Next-to-leading order QCD corrections to W+Z and W-Z production via vector-boson fusion

TL;DR

This paper delivers a complete calculation of next-to-leading order QCD corrections to electroweak W±Z production via vector-boson fusion at the LHC, including all relevant t-channel diagrams and leptonic decays. The authors implement a fully flexible parton-level Monte Carlo (vbfnlo) and use Catani–Seymour dipole subtraction, with advanced tensor-reduction techniques to handle virtual contributions, validated against independent generators. They show that NLO corrections yield cross sections with small K-factors near unity and reduce scale uncertainties to about 2%, while highlighting that next-to-leading-order distributions are sensitive to the chosen factorization scale and are better approximated by a dynamical scale μ0=Q. The results provide precise, experimentally relevant predictions for VBF WZ processes, aiding Higgs studies and beyond-Standard-Model investigations at the LHC.

Abstract

We present the calculation of the next-to-leading order QCD corrections to electroweak p p -> e+ nu_e mu+ mu- jj and p p -> e- nubar_e mu+ mu- jj production at the CERN LHC in the form of a fully flexible parton-level Monte Carlo program. The QCD corrections to the total cross sections are modest, changing the leading-order results by less than 10%. At the Born level, the shape of kinematic distributions can depend significantly on the choice of factorization scale. This theoretical uncertainty is strongly reduced by the inclusion of the next-to-leading order QCD corrections.

Figures (6)

• Figure 1: The six Feynman-graph topologies contributing to the Born process $us\,\hbox{$\rightarrow$}\, ds\,e^+\nu_e \,\mu^+\mu^-$. Not shown are the diagrams analogous to (a), (b), (c), (d), and (f), with $W^+$ and/or $V$ emission off the lower quark line and $t$-channel $W$ exchange (this one is illustrated in Fig. \ref{['fig:t-channel-W']}). $V$ denotes a $Z$ boson or a photon.
• Figure 2: Feynman-graph topology contributing to the Born process $us\,\hbox{$\rightarrow$}\, ds\,e^+\nu_e \,\mu^+\mu^-$ via $W$ exchange in the $t$-channel. The $s$-quark on the lower quark line is transformed into an up-type quark ($i=u,c,t$) by the attached weak bosons.
• Figure 3: Dependence of the total $pp\,\hbox{$\rightarrow$}\, e^+\nu_e \,\mu^+\mu^- jj$ cross section at the LHC on the factorization and renormalization scales for two different choices of $\mu_0$. The NLO curves show $\sigma_{\rm cuts}^{\rm NLO}$ as a function of the scale parameter $\xi$ for three different cases: $\mu_R=\mu_F=\xi\mu_0$ (solid red), $\mu_F=\xi\mu_0$ and $\mu_R=\mu_0$ (dot-dashed blue), $\mu_R=\xi\mu_0$ and $\mu_F=\mu_0$ (dashed green). The LO cross sections depend only on $\mu_F$ (dotted black).
• Figure 4: Transverse-momentum distribution of the tagging jet with the lowest $p_T$ in EW $e^+\nu_e \,\mu^+\mu^- jj$ production at the LHC for two different choices of $\mu_0$ [panels (a) and (b)]. Panel (c) shows the dynamical $K$ factors defined in Eq. (\ref{['eq:kfac']}) for $\mu_0=m_V$ (dot-dashed blue line) and $\mu_0=Q$ (solid black line). In panel (d) we have plotted the ratio $[d\sigma/dp_{T,{\rm tag}}^{\rm min}(\mu_0=m_V)/[d\sigma/dp_{T,{\rm tag}}^{\rm min}(\mu_0=Q)]$ at LO (dashed red line) and NLO (solid red line).
• Figure 5: Invariant-mass distribution of the tagging jets in EW $e^+\nu_e \,\mu^+\mu^- jj$ production at the LHC for two different choices of $\mu_0$ [panels (a) and (b)]. Panels (c) and (d) show the dynamical $K$ factors defined in Eq. (\ref{['eq:kfac']}) for $\mu_0=m_V$ (blue line) and $\mu_0=Q$ (black line).