The importance of kinematic twists and genuine saturation effects in dijet production at the Electron-Ion Collider

We compute the differential yield for quark anti-quark dijet production in high-energy electron-proton and electron-nucleus collisions at small x as a function of the relative momentum P_⊥ and momentum imbalance k_⊥ of the dijet system for different photon virtualities Q², and study the elliptic and quadrangular anisotropies in the relative angle between P_⊥ and k_⊥. We review and extend the analysis in [1], which compared the results of the Color Glass Condensate (CGC) with those obtained using the transverse momentum dependent (TMD) framework. In particular, we include in our comparison the improved TMD (ITMD) framework, which resums kinematic power corrections of the ratio k_⊥ over the hard scale Q_⊥. By comparing ITMD and CGC results we are able to isolate genuine higher saturation contributions in the ratio Q_s/Q_⊥ which are resummed only in the CGC. These saturation contributions are in addition to those in the Weizsäcker-Williams gluon TMD that appear in powers of Q_s/k_⊥. We provide numerical estimates of these contributions for inclusive dijet production at the future Electron-Ion Collider, and identify kinematic windows where they can become relevant in the measurement of dijet and dihadron azimuthal correlations. We argue that such measurements will allow the detailed experimental study of both kinematic power corrections and genuine gluon saturation effects.