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We establish an approach to analyze the free hadron and transition (nonperturbative) regions of near- side energy-energy correlators (EECs) based on dihadron fragmentation functions (DiFFs). We introduce a (nonperturbative) function we call the “EEC DiFF” and explicitly show that expanding it for large relative transverse momentum between the two hadrons gives the O(alphaS) expression for the “EEC jet” function used in the quark-gluon (perturbative) region. This connection indicates that a formal theoretical matching will be able to bridge the free-hadron region, transition, and quark-gluon regions and allow all of them to be analyzed simultaneously. We further derive a result valid for near- side EECs in the free hadron and transition regions of e+e- annihilation in terms of the EEC DiFF. Using a simple model for the function, we perform the first fit within the dihadron framework to experimental data in this regime. We find reasonable agreement with the measurements and reproduce the salient features of near-side EECs in the free hadron and transition regions. 

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 ( $H_T$, $E_T$, ${\tilde{H}}_T$, ${\tilde{E}}_T$). We also present numerical results for zero skewness using an $N_f=2+1+1$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, $-t$, ranging from $0.17$to $2.29{\mathrm{GeV}}^2$. 

We extend the formalism of asymmetric frames of reference for generalized parton distributions (GPDs) to the case of nonzero skewness, i.e., including longitudinal momentum transfer. The framework, based on Lorentz-invariant amplitudes and previously developed and numerically implemented for unpolarized, helicity and transversity GPDs at zero skewness, gives efficient access to a broad range of kinematics, making full mapping of GPDs from the lattice realistic. The general-skewness formalism is tested using lattice data with both transverse and longitudinal or only longitudinal momentum transfer, the latter being a special case with a reduced number of independent amplitudes. We extract the amplitudes in coordinate space and express the GPDs $H$and $E$in terms of these amplitudes. This is followed by reconstruction of quasidistributions and their matching to the light cone. We further identify and discuss the principal challenges for nonzero skewness GPDs. 

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 

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.