Single-Inclusive Particle Production from $pA$ Collision at Next-to-Leading Order

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.