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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>x</a:mi></a:math>, 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>x</c:mi></c:math> 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.