Quark counting, Drell-Yan West, and the pion wave function

The relation between the pion's quark distribution function, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>q</a:mi><a:mo>(</a:mo><a:mi>x</a:mi><a:mo>)</a:mo></a:mrow></a:math>, its light-front wave function, and the elastic charge form factor, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>F</b:mi><b:mo>(</b:mo><b:msup><b:mi mathvariant="normal">Δ</b:mi><b:mn>2</b:mn></b:msup><b:mo>)</b:mo></b:mrow></b:math>, is explored. The square of the leading-twist pion wave function at a special probe scale, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi>ζ</d:mi><d:mi>H</d:mi></d:msub></d:math>, is determined using models and Poincaré covariance from realistic results for <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>q</e:mi><e:mo>(</e:mo><e:mi>x</e:mi><e:mo>)</e:mo></e:mrow></e:math>. This wave function is then used to compute form factors with the result that the Drell-Yan-West and quark counting relationships are not satisfied. A new relationship between <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>q</f:mi><f:mo>(</f:mo><f:mi>x</f:mi><f:mo>)</f:mo></f:mrow></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>F</g:mi><g:mo>(</g:mo><g:msup><g:mi mathvariant="normal">Δ</g:mi><g:mn>2</g:mn></g:msup><g:mo>)</g:mo></g:mrow></g:math> is proposed. Published by the American Physical Society 2024