Twist-three quark TMDs from back-to-back dijet production in next-to-eikonal DIS

We study back-to-back dijet production in deep inelastic scattering (DIS) at next-to-eikonal accuracy within the Color Glass Condensate framework, focusing on the quark-background contributions. We compute the quark-gluon and quark-antiquark production cross sections through next-to-leading power in the correlation limit for longitudinally and transversely polarized photons. In the quark-gluon channel, we derive both the kinematic corrections to the hard parts accompanying the twist-two quark distribution and the genuine twist-three contributions involving three-body quark-gluon-quark correlators. In the quark-antiquark channel, the interference of the eikonal amplitude with the double $t$-channel quark-exchange amplitudes probes three-body correlators with a different transverse arrangement of the fields. We express the results in terms of transverse momentum dependent (TMD) correlators and provide the corresponding hard coefficients. Our analysis extends the operator-level connection between the next-to-eikonal CGC framework and quark TMDs beyond leading power in the correlation limit.