Saturation Correction to Projectile -- some ${\cal{O}}(g^5)$ results within LCPT

We revisited the first saturation correction to projectile in nucleus-nucleus collisions \cite{Chirilli:2015tea} within diagrammatic light cone perturbation theory (LCPT). To get an analytic expression for the saturation correction in projectile authors in \cite{Chirilli:2015tea} calculated complete ${\cal{O}}(g^3)$ amplitudes, where the main results are given in transverse coordinate space. However to find the complete first saturation correction in the projectile, one needs to calculate both ${\cal{O}}(g^3)$ and ${\cal{O}}(g^5)$ gluon production amplitudes. We here present a detailed calculation of a sample graph at ${\cal{O}}(g^5)$ in diagrammatic light cone perturbation theory.

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