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We compute next to eikonal (NE) and next to next to eikonal (NNE) correctionsto the Lipatov vertex due to a finite target thickness. These arise fromelectric field insertions into the eikonal Wilson lines. We then derive a$k_T$-factorization formula for single inclusive gluon production at NNEaccuracy and find that nuclear effects are absent. We also analyze NNEcorrections to two-gluon production where some of the contributions are foundto exhibit corrections proportional to $A^{2/3}$.

Particle production in high-energy collisions beyond the shockwave limit