Twist-3 partonic distributions from lattice QCD

<jats:p>Twist-3 partonic distributions contain important information that characterizes nucleon’s structure. In this work, we show our lattice exploration of the twist-3 PDFs <jats:inline-formula><jats:alternatives><jats:tex-math>g_T(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, and <jats:inline-formula><jats:alternatives><jats:tex-math>h_L(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>. We also present our preliminary results on the twist-3 GPD <jats:inline-formula><jats:alternatives><jats:tex-math>\tilde{G}_2(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mover><mml:mi>G</mml:mi><mml:mo accent="true">̃</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>. We use the quasi-distribution approach to connect the lattice-extracted matrix elements, renormalized in the RI/MOM scheme, to light-cone distributions, applying the matching procedure that we developed in parallel. We also calculate the twist-2 counterparts of <jats:inline-formula><jats:alternatives><jats:tex-math>g_T(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mi>T</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:tex-math>h_L(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mi>L</mml:mi></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, i.e. <jats:inline-formula><jats:alternatives><jats:tex-math>g_1(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>g</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, and <jats:inline-formula><jats:alternatives><jats:tex-math>h_1(x)</jats:tex-math><mml:math xmlns:mml="http://www.w3. org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>h</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math></jats:alternatives></jats:inline-formula>, and test the Wandzura-Wilczek approximation. </jats:p>