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Threshold enhanced perturbative QCD corrections to rapidity distributions of$Z$ and $W^\pm$ bosons at hadron colliders are presented using the Sudakovresummed cross sections at N${}^3$LO level. We have used renormalisation groupinvariance and the mass factorisation theorem that these hard scattering crosssections satisfy to construct the QCD amplitudes. We show that these higherorder threshold QCD corrections stabilise the theoretical predictions forvector boson production at the LHC under variations of both renormalisation andfactorisation scales.

Threshold corrections to rapidity distributions of Z and W^\pm bosons beyond N^2 LO at hadron colliders