Mixed NNLO QCD x electroweak corrections of O(N_f \alpha_s \alpha) to single-W/Z production at the LHC

Understand

First results on the radiative corrections of order O(N_f\alpha_s\alpha) are presented for the off-shell production of W or Z bosons at the LHC, where N_f is the number of fermion flavours.

• These corrections comprise all diagrams at O(\alpha_s\alpha) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD x electroweak type, and are the ones that concern the issue of mass renormalization of the W and Z resonances.
• The occurring irreducible two-loop diagrams, which involve only self-energy insertions, are calculated with current standard techniques, and explicit analytical results on the electroweak gauge-boson self-energies at O(\alpha_s\alpha) are given.
• Moreover, the generalization of the complex-mass scheme for a gauge-invariant treatment of the W/Z resonances is described for the order O(\alpha_s\alpha).