Valence quark PDFs of the proton from two-current correlations in lattice QCD

Following previous works on that topic, we consider Euclidean hadronic matrix elements in position space of two spatially separated local currents on the lattice, in order to extract the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math> dependence of parton distribution functions (PDFs). The corresponding approach is often referred to by the term . In this work we will consider valence quark PDFs of an unpolarized proton. We adapt the previously established formalism to our choice of operators. The calculation of the two-current matrix elements requires the evaluation of four-point functions. The corresponding calculation is carried out on a <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>n</c:mi></c:mrow><c:mrow><c:mi>f</c:mi></c:mrow></c:msub><c:mo>=</c:mo><c:mn>2</c:mn><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math> gauge ensemble with lattice spacing <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>a</e:mi><e:mo>=</e:mo><e:mn>0.0856</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>fm</e:mi></e:math> and pseudoscalar masses <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>m</g:mi><g:mi>π</g:mi></g:msub><g:mo>=</g:mo><g:mn>355</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>MeV</g:mi></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>m</i:mi><i:mi>K</i:mi></i:msub><i:mo>=</i:mo><i:mn>441</i:mn><i:mtext> </i:mtext><i:mtext> </i:mtext><i:mi>MeV</i:mi></i:math>. The four-point functions have been evaluated in a previous project. The lattice data is converted to the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mover accent="true"><k:mi>MS</k:mi><k:mo stretchy="true">¯</k:mo></k:mover></k:math> scheme at a scale <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>μ</o:mi><o:mo>=</o:mo><o:mn>2</o:mn><o:mtext> </o:mtext><o:mtext> </o:mtext><o:mi>GeV</o:mi></o:math> and improved with respect to lattice artifacts. We use a common model as fit ansatz for the lattice data in order to extract the PDFs. Published by the American Physical Society 2024