QCD corrections to ZZ production in gluon fusion at the LHC

TL;DR

This work computes the NLO QCD corrections to the loop-induced gluon-fusion process $gg \to ZZ$, including two-loop $gg \to ZZ$ and one-loop $gg \to ZZg$ amplitudes, using unitarity methods and the $q_t$-subtraction framework. By treating the first two qu generations as massless and neglecting top-quark triangle contributions, it provides a feasible, precise prediction for the $gg \to ZZ$ component fed into $pp \to ZZ$ at the LHC. The results show very large QCD corrections, boosting the gg contribution by ${\cal O}(60\%-110\%)$ at 8 TeV and ${\cal O}(40\%-90\%)$ at 13 TeV, which in turn shifts the total NNLO $pp \to ZZ$ cross section by several percent and impacts off-shell Higgs width studies. The paper also details the computational strategy, including a dedicated one-loop $gg \to ZZg$ amplitude via unitarity, and outlines future improvements to include mass effects and interference with $gg \to H^* \to ZZ$.

Abstract

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 distinct and, potentially, the dominant part of the N$^3$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 ${\cal O}(50\%-100\%)$ depending on the values of the renormalization and factorization scales used in the leading order computation, and the collider energy. The large corrections to $gg \to ZZ$ channel increase the $pp \to ZZ$ cross section by about six to eight percent, exceeding the estimated theoretical uncertainty of the recent NNLO QCD calculation.

Figures (3)

• 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 text for details.
• Figure 2: Up, left: cumulative cross section for $gg \to (Z/\gamma)(Z/\gamma) \to e^+e^-\mu^+ \mu^-$ at the $8~{\rm TeV}$ LHC as a function of the lower cut on 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 $8~{\rm TeV}$ LHC. Lower panes show ratios of the LO (yellow) and NLO (blue) distributions evaluated at three different scales to the LO distribution evaluated at $\mu = 2 m_Z$. Low: same as above for the $13~{\rm TeV}$ LHC.
• Figure 3: Left: transverse momentum distribution of an $e^+e^-$ pair at the $13~{\rm TeV}$ LHC. Right: the hardest lepton transverse momentum distribution at the $8~{\rm TeV}$ LHC. Lower panes show ratios of the LO (yellow) and NLO (blue) distributions evaluated at three different scales to the LO distribution evaluated at $\mu = 2 m_Z$.