  In this work, we report a lattice calculation of $x$-dependent valence pion
generalized parton distributions (GPDs) at zero skewness with multiple values
of the momentum transfer $-t$. The calculations are based on an $N_f=2+1$ 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 $-t$.
