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We study the production, in Deep Inelastic Scattering at high energy, of aquark-gluon dijet induced by $t$-channel quark exchange with the target, whichgoes beyond the eikonal approximation. Throughout this study we follow theColor Glass Condensate approach, keep full dependence on the quark mass andconsider the target to be unpolarized. We focus on the correlation limit inwhich the produced jets fly almost back-to-back and find a factorizedexpression for the cross section, for both longitudinal and transverse photons,involving the unpolarized quark transverse momentum dependent distribution.Quark-gluon dijets can be distinguished from other types of dijets at least inthe heavy quark case, thanks to heavy flavor tagging. In that case, thedominant background is expected to come from the eikonal production of aquark-antiquark-gluon system. We propose experimental cuts to suppress thatbackground contribution, making the process of quark-gluon dijet production inDeep Inelastic Scattering a new method to probe the quark transverse momentumdependent distribution at the Electron Ion Collider.

Probing quark transverse momentum distributions in the Color Glass  Condensate: quark-gluon dijets in Deep Inelastic Scattering at  next-to-eikonal accuracy