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Saturation in inclusive production beyond leading logarithm accuracy

We review recent progress on the calculations on the inclusive forward hadron production within the saturation formalism. After introducing the concept of perturbative parton saturation and nonlinear evolution we discuss the formalism for the forward hadron production at high energy in the leading and next-to-leading order. Numerical results are presented and compared with the experimental data on forward hadron production in $dA$ and $pA$. We discuss the problem of the negativity of the NLO cross section at high transverse momenta, study its origin in detail and present possible improvements which include the corrected kinematics and the suitable choice of the rapidity cutoff.