QCD corrections to tri-boson production

TL;DR

The paper addresses the challenge of computing next-to-leading order QCD corrections for a $2\to 3$ process, $pp \to ZZZ$, by developing a fully numerical framework that combines sector decomposition (for infrared singularity extraction) with contour deformation of Feynman-parameter integrals (to navigate internal thresholds). The authors compute real emission, collinear counterterms, and virtual corrections, using a numerically stabilized approach with a substantial set of kinematic points and VEGAS integration, verifying divergence cancellations and independence from contour-deformation parameters. They find large NLO corrections of about 50% across relevant scales, with LO predictions underestimating this size due to tiny LO scale dependence, while the NLO kinematic distributions largely preserve the LO shapes up to a constant $K$-factor. The work demonstrates a general, automated numerical method for NLO QCD in complex $2\to 3$ processes and provides concrete results for a key LHC background to SUSY tri-lepton signals, highlighting the practical impact of improved theoretical precision for LHC phenomenology.

Abstract

We present a computation of the next-to-leading order QCD corrections to the production of three Z bosons at the LHC. We calculate these corrections using a completely numerical method that combines sector decomposition to extract infrared singularities with contour deformation of the Feynman parameter integrals to avoid internal loop thresholds. The NLO QCD corrections to pp -> ZZZ are approximately 50%, and are badly underestimated by the leading order scale dependence. However, the kinematic dependence of the corrections is minimal in phase space regions accessible at leading order.

Figures (5)

• Figure 1: Representative Born-level diagram for $q\bar{q} \to ZZZ$.
• Figure 2: Representative diagrams contributing to $q\bar{q} \to ZZZg$.
• Figure 3: Representative one-loop diagrams contributing to $q\bar{q} \to ZZZ$.
• Figure 4:
• Figure 5: The transverse momentum and rapidity distributions of the $Z$ bosons at LO and NLO in $\alpha_s$, normalized by a factor $1/3$. The results obtained by re-scaling the LO distribution by a constant $K$-factor are also shown. The value of the factorization and the renormalization scales are set equal to $3 M_Z$.