Generalized parton distributions from the pseudodistribution approach on the lattice

Generalized parton distributions (GPDs) are key quantities for the description of a hadron’s three-dimensional structure. They are the current focus of all areas of hadronic physics—phenomenological, experimental and theoretical, including lattice QCD. Synergies between these areas are desirable and essential to achieve precise quantification and understanding of the structure of, particularly, nucleons, as the basic ingredients of matter. In this paper, we investigate, for the first time, the numerical implementation of the pseudodistribution approach for the extraction of zero-skewness GPDs for unpolarized quarks. Pseudodistributions are Euclidean parton correlators computable in lattice QCD that can be perturbatively matched to the light-cone parton distributions of interest. Although they are closely related to the quasidistributions and come from the same lattice-extracted matrix elements, they are, however, subject to different systematic effects. We use the data previously utilized for quasi-GPDs and extend it with other momentum transfers and nucleon boosts, in particular a higher one (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>P</a:mi></a:mrow><a:mrow><a:mn>3</a:mn></a:mrow></a:msub><a:mo>=</a:mo><a:mn>1.67</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>GeV</a:mi></a:mrow></a:math>) with eightfold larger statistics than the largest one used for quasidistributions (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>P</c:mi><c:mn>3</c:mn></c:msub><c:mo>=</c:mo><c:mn>1.25</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>GeV</c:mi></c:math>). We renormalize the matrix elements with a ratio scheme and match the resulting Ioffe time distributions to the light cone in coordinate space. The matched distributions are then used to reconstruct the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>x</e:mi></e:math> dependence with a fitting . We investigate some systematic effects related to this procedure, and we also compare the results with the ones obtained in the framework of quasi-GPDs. Our final results involve the invariant four-momentum transfer squared (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mo>−</g:mo><g:mi>t</g:mi></g:math>) dependence of the flavor nonsinglet (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>u</i:mi><i:mo>−</i:mo><i:mi>d</i:mi></i:math>) <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>H</k:mi></k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>E</m:mi></m:math> GPDs. Published by the American Physical Society 2024