Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Tensor case

The calculation of generalized parton distributions (GPDs) in lattice QCD was traditionally done by calculating matrix elements in the symmetric frame. Recent advancements have significantly reduced computational costs by calculating these matrix elements in the asymmetric frame, allowing us to choose the momentum transfer to be in either the initial or final states only. The theoretical methodology requires a new parametrization of the matrix element to obtain Lorentz-invariant amplitudes, which are then related to the GPDs. The formulation and implementation of this approach have already been established for the unpolarized and helicity GPDs. Building upon this idea, we extend this formulation to the four leading-twist quark transversity GPDs ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>H</a:mi> <a:mi>T</a:mi> </a:msub> </a:math> , <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>E</c:mi> <c:mi>T</c:mi> </c:msub> </c:math> , <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mover accent="true"> <e:mi>H</e:mi> <e:mo stretchy="false">˜</e:mo> </e:mover> <e:mi>T</e:mi> </e:msub> </e:math> , <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mover accent="true"> <i:mi>E</i:mi> <i:mo stretchy="false">˜</i:mo> </i:mover> <i:mi>T</i:mi> </i:msub> </i:math> ). We also present numerical results for zero skewness using an <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>N</m:mi> <m:mi>f</m:mi> </m:msub> <m:mo>=</m:mo> <m:mn>2</m:mn> <m:mo>+</m:mo> <m:mn>1</m:mn> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:math> ensemble of twisted mass fermions with a clover improvement. The light quark masses employed in these calculations correspond to a pion mass of about 260 MeV. Furthermore, we include a comparison between the symmetric and asymmetric frame calculations to demonstrate frame independence of the Lorentz-invariant amplitudes. Analysis of the matrix elements in the asymmetric frame is performed at several values of the momentum transfer squared, <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mo>−</o:mo> <o:mi>t</o:mi> </o:math> , ranging from <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mrow> <q:mn>0.17</q:mn> </q:mrow> </q:math> to <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mn>2.29</s:mn> <s:mtext> </s:mtext> <s:mtext> </s:mtext> <s:msup> <s:mi>GeV</s:mi> <s:mn>2</s:mn> </s:msup> </s:math> .