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The unique forward LHCb acceptance opens the possibility for performingprecision Standard Model (SM) processes in a kinematical regime beyond thereach of both ATLAS and CMS experiments. In this article we discuss thefeasibility of performing $W^{\pm}j$ measurements with 14 TeV LHCb data, andfind that the leptonic asymmetry at high pseudorapidity, with appropriate cutson the associated jet, can provide a factor of three reduction on the $d$ quarkPDF uncertainty in a region of Bjorken $x > 0.5$.

The leptonic $W^{\pm}$ boson asymmetry in association with jets at LHCb, and PDF constraints at large-$x$