Weak boson emission in hadron collider processes

The $\mathcal{O}(\alpha )$ virtual weak radiative corrections to many hadron collider processes are known to become large and negative at high energies, due to the appearance of Sudakov-like logarithms. At the same order in perturbation theory, weak boson emission diagrams contribute. Since the $W$ and $Z$ bosons are massive, the $\mathcal{O}(\alpha )$ virtual weak radiative corrections and the contributions from weak boson emission are separately finite. Thus, unlike in QED or QCD calculations, there is no technical reason for including gauge boson emission diagrams in calculations of electroweak radiative corrections. In most calculations of the $\mathcal{O}(\alpha )$ electroweak radiative corrections, weak boson emission diagrams are therefore not taken into account. Another reason for not including these diagrams is that they lead to final states which differ from that of the original process. However, in experiment, one usually considers partially inclusive final states. Weak boson emission diagrams thus should be included in calculations of electroweak radiative corrections. In this paper, I examine the role of weak boson emission in those processes at the Fermilab Tevatron and the CERN LHC for which the one-loop electroweak radiative corrections are known to become large at high energies (inclusive jet, isolated photon, $Z+1$ jet, Drell-Yan, di-boson, $\overline{t}t$, and single top production). In general, I find that the cross section for weak boson emission is substantial at high energies and that weak boson emission and the $\mathcal{O}(\alpha )$ virtual weak radiative corrections partially cancel.