Chiral-even twist-3 GPDs for the proton in a spectator diquark model

We investigate the chiral-even twist-3 generalized parton distributions (GPDs) of valence quarks in the proton at nonzero skewness <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ξ</a:mi></a:math>, using a spectator model with scalar and axial-vector diquarks. We consider the exponential form factor for the nucleon-quark-diquark vertex and the axial-vector diquark with light-cone transverse polarization. We analyze the dependence of GPDs on the longitudinal momentum fraction <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>x</c:mi></c:math> at different <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ξ</e:mi></e:math>, and on the square of the transverse momentum transfer <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi mathvariant="bold">Δ</g:mi><g:mi>T</g:mi><g:mn>2</g:mn></g:msubsup></g:math> at different <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>x</j:mi></j:math>. Our numerical results reveal distinct discontinuities in all twist-3 GPDs except <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msub><l:mi>G</l:mi><l:mn>1</l:mn></l:msub></l:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:msub><n:mover accent="true"><n:mi>G</n:mi><n:mo stretchy="false">˜</n:mo></n:mover><n:mn>1</n:mn></n:msub></n:math>. By taking the forward limit, we obtain the twist-3 parton distribution function <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:msub><r:mi>g</r:mi><r:mi>T</r:mi></r:msub></r:math>, which encodes the transverse spin distribution of quarks. We also compare the kinetic orbital angular momentum and the spin-orbit correlations of quarks defined by the twist-2 and twist-3 GPDs, respectively. Published by the American Physical Society 2024