for the nucleon's leading-twist spin-independent valence parton distribution functions obtained from a theoretical framework based on the Dyson–Schwinger equations (DSEs) of QCD that previously gave an excellent description of nucleon electromagnetic form factors. Key dynamical elements selected by experience with the rainbow-ladder truncation of the DSEs are implemented. We utilize nucleon bound state amplitudes from the Poincaré-covariant Faddeev equation that implements the dominant scalar and axial-vector quark–quark correlations. This framework is used to numerically evaluate the first 20 moments of the valence u and d quark distribution functions, from which the x-dependence of the distributions is found to be well constrained. We find good agreement with empirical parameterizations of experimental data and make the prediction that the d/u ratio in the x→1 limit, invariant under scale evolution, takes the value d/u→0.087±0.010. We find that this ratio is rather sensitive to the strength of axial-vector diquark correlations. However, contrary to a naive expectation, our result for the d/u ratio in the x→1 limit does not vanish when only scalar diquark correlations are present, although it is an order-of-magnitude smaller than our d/u result that also includes axial-vector diquarks. The valence quark distribution results are set in a broader context via a simple pion cloud model estimate of sea-quark light-cone momenta and gluon light-cone momentum.