NLO QCD corrections to W+W- gamma and Z Z gamma production with leptonic decays

TL;DR

This work provides a complete ${\cal O}(\alpha_s)$ QCD treatment of $pp/p\bar p \to W^+W^-\gamma$ and $pp/p\bar p \to ZZ\gamma$ with leptonic decays, implemented in a flexible $VBFNLO$-based Monte Carlo framework. The calculation combines real-emission and virtual corrections using Catani-Seymour subtraction, employs Frixione photon isolation to avoid fragmentation contributions, and applies Denner-Dittmaier pentagon reduction to maintain numerical stability. Numerically, NLO corrections are sizeable and reshape key distributions, with $W^+W^-\gamma$ K-factors around $1.7$ and $ZZ\gamma$ around $1.36$, while LO scale variations substantially underestimate the true uncertainties. The results demonstrate the necessity of fully exclusive NLO predictions for accurate LHC phenomenology of multi-boson final states and quartic gauge couplings, and the authors plan to integrate these processes into a public release of $VBFNLO$.

Abstract

The computation of the NLO QCD corrections to the cross sections for W+W- gamma and ZZgamma production in hadronic collisions is presented. We consider the case of a real photon in the final state, but include full leptonic decays of the W and Z bosons. Numerical results for the LHC and the Tevatron are obtained through a fully flexible parton level Monte Carlo based on the structure of the VBFNLO program, allowing an easy implementation of arbitrary cuts and distributions. We show the dependence on scale variations of the integrated cross sections and provide evidence that NLO QCD corrections strongly modify the LO predictions for observables at the LHC both in magnitude and in shape.

Figures (5)

• Figure 1: Examples of the three topologies of Feynman diagrams contributing to the process $pp\to$$W^+W^-\gamma$ + X at tree-level.
• Figure 2: Left:Scale dependence of the total LHC cross section for $p p \to W^+W^-\gamma+X \to \ell^+ \ell^- \gamma +=\hbox{$p$}p \hbox{/} _T+X$ at LO and NLO within the cuts of Eqs. (\ref{['eq:cuts']},\ref{['eq:isol']}). The factorization and renormalization scales are together or independently varied in the range from $0.1 \cdot \mu_0$ to $10 \cdot \mu_0$.Right:Same as in the left panel but for the different NLO contributions at $\mu_F=\mu_R=\xi\mu_0$.
• Figure 3: Left:Scale dependence of the total LHC cross section for $p p \to ZZ\gamma+X \to \ell^+_1 \ell^-_1\ell^+_2 \ell^-_2 \gamma+X$ at LO and NLO within the cuts of Eqs. (\ref{['eq:cuts']},\ref{['eq:isol']}). The factorization and renormalization scales are together or independently varied in the range from $0.1 \cdot \mu_0$ to $10 \cdot \mu_0$.Right:Same as in the left panel but for the different NLO contributions at $\mu_F=\mu_R=\xi\mu_0$.
• Figure 4: Left:Transverse-momentum distribution of the photon in $W^+W^-\gamma$ production at the LHC. LO and NLO results are shown for $\mu_F=\mu_R=\mu_0$ and the cuts of Eq. (\ref{['eq:cuts']}).Right:K-factor for the transverse-momentum distribution of the photon as defined in Eq.(\ref{['eq:kfactor']}).
• Figure 5: Left:Separation between the photon and the softest lepton in $W^+W^-\gamma$ production at the LHC, at LO and NLO with $\mu_F=\mu_R=\mu_0$ and the cuts of Eq. (\ref{['eq:cuts']}).Right:K-factor for the separation between the photon and the softest lepton as defined in Eq.(\ref{['eq:kfactor']}).