Method for high-precision determination of the nucleon axial structure using lattice QCD: Removing πN -state contamination

We perform a precise calculation of physical quantities related to the axial structure of the nucleon using <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 lattice QCD gauge configuration (PACS10 configuration) generated at the physical point with lattice volume larger than <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mo stretchy="false">(</c:mo><c:mn>10</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>fm</c:mi><c:msup><c:mrow><c:mo stretchy="false">)</c:mo></c:mrow><c:mrow><c:mn>4</c:mn></c:mrow></c:msup></c:mrow></c:math> by the PACS Collaboration. The nucleon matrix element of the axial-vector current has two types of the nucleon form factors, the axial-vector (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>F</g:mi><g:mi>A</g:mi></g:msub></g:math>) form factor and the induced pseudoscalar (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>F</i:mi><i:mi>P</i:mi></i:msub></i:math>) form factor. Recently, lattice QCD simulations have succeeded in reproducing the experimental value of the axial-vector coupling, <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>g</k:mi><k:mi>A</k:mi></k:msub></k:math>, determined from <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>F</m:mi><m:mi>A</m:mi></m:msub><m:mo stretchy="false">(</m:mo><m:msup><m:mi>q</m:mi><m:mn>2</m:mn></m:msup><m:mo stretchy="false">)</m:mo></m:math> at zero momentum transfer <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msup><q:mi>q</q:mi><q:mn>2</q:mn></q:msup><q:mo>=</q:mo><q:mn>0</q:mn></q:math>, at a percent level of statistical accuracy. However, the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:msub><s:mi>F</s:mi><s:mi>P</s:mi></s:msub></s:math> form factor so far has not reproduced the experimental values well due to strong <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>π</u:mi><u:mi>N</u:mi></u:math> excited-state contamination. Therefore, we propose a simple subtraction method for removing the so-called leading <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>π</w:mi><w:mi>N</w:mi></w:math>-state contribution. This method succeeds in reproducing the values obtained by two experiments of muon capture on the proton and pion electroproduction for <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>F</y:mi><y:mi>P</y:mi></y:msub><y:mo stretchy="false">(</y:mo><y:msup><y:mi>q</y:mi><y:mn>2</y:mn></y:msup><y:mo stretchy="false">)</y:mo></y:math>. The novel approach can also be applied to determine the pseudoscalar (<cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:msub><cb:mi>G</cb:mi><cb:mi>P</cb:mi></cb:msub></cb:math>) form factor from the nucleon pseudoscalar matrix element with the help of the axial Ward-Takahashi identity. The resulting form factors, <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msub><eb:mi>F</eb:mi><eb:mi>P</eb:mi></eb:msub><eb:mo stretchy="false">(</eb:mo><eb:msup><eb:mi>q</eb:mi><eb:mn>2</eb:mn></eb:msup><eb:mo stretchy="false">)</eb:mo></eb:math> and <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:msub><ib:mi>G</ib:mi><ib:mi>P</ib:mi></ib:msub><ib:mo stretchy="false">(</ib:mo><ib:msup><ib:mi>q</ib:mi><ib:mn>2</ib:mn></ib:msup><ib:mo stretchy="false">)</ib:mo></ib:math>, are in good agreement with the prediction of the pion-pole dominance model. In the new analysis, the induced pseudoscalar coupling <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"><mb:msubsup><mb:mi>g</mb:mi><mb:mi>P</mb:mi><mb:mo>*</mb:mo></mb:msubsup></mb:math> and the pion-nucleon coupling <ob:math xmlns:ob="http://www.w3.org/1998/Math/MathML" display="inline"><ob:msub><ob:mi>g</ob:mi><ob:mrow><ob:mi>π</ob:mi><ob:mi>N</ob:mi><ob:mi>N</ob:mi></ob:mrow></ob:msub></ob:math> can be evaluated with a few percent accuracy including systematic uncertainties using existing data calculated at two lattice spacings.