Abstract
We consider the {{mathcal {O}}(alpha alpha _s)},corrections to single on-shell gauge boson production at hadron colliders. We concentrate on the contribution of all the subprocesses where the gauge boson is accompanied by the emission of two additional real partons and we evaluate the corresponding total cross sections. The latter are divergent quantities, because of soft and collinear emissions, and are expressed as Laurent series in the dimensional regularization parameter. The total cross sections are evaluated by means of reverse unitarity, i.e. expressing the phase-space integrals in terms of two-loop forward box integrals with cuts on the final-state particles. The results are reduced to a combination of master integrals, which eventually are evaluated in terms of generalized polylogarithms. The presence of internal massive lines in the Feynman diagrams, due to the exchange of electroweak gauge bosons, causes the appearance of 14 master integrals which were not previously known in the literature and have been evaluated via differential equations.
Highlights
In specific cases like the Weinberg mixing angle or the W boson mass measurements, with a final precision goal in the 1–2 ×10−4 range, all the elements entering the theoretical predictions need to be scrutinized
The master integrals (MIs) necessary to compute the total cross sections of processes (7)–(14) involve at least one massive line and possibly an additional one from those diagrams where a photon is emitted off a W leg
In this work we presented the analytical calculation of the total cross sections of all the partonic subprocesses that contribute at O(ααs) to inclusive single on-shell gauge boson production, with two additional partons in the final state
Summary
In specific cases like the Weinberg mixing angle or the W boson mass measurements, with a final precision goal in the 1–2 ×10−4 range, all the elements entering the theoretical predictions need to be scrutinized. The respective contributions to the total cross section for on-shell gauge boson production are obtained by computing the two-loop virtual corrections to the lowest-order amplitude or by integrating the relevant squared matrix elements over the full phase space of the additional partons. In the latter cases we adopt a technique called reverse unitarity, developed for the evaluation of the total cross section for Higgs production [64,65,66]. The complete set of cross sections and of all the MIs is given in an ancillary file that we include in the arXiv submission
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