Nucleon axial radius

We present the first systematic study of the relativistic axial-vector four-current distributions inside a nucleon. We show in particular that the slope of the axial form factor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>G</a:mi><a:mi>A</a:mi></a:msub><a:mo stretchy="false">(</a:mo><a:msup><a:mi>Q</a:mi><a:mn>2</a:mn></a:msup><a:mo stretchy="false">)</a:mo></a:math> in the forward limit—conventionally denoted as <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>R</e:mi><e:mi>A</e:mi><e:mn>2</e:mn></e:msubsup></e:math> in the literature—does not represent the three-dimensional mean-square axial radius in the Breit frame, but corresponds instead to a contribution to the mean-square spin radius. We derive explicit expressions for the latter in different frames and find in general additional contributions that depend on both the nucleon mass and the forward values of the axial-vector form factors <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>G</g:mi><g:mi>A</g:mi></g:msub><g:mo stretchy="false">(</g:mo><g:mn>0</g:mn><g:mo stretchy="false">)</g:mo></g:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>G</k:mi><k:mi>P</k:mi></k:msub><k:mo stretchy="false">(</k:mo><k:mn>0</k:mn><k:mo stretchy="false">)</k:mo></k:math>. This provides an additional key motivation for ongoing lattice quantum chromodynamics (QCD) calculations and future experimental measurements of the induced pseudoscalar form factor <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>G</o:mi><o:mi>P</o:mi></o:msub><o:mo stretchy="false">(</o:mo><o:msup><o:mi>Q</o:mi><o:mn>2</o:mn></o:msup><o:mo stretchy="false">)</o:mo></o:math>. Published by the American Physical Society 2024