QCD corrections to the Drell-Yan process for the Large Hadron Collider (LHC): Vertex functions and gluon bremsstrahlung

With an eye to future experiments at the Large Hadron Collider (LHC), $ mathcal{O}left( {alpha alpha _s } right) $ mathcal{O}left( {alpha alpha _s } right) QCD corrections to the Drell-Yan process are calculated for vertex functions and gluon bremsstrahlung. Use is made of fully differential cross sections, so that the result obtained in the present study can readily be applied in analyzing experimental data (in correcting data from future experiments at LHC). It is shown both analytically and numerically that the results are independent of unphysical parameters, including the parameter separating the regions of soft and hard gluons and the quark mass. A numerical analysis of radiative effects was performed by means of the FORTRAN code READY with allowance for the experimental cuts used at the Compact Muon Solenoid (CMS) detector.