  We analyze the effects of next-to-eikonal corrections on dijet production in
Deep Inelastic Scattering off nuclear targets in the framework of the Color
Glass Condensate. They require the knowledge of correlators of fields in the
target beyond those computed in the standard McLerran-Venugopalan model,
specifically those between transverse and boost-enhanced components, and of the
recoil of the fields. We neglect the latter, while for the former we develop a
linear model valid for large nuclei. We considered the unpolarized cross
sections for dijet production in the approximation of a homogenous dilute
nucleus, obtaining simple analytic expressions for the cross sections at
nex-to-eikonal accuracy, valid in the limit of total dijet momentum and dijet
momentum imbalance larger than the saturation scale of the nucleus. We perform
a numerical study of the results at energies of the Electron Ion Collider,
finding $\mathcal{O}(10\%)$ effects in the cross sections at large total
momentum. We also analyze the azimuthal asymmetries between total momentum and
imbalance, finding that non-eikonal corrections induce odd azimuthal harmonics
for the situation of jets with equal momentum fractions from the virtual
photon, where they are absent in the eikonal approximation. Finally, in the
eikonal approximation we have compared the results of our analytic expansion
valid in the dilute limit of the target, and the full Color Glass Condensate
results in the McLerran-Venugopalan model and their correlation limit. Our
analytic expressions match the correlation limit ones in the region where both
should be simultaneously valid and reproduce very well the full Color Glass
Condensate results in its validity region.
