Complete Next-to-Leading Order Calculation of Single Inclusive $\pi^0$ Production in Forward Proton-Nucleus Collisions

We present the first fully consistent calculation of inclusive $\pi^0$ production at forward rapidities at next-to-leading order (NLO) accuracy in proton-lead collisions at $\sqrt{s}=8.16$ TeV within the Color Glass Condensate approach. The center-of-mass energy dependence is determined by the Balitsky-Kovchegov equation with the initial condition constrained at NLO accuracy by the proton structure function measurements. We find that the LHCb data further constrain this non-perturbative input, and that both the NLO corrections to the evolution equation and to the impact factor have significant effects on the nuclear modification factor $R_{p\mathrm{Pb}}$. The complete NLO calculation is shown to be in qualitative agreement with the LHCb data, and the predictions are found to be sensitive to the details of the applied deep inelastic scattering (DIS) fit. These results demonstrate the need to perform global analyses of DIS and LHC data in order to probe gluon saturation phenomena at precision level at very small momentum fraction $x$.