Implementing the exact kinematical constraint in the saturation formalism

TL;DR

This paper improves the saturation formalism by implementing exact kinematical constraints, leading to positive NLO corrections, extended applicability to higher transverse momenta, and better agreement with experimental data.

Contribution

The authors introduce an exact kinematical constraint into the saturation formalism, resulting in new positive NLO terms and extending the formalism's valid kinematic range.

Findings

Two positive NLO correction terms are identified.

The saturation formalism's applicable kinematic window is extended.

Excellent agreement with LHC and RHIC data is achieved.

Abstract

We revisit the issue of the large negative next-to-leading order (NLO) cross section for single inclusive hadron production in $pA$ 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 $k_\perp$ 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 $k_\perp$ window, where the exact matching between the saturation formalism (in the asymptotic $k_\perp$ 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.