  We present the first fully consistent NLO calculation of the single-inclusive
forward hadron production in proton-nucleus (pA) collisions under the color
glass condensate (CGC) framework. In the dilute-dense limit, the NLO
cross-section can be written as a convolution of the NLO impact factor, NLO
parton distribution function (PDF), NLO fragmentation function (FF) and
dipole-target scattering amplitude which satisfies the NLO small-$x$
Balitsky-Kovchegov (BK) evolution. We demonstrate that, without the NLO
corrections to the impact factor, we obtain a significant Cronin peak when the
dipole amplitude satisfies the NLO BK equation. This would contradict the
recent LHCb results. However, the Cronin peak becomes suppressed when the NLO
correction to the impact factor is included. This is the main result of this
work. The dependence on resummation schemes for the NLO BK evolution will also
be discussed.
