Final states with a vector boson and a hadronic jet allow one to infer the Born-level kinematics of the underlying hard scattering process, thereby probing the partonic structure of the colliding protons. At forward rapidities, the parton collisions are highly asymmetric and resolve the parton distributions at very large or very small momentum fractions, where they are less well constrained by other processes. Using theory predictions accurate to next-to-next-to-leading order (NNLO) in QCD for both $mathrm{W}^{pm}$ and $mathrm{Z}$ production in association with a jet at large rapidities at the LHC, we perform a detailed phenomenological analysis of recent LHC measurements. The increased theory precision allows us to clearly identify specific kinematical regions where the description of the data is insufficient. By constructing ratios and asymmetries of these cross sections, we aim to identify possible origins of the deviations, and highlight the potential impact of the data on improved determinations of parton distributions.
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