Isoscalar octet axial form factor of the nucleon from lattice QCD

The isoscalar axial-vector form factor of the nucleon plays a key role in understanding the electroweak interaction of nucleons. For the interpretation of the spin structure of the nucleon the nonsinglet isoscalar axial charge is indispensable. Moreover, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>G</a:mi><a:mi>A</a:mi><a:mrow><a:mi>u</a:mi><a:mo>+</a:mo><a:mi>d</a:mi><a:mo>−</a:mo><a:mn>2</a:mn><a:mi>s</a:mi></a:mrow></a:msubsup><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> together with the isovector and singlet isoscalar form factors are needed for the flavor decomposition of the axial-vector form factor. Detailed knowledge of the flavor decomposition facilitates extractions of Standard Model (SM) parameters from low energy experiments such as the electroweak charge of the proton in the P2 experiment. Here we present a lattice determination of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msubsup><e:mi>G</e:mi><e:mi>A</e:mi><e:mrow><e:mi>u</e:mi><e:mo>+</e:mo><e:mi>d</e:mi><e:mo>−</e:mo><e:mn>2</e:mn><e:mi>s</e:mi></e:mrow></e:msubsup><e:mo stretchy="false">(</e:mo><e:msup><e:mi>Q</e:mi><e:mn>2</e:mn></e:msup><e:mo stretchy="false">)</e:mo></e:math> on <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msub><i:mi>N</i:mi><i:mi>f</i:mi></i:msub><i:mo>=</i:mo><i:mn>2</i:mn><i:mo>+</i:mo><i:mn>1</i:mn></i:math> <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi mathvariant="script">O</k:mi><k:mo stretchy="false">(</k:mo><k:mi>a</k:mi><k:mo stretchy="false">)</k:mo></k:math> improved Wilson fermions, with a full error budget concerning extrapolations and interpolations to the continuum and infinite volume and physical quark masses.