Production of two Z-bosons in gluon fusion in the heavy top quark approximation

TL;DR

The paper addresses the problem of estimating QCD corrections to continuum $gg\to ZZ$ production proceeding through top-quark loops, using a heavy-top expansion with $m_t$ much larger than all invariants. The authors decompose the amplitude into axial and vector components and compute the leading heavy-mass terms for both the one- and two-loop axial contributions, as well as the real-emission process, enabling a NLO analysis via a $1/m_t$ expansion. They present the partonic cross-section in a form that isolates the leading logarithmic and hard emission contributions, and quantify the QCD corrections through $K$-factors that are sizable and comparable to Higgs-mediated processes, with the heavy-top approximation validating near threshold but diverging at high $q^2$. The results suggest significant gluon-fusion backgrounds for vector-boson pair production and motivate further work on interference with $gg\to H\to ZZ$, higher-order mass corrections, and combining massless and massive quark contributions for a complete prediction. Overall, this work provides the first quantitative estimate of NLO QCD corrections to $gg\to ZZ$ in the heavy-top limit and highlights their potential impact on precision Higgs and off-shell measurements at the LHC.

Abstract

We compute QCD radiative corrections to the continuum production of a pair of Z-bosons in the annihilation of two gluons. We only consider the contribution of the top quark loops and we treat them assuming that $m_t$ is much larger than any other kinematic invariant in the problem. We estimate the QCD corrections to $pp \to ZZ$ using the first non-trivial term in the expansion in the inverse top quark mass and we compare them to QCD corrections of the signal process, $pp \to H \to ZZ$.

Figures (3)

• Figure 1: Representative two-loop diagrams that describe production of Z-boson pairs in gluon fusion.
• Figure 2: Main plot: NLO $K$-factor for $gg \to ZZ$ production through the top quark loop as a function of the invariant mass of the $Z$-boson pair $q$, in GeV. Inset: NLO $K$-factor for $gg \to H$ as a function of the Higgs boson mass $q$, in GeV. Bands correspond to variations of the renormalization and factorization scales in the interval $q/4 \le \mu \le q$. The dashed line shows the $K$-factors computed for the renormalization and factorization scales set to $\mu = q/2$. We used the program MCFM mcfm to compute the $K$-factor for the Higgs boson production.
• Figure 3: LO $pp \to ZZ$ production cross-section ( gluon fusion through top loop only) ${\rm d}\sigma/{\rm d} q^2$ in ${\rm fb/GeV}^2$, as a function of the invariant mass squared of the $Z$-boson pair, $q^2$, in GeV${}^2$ with a top mass of 173 GeV. We compare our cross-section, which is valid in the $m_t \to \infty$ limit, with the one implemented in MCFM, which has exact $m_t$ dependence. The dots and squares correspond to the results from MCFM and this paper respectively. We set the renormalization scale and the factorization scale to $200~\mathrm{GeV}$. The difference between the values ranges from $\sim 20\%$ to $\sim 220\%$ for the values of $q^2$ considered. The inset shows the MCFM cross-section computed for a larger range of the invariant masses.