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

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