QCD corrections to $ZZ$ production in gluon fusion at the LHC

We compute the next-to-leading-order QCD corrections to the production of two $Z$-bosons in the annihilation of two gluons at the LHC. Being enhanced by a large gluon flux, these corrections provide a distinct and, potentially, the dominant part of the ${\mathrm{N}}^3\mathrm{LO}$ QCD contributions to $Z$-pair production in proton collisions. The $gg\to ZZ$ annihilation is a loop-induced process that receives the dominant contribution from loops of five light quarks, that are included in our computation in the massless approximation. We find that QCD corrections increase the $gg\to ZZ$ production cross section by $\mathcal{O}(50\%–100\%)$ depending on the values of the renormalization and factorization scales used in the leading-order computation and the collider energy. The large corrections to the $gg\to ZZ$ channel increase the $pp\to ZZ$ cross section by about 6% to 8%, exceeding the estimated theoretical uncertainty of the recent next-to-next-to-leading-order QCD calculation.

Figure 1

Representative Feynman diagrams for the $0\to gggZ(\to e^{-}{e}^{+})Z(\to {\mu }^{-}{\mu }^{+})$ amplitude. Double resonant diagrams (a) are relevant for both the on-shell and the off-shell production. Single resonant diagrams (b) are only relevant for the off-shell production and are not included in our computation. See the text for details.

Figure 2

Up, left: cumulative cross section for $gg\to (Z/\gamma )(Z/\gamma )\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ at the 8 TeV LHC as a function of the lower cut on the four-lepton invariant mass. Up, right: distribution of the invariant mass of the four leptons in the reaction $gg\to (Z/\gamma )(Z/\gamma )\to e^{+}{e}^{-}{\mu }^{+}{\mu }^{-}$ at the 8 TeV LHC. Lower panes show ratios of the LO (yellow) and NLO (blue) distributions evaluated at three different scales to the LO distribution evaluated at $\mu =2m_Z$. Low: same as above for the 13 TeV LHC.

Figure 3

Left: transverse momentum distribution of an $e^{+}{e}^{-}$ pair at the 13 TeV LHC. Right: the hardest lepton transverse momentum distribution at the 8 TeV LHC. Lower panes show ratios of the LO (yellow) and NLO (blue) distributions evaluated at three different scales to the LO distribution evaluated at $\mu =2m_Z$.