Nucleon form factors in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> lattice QCD at the physical point: Finite lattice spacing effect on the root-mean-square radii

Abstract

We present results for the nucleon form factors: electric (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>G</a:mi></a:mrow><a:mrow><a:mi>E</a:mi></a:mrow></a:msub></a:mrow></a:math>), magnetic (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msub><c:mrow><c:mi>G</c:mi></c:mrow><c:mrow><c:mi>M</c:mi></c:mrow></c:msub></c:mrow></c:math>), axial (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>F</e:mi><e:mi>A</e:mi></e:msub></e:math>), induced pseudoscalar (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>F</g:mi><g:mi>P</g:mi></g:msub></g:math>), and pseudoscalar (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>G</i:mi><i:mi>P</i:mi></i:msub></i:math>) form factors, using the second PACS10 ensemble that is one of three sets of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>2</k:mn><k:mo>+</k:mo><k:mn>1</k:mn></k:math> flavor lattice QCD configurations at physical quark masses in large spatial volumes [exceeding <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mo stretchy="false">(</m:mo><m:mn>10</m:mn><m:mtext> </m:mtext><m:mtext> </m:mtext><m:mi>fm</m:mi><m:msup><m:mrow><m:mo stretchy="false">)</m:mo></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow></m:msup></m:mrow></m:math>]. The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>O</q:mi><q:mo stretchy="false">(</q:mo><q:mi>a</q:mi><q:mo stretchy="false">)</q:mo></q:math> improved Wilson quark action and Iwasaki gauge action at the second gauge coupling <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>β</u:mi><u:mo>=</u:mo><u:mn>2.00</u:mn></u:math> corresponding to the lattice spacing of <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>a</w:mi><w:mo>=</w:mo><w:mn>0.063</w:mn><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mi>fm</w:mi></w:math>. We determine the isovector electric, magnetic and axial radii, and magnetic moment from the corresponding form factors, as well as the axial-vector coupling <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>g</y:mi><y:mi>A</y:mi></y:msub></y:math>. Combining our previous results for the coarser lattice spacing [E. Shintani , ; ], the finite lattice spacing effects on the isovector radii, magnetic moment, and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"><ab:msub><ab:mi>g</ab:mi><ab:mi>A</ab:mi></ab:msub></ab:math> is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial-vector current relation using a set of nucleon three-point correlation functions in order to verify the effect by <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>O</cb:mi><cb:mo stretchy="false">(</cb:mo><cb:mi>a</cb:mi><cb:mo stretchy="false">)</cb:mo></cb:math> improvement of the axial-vector current. Published by the American Physical Society 2024

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