Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Axial-vector case

Abstract

Recently, we made significant advancements in improving the computational efficiency of lattice QCD calculations for generalized parton distributions (GPDs). This progress was achieved by adopting calculations of matrix elements in asymmetric frames, deviating from the computationally-expensive symmetric frame typically used, and allowing freedom in the choice for the distribution of the momentum transfer between the initial and final states. A crucial aspect of this approach involves the adoption of a Lorentz covariant parametrization for the matrix elements, introducing Lorentz-invariant amplitudes. This approach also allows us to propose an alternative definition of quasi-GPDs, ensuring frame independence and potentially reduce power corrections in matching to light cone GPDs. In our previous work, we presented lattice QCD results for twist-2 unpolarized GPDs (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>H</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>E</c:mi></c:math>) of quarks obtained from calculations performed in asymmetric frames at zero skewness. Building upon this work, we now introduce a novel Lorentz covariant parametrization for the axial-vector matrix elements. We employ this parametrization to compute the axial-vector GPD <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mover accent="true"><e:mi>H</e:mi><e:mo stretchy="false">˜</e:mo></e:mover></e:math> at zero skewness, using an <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:mo>+</i:mo><i:mn>1</i:mn></i:math> ensemble of twisted mass fermions with clover improvement. The light-quark masses employed in our calculations correspond to a pion mass of approximately 260 MeV. Published by the American Physical Society 2024