Mixed NNLO QCD×electroweak corrections of $$ \mathcal{O} $$(Nfαsα) to single-W/Z production at the LHC

Abstract

First results on the radiative corrections of order $$ \mathcal{O} $$ O (Nfαsα) are presented for the off-shell production of W or Z bosons at the LHC, where Nf is the number of fermion flavours. These corrections comprise all diagrams at $$ \mathcal{O} $$ O (αsα) with closed fermion loops, form a gauge-invariant part of the next-to-next-to-leading-order corrections of mixed QCD×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 $$ \mathcal{O} $$ O (αsα) 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 $$ \mathcal{O} $$ O (αsα). While the corrections, which are implemented in the Monte Carlo program Rady, are negligible for observables that are dominated by resonant W/Z bosons, they affect invariant-mass distributions at the level of up to 2% for invariant masses of ≳ 500 GeV and are, thus, phenomenologically relevant. The impact on transverse-momentum distributions is similar, taking into account that leading-order predictions to those distributions underestimate the spectrum.

Mixed EW-QCD two-loop amplitudes for $$ q\overline{q}\to {\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ and γ5 scheme independence of multi-loop corrections

“…Due to the size of the next-to-leading order electroweak corrections, it has long been of interest to calculate the mixed EW-QCD corrections of relative order αα s as well. Indeed, many partial results in this direction have been put forth over the last decade [20][21][22][23][24][25][26][27], but a complete calculation in the regime of large lepton pair invariant mass is not available yet.…”

“…The most important two-loop corrections we omit are those which involve a closed fermion loop; these contributions arise due to electroweak gauge boson self-energy insertions and are already known, see e.g. [26,75]. We also do not consider bb initial states, which lead to double W exchange diagrams involving the top quark; in other words, we restrict ourselves to four light flavors in the initial state.…”

The qT and ∆ϕ spectra in W and Z production at the LHC at N3LL′+N2LO

“…Similarly, the transverse momentum spectrum of the gauge boson at finite q T is known also up to O(α 3 s ) [39][40][41][42][43][44][45][46][47][48][49][50]. In addition to the QCD corrections higher-order electro-weak (EW) effects [51][52][53][54][55][56][57][58][59][60][61][62] and QCD-EW mixed corrections emerging at two-loop order [63][64][65][66][67][68][69][70][71][72][73] are of importance at this level of accuracy as well.…”

Estimating the impact of mixed QCD-electroweak corrections on the $W$-mass determination at the LHC

“…The computation of the remaining mixed QCD-EW corrections to the Z and W production processes was recently completed [34][35][36][37][38][39][40][41]. The goal of this note is to estimate how these corrections affect the value of the W mass extracted from the transverse momentum distribution of a charged lepton.…”