Nucleon isovector axial form factors

Abstract

We present results for the isovector axial vector form factors obtained using thirteen <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>-flavor highly improved staggered quark (HISQ) ensembles generated by the MILC collaboration. The calculation of nucleon two- and three-point correlation functions has been done using Wilson-clover fermions. In the analysis of these data, we quantify the sensitivity of the results to strategies used for removing excited state contamination and invoke the partially conserved axial current relation between the form factors to choose between them. Our data driven analysis includes removing contributions from multihadron <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>N</c:mi><c:mi>π</c:mi></c:math> states that make significant contributions. Our final results are <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:msub><e:mrow><e:mi>g</e:mi></e:mrow><e:mrow><e:mi>A</e:mi></e:mrow></e:msub><e:mo>=</e:mo><e:mn>1.292</e:mn><e:mo stretchy="false">(</e:mo><e:mn>53</e:mn><e:msub><e:mrow><e:mo stretchy="false">)</e:mo></e:mrow><e:mrow><e:mi>stat</e:mi></e:mrow></e:msub><e:mo stretchy="false">(</e:mo><e:mn>24</e:mn><e:msub><e:mrow><e:mo stretchy="false">)</e:mo></e:mrow><e:mrow><e:mi>sys</e:mi></e:mrow></e:msub></e:mrow></e:math> for the axial charge; <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mrow><k:msub><k:mrow><k:mi>g</k:mi></k:mrow><k:mrow><k:mi>S</k:mi></k:mrow></k:msub><k:mo>=</k:mo><k:mn>1.085</k:mn><k:mo stretchy="false">(</k:mo><k:mn>50</k:mn><k:msub><k:mrow><k:mo stretchy="false">)</k:mo></k:mrow><k:mrow><k:mi>stat</k:mi></k:mrow></k:msub><k:mo stretchy="false">(</k:mo><k:mn>103</k:mn><k:msub><k:mrow><k:mo stretchy="false">)</k:mo></k:mrow><k:mrow><k:mi>sys</k:mi></k:mrow></k:msub></k:mrow></k:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>g</q:mi><q:mi>T</q:mi></q:msub><q:mo>=</q:mo><q:mn>0.991</q:mn><q:mo stretchy="false">(</q:mo><q:mn>21</q:mn><q:msub><q:mo stretchy="false">)</q:mo><q:mrow><q:mi>stat</q:mi></q:mrow></q:msub><q:mo stretchy="false">(</q:mo><q:mn>10</q:mn><q:msub><q:mo stretchy="false">)</q:mo><q:mi>sys</q:mi></q:msub></q:math> for the scalar and tensor charges; <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mrow><w:mo stretchy="false">⟨</w:mo><w:msubsup><w:mrow><w:mi>r</w:mi></w:mrow><w:mrow><w:mi>A</w:mi></w:mrow><w:mrow><w:mn>2</w:mn></w:mrow></w:msubsup><w:mo stretchy="false">⟩</w:mo><w:mo>=</w:mo><w:mn>0.439</w:mn><w:mo stretchy="false">(</w:mo><w:mn>56</w:mn><w:msub><w:mrow><w:mo stretchy="false">)</w:mo></w:mrow><w:mrow><w:mi>stat</w:mi></w:mrow></w:msub><w:mo stretchy="false">(</w:mo><w:mn>34</w:mn><w:msub><w:mrow><w:mo stretchy="false">)</w:mo></w:mrow><w:mrow><w:mi>sys</w:mi></w:mrow></w:msub><w:mtext> </w:mtext><w:mtext> </w:mtext><w:mrow><w:msup><w:mrow><w:mi>fm</w:mi></w:mrow><w:mrow><w:mn>2</w:mn></w:mrow></w:msup></w:mrow></w:mrow></w:math> for the mean squared axial charge radius, <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msubsup><eb:mi>g</eb:mi><eb:mi>P</eb:mi><eb:mo>*</eb:mo></eb:msubsup><eb:mo>=</eb:mo><eb:mn>9.03</eb:mn><eb:mo stretchy="false">(</eb:mo><eb:mn>47</eb:mn><eb:msub><eb:mo stretchy="false">)</eb:mo><eb:mrow><eb:mi>stat</eb:mi></eb:mrow></eb:msub><eb:mo stretchy="false">(</eb:mo><eb:mn>42</eb:mn><eb:msub><eb:mo stretchy="false">)</eb:mo><eb:mi>sys</eb:mi></eb:msub></eb:math> for the induced pseudoscalar charge; and <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:msub><kb:mi>g</kb:mi><kb:mrow><kb:mi>π</kb:mi><kb:mi>N</kb:mi><kb:mi>N</kb:mi></kb:mrow></kb:msub><kb:mo>=</kb:mo><kb:mn>14.14</kb:mn><kb:mo stretchy="false">(</kb:mo><kb:mn>81</kb:mn><kb:msub><kb:mo stretchy="false">)</kb:mo><kb:mrow><kb:mi>stat</kb:mi></kb:mrow></kb:msub><kb:mo stretchy="false">(</kb:mo><kb:mn>85</kb:mn><kb:msub><kb:mo stretchy="false">)</kb:mo><kb:mi>sys</kb:mi></kb:msub></kb:math> for the pion-nucleon coupling. We also provide a parametrization of the axial form factor <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"><qb:msub><qb:mi>G</qb:mi><qb:mi>A</qb:mi></qb:msub><qb:mo stretchy="false">(</qb:mo><qb:msup><qb:mi>Q</qb:mi><qb:mn>2</qb:mn></qb:msup><qb:mo stretchy="false">)</qb:mo></qb:math> over the range <ub:math xmlns:ub="http://www.w3.org/1998/Math/MathML" display="inline"><ub:mn>0</ub:mn><ub:mo>≤</ub:mo><ub:msup><ub:mi>Q</ub:mi><ub:mn>2</ub:mn></ub:msup><ub:mo>≤</ub:mo><ub:mn>1</ub:mn><ub:mtext> </ub:mtext><ub:mtext> </ub:mtext><ub:mrow><ub:msup><ub:mrow><ub:mi>GeV</ub:mi></ub:mrow><ub:mrow><ub:mn>2</ub:mn></ub:mrow></ub:msup></ub:mrow></ub:math> for use in phenomenology and a comparison with other lattice determinations. We find that the various lattice data agree within 10% but are significantly different from the extraction of <wb:math xmlns:wb="http://www.w3.org/1998/Math/MathML" display="inline"><wb:msub><wb:mi>G</wb:mi><wb:mi>A</wb:mi></wb:msub><wb:mo stretchy="false">(</wb:mo><wb:msup><wb:mi>Q</wb:mi><wb:mn>2</wb:mn></wb:msup><wb:mo stretchy="false">)</wb:mo></wb:math> from the <ac:math xmlns:ac="http://www.w3.org/1998/Math/MathML" display="inline"><ac:mi>ν</ac:mi></ac:math>-deuterium scattering data. Published by the American Physical Society 2024

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