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

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