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We investigate the transverse energy-energy correlators (TEEC) in thesmall-$x$ regime at the upcoming Electron-Ion Collider (EIC). Focusing on theback-to-back production of electron-hadron pairs in both $ep$ and $eA$collisions, we establish a factorization theorem given in terms of the hardfunction, quark distributions, soft functions, and TEEC jet functions, wherethe gluon saturation effect is incorporated. Numerical results for TEEC in both$ep$ and $eA$ collisions are presented, together with the nuclear modificationfactor $R_A$. Our analysis reveals that TEEC observables in deep inelasticscattering provide a valuable approach for probing gluon saturation phenomena.Our findings underscore the significance of measuring TEEC at the EIC,emphasizing its efficacy in advancing our understanding of gluon saturation andnuclear modifications in high-energy collisions.

Transverse Energy-Energy Correlators in the Color-Glass Condensate at the Electron-Ion Collider