Next-to-leading order forward hadron production in the small-$x$ regime: rapidity factorization

Abstract: Single inclusive hadron production at forward rapidity in high energy p+A collisions is an important probe of the high gluon density regime of QCD and the associated small-$x$ formalism. We revisit an earlier one-loop calculation to illustrate the significance of the "rapidity factorization" approach in this regime. Such factorization separates the very small-$x$ unintegrated gluon density evolution and leads to a new correction term to the physical cross section at one-loop level. Importantly, this rapidity factorization formalism remedies the previous unphysical negative next-to-leading order contribution to the cross section. It is much more stable with respect to "rapidity" variation when compared to the leading-order calculation and provides improved agreement between theory and experiment in the forward rapidity region.