Implementing the exact kinematical constraint in the saturation formalism

We revisit the issue of the large negative next-to-leading-order (NLO) cross section for single inclusive hadron production in p A collisions in the saturation formalism. By implementing the exact kinematical constraint in the modified dipole splitting functions, two additional positive NLO correction terms are obtained. In the asymptotic large-k_⊥ limit, we analytically show that these two terms become as large as the negative NLO contributions found in our previous calculation. Furthermore, the numerical results demonstrate that the applicable regime of the saturation formalism can be extended to a larger k_⊥ window, where the exact matching between the saturation formalism (in the asymptotic k_⊥ regime) and the collinear factorization calculations will have to be performed separately. In addition, after significantly improving the numerical accuracy of the NLO correction, we obtain excellent agreement with the LHC and RHIC data for forward hadron productions.