Precise predictions for the associated production of a $W$ boson with a top-antitop quark pair at the LHC

TL;DR

This work delivers the first NNLO QCD calculation for $t\bar{t}W$ production at the LHC, using two independent approximations—the soft-$W$ method and a massification approach—to estimate the unknown two-loop amplitude, then combines these with full NLO QCD+EW results. At $\sqrt{s}=13$ TeV, the NNLO QCD corrections rise the NLO prediction by about $15\%$, while EW corrections add roughly $5\%$, yielding a highly precise inclusive cross section: $\sigma(t\bar{t}W^+)=497.5$ fb, $\sigma(t\bar{t}W^-)=247.9$ fb, total $745.3$ fb, with total theory uncertainties around $\mathcal{O}(2\%)$. The results are compatible with the FxFx reference and lie within the 1–2$\sigma$ contours of ATLAS and CMS measurements, tightening the SM tests for this heavy final state. This precision enables more stringent comparisons between theory and experiment as data accumulate and paves the way for robust probes of potential deviations in the top-quark sector.

Abstract

The production of a top-antitop quark pair in association with a $W$ boson ($t\bar tW$) is one of the heaviest signatures currently probed at the Large Hadron Collider (LHC). Since the first observation reported in 2015 the corresponding rates have been found to be consistently higher than the Standard Model predictions, which are based on next-to-leading order~(NLO) calculations in the QCD and electroweak (EW) interactions. We present the first next-to-next-to-leading order (NNLO) QCD computation of $t\bar tW$ production at hadron colliders. The calculation is exact, except for the finite part of the two-loop virtual corrections, which is estimated using two different approaches that lead to consistent results within their uncertainties. We combine the newly computed NNLO QCD corrections with the complete NLO QCD+EW results, thus obtaining the most advanced perturbative prediction available to date for the \ttW inclusive cross section. The tension with the latest ATLAS and CMS results remains at the $1σ-2σ$ level.

Figures (3)

• Figure 1: Results for $\Delta\sigma_{\rm NLO,H}$ (upper panel) and $\Delta\sigma_{\rm NNLO,H}$ (lower panel), in the case of $t \bar{t} W^-$ production, obtained with the two approximations presented in this work, for different cuts on the transverse momenta of the top quarks. At NLO the approximations are normalized to the exact result, while at NNLO to their average. The uncertainties of each approximation at NNLO are presented, as well as their combination. Similar results are obtained for $t \bar{t} W^+$.
• Figure 2: Inclusive $t \bar{t} W$ cross sections at different orders in the QCD expansion, for different choices of the central renormalization and factorization scales.
• Figure 3: Comparison of our NNLO$_{\rm QCD}$+NLO$_{\rm EW}$ result to the measurement performed by the CMS (red) and ATLAS (blue) collaborations in Refs. CMS:2022tkvATLAS:2023gon, at 68% (solid) and 95% (dashed) confidence level. We indicate in black and orange the scale and the approximation uncertainties, respectively, of the NNLO$_{\rm QCD}$+NLO$_{\rm EW}$ result.