Approximate N$^2$LO and N$^3$LO QCD Predictions for $tW$ Production

Abstract

We present high-precision predictions for associated $tW$ production at the LHC that incorporate the next-to-next-to-leading order hard and soft functions as well as the complete next-to-next-to-next-to-leading order scale-dependent terms derived from the corresponding anomalous dimensions. These higher-order corrections, which dominate the full perturbative results, increase the next-to-leading order cross section by more than 10\%. Based on the comparison with ATLAS and CMS measurements, we directly extract the Cabibbo-Kobayashi-Maskawa matrix element $|V_{tb}|=0.99\pm 0.03({\rm expt})\pm 0.03({\rm theor})$ without assuming unitarity, achieving a precision comparable with the current world average value.