QCD corrections to vector boson pair production in gluon fusion including interference effects with off-shell Higgs at the LHC

TL;DR

This work computes NLO QCD corrections to loop-induced gg -> VV production with off-shell Higgs interference at the LHC, including off-shell decays to leptons and both prompt and Higgs-mediated amplitudes. For ZZ, it employs a heavy-top expansion for the massive-top loop contributions, valid when $m_{4l} < 2m_t$, and validates the approach with jet cuts to control expansion convergence; for WW, only massless-quark contributions are included, with an approximate scheme proposed for the full NLO interference. The authors find large, nontrivial QCD corrections to the interference that are comparable to those of the signal and background, with strong dependence on the four-lepton invariant mass near the $2m_Z$ and $2m_t$ thresholds. These results enhance the precision of off-shell Higgs analyses and Higgs-width constraints, though complete massive-quark effects for WW remain an area for future work.

Abstract

We compute next-to-leading order (NLO) QCD corrections to the production of two massive electroweak bosons in gluon fusion. We consider both the prompt production process $gg \to VV$ and the production mediated by an exchange of an s-channel Higgs boson, $gg \to H^* \to V V$. We include final states with both on- and off-shell vector bosons with leptonic decays. The gluonic production of vector bosons is a loop-induced process, including both massless and massive quarks in the loop. For $gg \to ZZ$ production, we obtain the NLO QCD corrections to the massive loops through an expansion around the heavy top limit. This approximation is valid below the top production threshold, giving a broad range of invariant masses between the Higgs production and the top production thresholds in which our results are valid. We explore the NLO QCD effects in $gg \to ZZ$ focusing, in particular, on the interference between prompt and Higgs-mediated processes. We find that the QCD corrections to the interference are large and similar in size to the corrections to both the signal and the background processes. At the same time, we observe that corrections to the interference change rapidly with the four-lepton invariant mass in the region around the ZZ production threshold. We also study the interference effects in $gg \to WW$ production where, due to technical limitations, we only consider contributions of massless loops. We find that the QCD corrections to the interference in this case are somewhat larger than those for either the signal or the background.

Figures (10)

• Figure 1: Representative Feynman diagrams for the Higgs-mediated signal amplitude $gg \to H \to ZZ$ (a) and the background amplitude $gg \to ZZ$ (b) at LO in pQCD. The decays of the $Z$-bosons to leptons are understood.
• Figure 2: Representative Feynman diagrams at NLO. Shown are the two-loop and real emission contributions to the signal amplitude ${\cal A}_{H}$ ((a) and (b)) and to the background amplitude ${\cal A}_{p}$ ((c)-(f)). The decays of the $Z$-bosons to leptons are only shown in (f).
• Figure 3: LO invariant mass of the four lepton system at the $13$ TeV LHC, background only. In both plots, the vertical line marks the top threshold. Left, upper panel: results using a massive loop only, with the amplitude evaluated in the heavy-top expansion up to various orders in $1/m_t$, compared to the exact mass dependence. The lower panel shows the ratio of the various $1/m_t$ approximations to the exact result. Right, upper panel: distribution using both massless and massive loops compared to massless-only and (exact) massive-only. Note that the latter is multiplied by 100. The lower panel shows the ratio of the (exact) massive contribution to the full result.
• Figure 4: LO results for signal/background interference at the 13 TeV LHC. Both the full result as well as massless/massive-only contributions are shown. Solid line: exact result. Dashed line: $1/m_t$ expansion, including up to $1/m_t^8$ terms. The vertical line marks the top threshold.
• Figure 5: Interference pattern in $gg \to ZZ + {\rm jet}$ between the Higgs signal and the prompt production, at the $\sqrt{s}=13$ TeV LHC for a scale $\mu=m_{ZZ}/2$, including both massless and massive contributions. A comparison of expanded in $1/m_t$ and exact results are shown, with the latter taken from Ref. Campbell:2014gua.