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

TL;DR

This paper advances the theoretical understanding of dijet production in deep inelastic scattering at small x by incorporating next-to-eikonal and twist-3 gluon TMD effects, refining the TMD factorization framework.

Contribution

It introduces a next-to-eikonal expansion in the back-to-back dijet limit, explicitly including twist-3 gluon TMDs and their correlators, extending previous high-energy limit results.

Findings

Identified twist-2 phase contributions in gluon TMDs.

Derived twist-3 unpolarized gluon TMDs and three-gluon correlators.

Reformulated results within the TMD factorization framework.

Abstract

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.