Nucleon Quark Distribution Functions from the Dyson-Schwinger Equations

TL;DR

This paper uses Dyson-Schwinger equations to calculate nucleon quark distributions, successfully matching experimental data and predicting the high-x d/u ratio, highlighting the role of diquark correlations.

Contribution

It provides a novel calculation of nucleon valence quark distributions from DSEs, including axial-vector diquark effects, and predicts the d/u ratio at x→1.

Findings

Good agreement with experimental data.

Predicted d/u ratio at x→1 is approximately 0.087.

Diquark correlations significantly influence the d/u ratio.

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. We employ the rainbow-ladder truncation of the DSEs and utilize nucleon bound state amplitudes from the Poincar\'e-covariant Faddeev equation, where the dominant scalar and axial-vector quark-quark correlations are included. This DSE 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 $x\to 1$ limit, invariant under scale evolution, takes the value $d/u \to 0.087 \pm 0.010$. 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 $x\to 1$ 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.