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A<sc>bstract</sc> In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD),$$ \overset{\sim }{H}\left(x,\xi, t\right) $$ $\tilde{H}\left(x,\xi ,t\right)$, at zero skewness,ξ, with multiple values of the momentum transfer,t. Our analysis employs the short-distance factorization framework on ratio-scheme renormalized quasi-GPD matrix elements. The calculations are based on anN_f= 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing ofa= 0.093 fm, and a pion mass ofm_π= 260 MeV. We consider both the iso-vector and iso-scalar cases, utilizing next-to-leading-order perturbative matching while omitting the disconnected contributions and gluon mixing in the iso-scalar case. For the first time, we determine the Mellin moments of$$ \overset{\sim }{H} $$ $\tilde{H}$up to the fifth order. From these moments, we discuss the quark helicity and orbital angular momentum contributions to the nucleon spin, as well as the spin-orbit correlations of the quarks. Additionally, we perform a Fourier transform over the momentum transfer, which allows us to explore the spin structure in the impact-parameter space. 

Generalized parton distributions (GPDs) are key quantities for the description of a hadron’s three-dimensional structure. They are the current focus of all areas of hadronic physics—phenomenological, experimental and theoretical, including lattice QCD. Synergies between these areas are desirable and essential to achieve precise quantification and understanding of the structure of, particularly, nucleons, as the basic ingredients of matter. In this paper, we investigate, for the first time, the numerical implementation of the pseudodistribution approach for the extraction of zero-skewness GPDs for unpolarized quarks. Pseudodistributions are Euclidean parton correlators computable in lattice QCD that can be perturbatively matched to the light-cone parton distributions of interest. Although they are closely related to the quasidistributions and come from the same lattice-extracted matrix elements, they are, however, subject to different systematic effects. We use the data previously utilized for quasi-GPDs and extend it with other momentum transfers and nucleon boosts, in particular a higher one ( $P_3=1.67\mathrm{GeV}$) with eightfold larger statistics than the largest one used for quasidistributions ( $P_3=1.25\mathrm{GeV}$). We renormalize the matrix elements with a ratio scheme and match the resulting Ioffe time distributions to the light cone in coordinate space. The matched distributions are then used to reconstruct the $x$dependence with a fitting . We investigate some systematic effects related to this procedure, and we also compare the results with the ones obtained in the framework of quasi-GPDs. Our final results involve the invariant four-momentum transfer squared ( $-t$) dependence of the flavor nonsinglet ( $u-d$) $H$and $E$GPDs. Published by the American Physical Society2024