Back-to-back dijet production in DIS at next-to-eikonal accuracy and twist-3 gluon TMDs

We consider dijet production in deep inelastic scattering at small $x$, on a purely gluonic unpolarized target. Starting from earlier results obtained at next-to-eikonal accuracy in the high-energy limit, we perform the expansion in the back-to-back dijet limit, at next-to-leading power accuracy. We rewrite our results in the language of transverse-momentum-dependent (TMD) factorization, in terms of twist-2 and twist-3 TMD gluon distributions (gluon TMDs). Among the next-to-eikonal corrections, we find in particular twist-2 contributions corresponding to the $x$ dependent phase of the twist-2 gluon TMDs. We also find two types of twist-3 unpolarized gluon TMDs, as well as correlators of three gluon field strength tensors.