Theoretically Predicted Production Cross Section of Single Vector Boson

The cross sections of $Z$ and $W$ boson and their ratios is experimentally measured at the ATLAS and CMS detector at the Large Hadron Collider~(LHC) in proton-proton collision at various center of mass energies. Theoretically predicted cross section of the $W$ and $Z$ boson production cross section in a proton-proton collision at $\sqrt{s}=13~TeV$ and $14~TeV$ are presented in this thesis. The vector boson production cross section measurement at hadron collision provides a deep understanding of quantum chromodynamics (QCD) and electroweak (EW) processes. The production of $W$ and $Z$ bosons are best examples of hard scattering processes at Large Hadron Collider. Theoretical predictions in perturbative chromodynamics are available at next-to-next-to-leading order~(NNLO). Theoretically predicted production cross section and cross section ratios of $W$ and $Z$ vector bosons are compared with the measured results at various center of mass energies. Kinematics of these vector bosons and corresponding leptons are also presented.