Multi-gluon 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 $\mathbf{P}$ and recoil momentum $\mathbf{\Delta}$, as well as the anisotropy in the relative angle between $\mathbf{P}$ and $\mathbf{\Delta}$. We use the nonlinear Gaussian approximation to compute multiparticle correlators for general small $x$ kinematics, employing running coupling Balitsky-Kovchegov evolution to determine the dipole amplitude at small $x$. Our results cover a much larger kinematic range than accessible in previous computations performed in the correlation limit approximation, where it is assumed that $|\mathbf{P}| \gg |\mathbf{\Delta}|$. We validate this approximation in its range of applicability and quantify its failure for $|\mathbf{P}| \lesssim |\mathbf{\Delta}|$. We also predict significant target-dependent deviations from the correlation limit approximation for $|\mathbf{P}| > |\mathbf{\Delta}|$ and $|\mathbf{P}| \lesssim Q_s$, which offers a straightforward test of gluon saturation and access to multi-gluon distributions at a future electron ion collider.