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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 $\mathbfΔ$, as well as the anisotropy in the relative angle between $\mathbf{P}$ and $\mathbfΔ$. 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 $|\mathbf{P}| \gg |\mathbfΔ|$. We validate this approximation in its range of applicability and quantify its failure for $|\mathbf{P}| \lesssim |\mathbfΔ|$. We also predict significant target-dependent deviations from the correlation limit approximation for $|\mathbf{P}| > |\mathbfΔ|$ 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.