Systematic improvement of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>x</mml:mi></mml:math>-dependent unpolarized nucleon generalized parton distributions in lattice-QCD calculation

Abstract

We present a first study of the effects of renormalization-group resummation (RGR) and leading-renormalon resummation (LRR) on the systematic errors of the unpolarized isovector nucleon generalized parton distribution in the framework of large-momentum effective theory. This work is done using lattice gauge ensembles generated by the MILC Collaboration, consisting of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math> flavors of highly improved staggered quarks with a physical pion mass at lattice spacing <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>a</c:mi><c:mo>≈</c:mo><c:mn>0.09</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>fm</c:mi></c:math> and a box width <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>L</e:mi><e:mo>≈</e:mo><e:mn>5.76</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>fm</e:mi></e:math>. We present results for the nucleon <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>H</g:mi></g:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>E</i:mi></i:math> generalized parton distributions (GPDs) with average boost momentum <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>P</k:mi><k:mi>z</k:mi></k:msub><k:mo>≈</k:mo><k:mn>2</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>GeV</k:mi></k:math> at momentum transfers <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:msup><m:mrow><m:mi>Q</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msup><m:mo>=</m:mo><m:mo stretchy="false">[</m:mo><m:mn>0</m:mn><m:mo>,</m:mo><m:mn>0.97</m:mn><m:mo stretchy="false">]</m:mo><m:mtext> </m:mtext><m:mtext> </m:mtext><m:msup><m:mrow><m:mi>GeV</m:mi></m:mrow><m:mrow><m:mn>2</m:mn></m:mrow></m:msup></m:mrow></m:math> at skewness <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>ξ</q:mi><q:mo>=</q:mo><q:mn>0</q:mn></q:math> as well as <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msup><s:mi>Q</s:mi><s:mn>2</s:mn></s:msup><s:mo>∈</s:mo><s:mn>0.23</s:mn><s:mtext> </s:mtext><s:mtext> </s:mtext><s:msup><s:mrow><s:mi>GeV</s:mi></s:mrow><s:mrow><s:mn>2</s:mn></s:mrow></s:msup></s:math> at <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>ξ</u:mi><u:mo>=</u:mo><u:mn>0.1</u:mn></u:math>, renormalized in the modified minimal subtraction (<w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mover accent="true"><w:mi>MS</w:mi><w:mo stretchy="true">¯</w:mo></w:mover></w:math>) scheme at scale <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:mi>μ</ab:mi><ab:mo>=</ab:mo><ab:mn>2.0</ab:mn><ab:mtext> </ab:mtext><ab:mtext> </ab:mtext><ab:mi>GeV</ab:mi></ab:math>, with two- and one-loop matching, respectively. We demonstrate that the simultaneous application of RGR and LRR significantly reduces the systematic errors in renormalized matrix elements and distributions for both the zero and nonzero skewness GPDs, and that it is necessary to include both RGR and LRR at higher orders in the matching and renormalization processes. Published by the American Physical Society 2024