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A<sc>bstract</sc> In this work, we report a lattice calculation ofx-dependent valence pion generalized parton distributions (GPDs) at zero skewness with multiple values of the momentum transfer −t. The calculations are based on anN_f= 2 + 1 gauge ensemble of highly improved staggered quarks with Wilson-Clover valence fermion. The lattice spacing is 0.04 fm, and the pion valence mass is tuned to be 300 MeV. We determine the Lorentz-invariant amplitudes of the quasi-GPD matrix elements for both symmetric and asymmetric momenta transfers with similar values and show the equivalence of both frames. Then, focusing on the asymmetric frame, we utilize a hybrid scheme to renormalize the quasi-GPD matrix elements obtained from the lattice calculations. After the Fourier transforms, the quasi-GPDs are then matched to the light-cone GPDs within the framework of large momentum effective theory with improved matching, including the next-to-next-to-leading order perturbative corrections, and leading renormalon and renormalization group resummations. We also present the 3-dimensional image of the pion in impact-parameter space through the Fourier transform of the momentum transfer −t. 

We report the first lattice QCD computation of pion and kaon electromagnetic form factors, $F_M\left(Q^2\right)$, at large momentum transfer up to 10 and $28{\mathrm{GeV}}^2$, respectively. Utilizing physical masses and two fine lattices, we achieve good agreement with JLab experimental results at $Q^2\lesssim 4{\mathrm{GeV}}^2$. For $Q^2\gtrsim 4{\mathrm{GeV}}^2$, our results provide QCD benchmarks for the forthcoming experiments at JLab 12 GeV and future electron-ion colliders. We also test the QCD collinear factorization framework utilizing our high- $Q^2$form factors at next-to-next-to-leading order in perturbation theory, which relates the form factors to the leading Fock-state meson distribution amplitudes. Comparisons with independent lattice QCD calculations using the same framework demonstrate, within estimated uncertainties, the universality of these nonperturbative quantities. Published by the American Physical Society2024