Nonlocal nucleon matrix elements in the rest frame

Extracting parton structure from lattice quantum chromodynamics (QCD) calculations requires studying the coordinate scale <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>z</a:mi><a:mn>3</a:mn></a:msub></a:math> dependence of the matrix elements of bilocal operators. The most significant contribution comes from the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>z</c:mi><c:mn>3</c:mn></c:msub></c:math> dependence induced by ultraviolet (UV) renormalization of the Wilson line. We demonstrate that the next-to-leading order perturbative calculations of the renormalization factor can describe, to a few percent accuracy, the logarithm of the lattice QCD rest frame matrix elements with separations up to distances of 0.6 fm on multiple lattice spacings. The residual discrepancies can be modeled by a leading effect from the structure of the nucleon.