Electromagnetic form factors of the nucleon from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> lattice QCD

Abstract

There is a long-standing discrepancy between different measurements of the electric and magnetic radii of the proton. Lattice QCD calculations are a well-suited tool for theoretical investigations of the structure of the nucleon from first principles. However, all previous lattice studies of the proton’s electromagnetic radii have either neglected quark-disconnected contributions or were not extrapolated to the continuum and infinite-volume limit. Here, we present results for the electromagnetic form factors of the proton and neutron computed on the (<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:mrow></a:math>)-flavor coordinated lattice simulations (CLS) ensembles including both quark-connected and -disconnected contributions. From simultaneous fits to the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mi>Q</c:mi><c:mn>2</c:mn></c:msup></c:math>-, pion-mass, lattice-spacing, and finite-volume dependence of the form factors, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain as our final values <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mo stretchy="false">⟨</e:mo><e:msubsup><e:mrow><e:mi>r</e:mi></e:mrow><e:mrow><e:mi>E</e:mi></e:mrow><e:mrow><e:mn>2</e:mn></e:mrow></e:msubsup><e:msup><e:mrow><e:mo stretchy="false">⟩</e:mo></e:mrow><e:mrow><e:mi>p</e:mi></e:mrow></e:msup><e:mo>=</e:mo><e:mo stretchy="false">(</e:mo><e:mn>0.672</e:mn><e:mo>±</e:mo><e:mn>0.014</e:mn><e:mrow><e:mo stretchy="false">(</e:mo><e:mi>stat</e:mi><e:mo stretchy="false">)</e:mo></e:mrow><e:mo>±</e:mo><e:mspace linebreak="goodbreak"/><e:mn>0.018</e:mn><e:mrow><e:mo stretchy="false">(</e:mo><e:mi>syst</e:mi><e:mo stretchy="false">)</e:mo></e:mrow><e:mo stretchy="false">)</e:mo><e:mtext> </e:mtext><e:mtext> </e:mtext><e:msup><e:mrow><e:mi>fm</e:mi></e:mrow><e:mrow><e:mn>2</e:mn></e:mrow></e:msup></e:mrow></e:math>, <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mrow><p:mo stretchy="false">⟨</p:mo><p:msubsup><p:mrow><p:mi>r</p:mi></p:mrow><p:mrow><p:mi>M</p:mi></p:mrow><p:mrow><p:mn>2</p:mn></p:mrow></p:msubsup><p:msup><p:mrow><p:mo stretchy="false">⟩</p:mo></p:mrow><p:mrow><p:mi>p</p:mi></p:mrow></p:msup><p:mo>=</p:mo><p:mo stretchy="false">(</p:mo><p:mn>0.658</p:mn><p:mo>±</p:mo><p:mn>0.012</p:mn><p:mrow><p:mo stretchy="false">(</p:mo><p:mi>stat</p:mi><p:mo stretchy="false">)</p:mo></p:mrow><p:mo>±</p:mo><p:mn>0.008</p:mn><p:mrow><p:mo stretchy="false">(</p:mo><p:mi>syst</p:mi><p:mo stretchy="false">)</p:mo></p:mrow><p:mo stretchy="false">)</p:mo><p:mtext> </p:mtext><p:mtext> </p:mtext><p:msup><p:mrow><p:mi>fm</p:mi></p:mrow><p:mrow><p:mn>2</p:mn></p:mrow></p:msup></p:mrow></p:math>, and <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mrow><z:msubsup><z:mrow><z:mi>μ</z:mi></z:mrow><z:mrow><z:mi>M</z:mi></z:mrow><z:mrow><z:mi>p</z:mi></z:mrow></z:msubsup><z:mo>=</z:mo><z:mo stretchy="false">(</z:mo><z:mn>2.739</z:mn><z:mo>±</z:mo><z:mn>0.063</z:mn><z:mrow><z:mo stretchy="false">(</z:mo><z:mi>stat</z:mi><z:mo stretchy="false">)</z:mo></z:mrow><z:mo>±</z:mo><z:mspace linebreak="goodbreak"/><z:mn>0.018</z:mn><z:mrow><z:mo stretchy="false">(</z:mo><z:mi>syst</z:mi><z:mo stretchy="false">)</z:mo></z:mrow></z:mrow></z:math>. The magnetic moment is in good agreement with the experimental value, as is the one of the neutron. On the one hand, our result for the electric (charge) radius of the proton clearly points towards a small value, as favored by muonic hydrogen spectroscopy and the recent <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"><hb:mi>e</hb:mi><hb:mi>p</hb:mi></hb:math>-scattering experiment by PRad. Our estimate for the magnetic radius, on the other hand, is well compatible with that inferred from the A1 <jb:math xmlns:jb="http://www.w3.org/1998/Math/MathML" display="inline"><jb:mrow><jb:mi>e</jb:mi><jb:mi>p</jb:mi></jb:mrow></jb:math>-scattering experiment. Published by the American Physical Society 2024

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