Multigluon Correlations and Evidence of Saturation from Dijet Measurements at an Electron-Ion Collider

We study inclusive and diffractive dijet production in electron-proton and electron-nucleus collisions within the color glass condensate effective field theory. We compute dijet cross sections differentially in both mean dijet transverse momentum P and recoil momentum Delta, as well as the anisotropy in the relative angle between P and Delta. Our results cover a much larger kinematic range than accessible in previous computations performed in the correlation limit approximation, where it is assumed that vertical bar P vertical bar >>vertical bar Delta vertical bar. We validate this approximation in its range of applicability and quantify its failure for vertical bar P vertical bar less than or similar to vertical bar Delta vertical bar. We also predict significant target-dependent deviations from the correlation limit approximation for vertical bar P vertical bar>vertical bar Delta vertical bar and vertical bar P vertical bar less than or similar to Q(s), which offers a straightforward test of gluon saturation and access to multigluon distributions at a future Electron-lon Collider.