NNLO predictions for Z-boson pair production at the LHC

TL;DR

This paper computes NNLO QCD corrections to ZZ production at the LHC using N-jettiness subtraction and SCET-based factorization. It includes both qqbar-initiated and loop-induced gg→ZZ contributions, with a detailed treatment of IR subtraction and phase-space slicing. The NNLO corrections increase the NLO cross section by about 18%, with roughly 60% arising from gg→ZZ, and predictions show improved agreement with ATLAS and CMS data at 13 TeV, including differential distributions that reflect the gg channel's impact. The work underscores the importance of NNLO accuracy for diboson production and notes future extensions to include massive top-quark effects in gg and additional two-loop contributions.

Abstract

We present a calculation of the NNLO QCD corrections to Z-boson pair production at hadron colliders, based on the N-jettiness method for the real radiation parts. We discuss the size and shape of the perturbative corrections along with their associated scale uncertainties and compare our results to recent LHC data at $\sqrt{s}=13$ TeV.

Figures (4)

• Figure 1: (a) NLO coefficient to the inclusive $ZZ$ cross section computed with $N$-jettiness subtraction (dashed-lines) and antenna subtraction (solid lines) as a function of ${\cal T}_0^{cut}$. We show separately the contributions of the $2\to3$ and $2\to2$ phase space integrals for antenna subtraction, and the $\sigma_{NLO}({\cal T}_0 > {\cal T}_0^{cut})$ and $\sigma_{NLO}({\cal T}_0 < {\cal T}_0^{cut})$ phase space integrals for $N$-jettiness. The ratio plot shows $\Delta\sigma_{NLO}$($N$-jettiness) over $\Delta\sigma_{NLO}$(antenna). (b) NNLO coefficient to the inclusive $ZZ$ cross section computed with $N$-jettiness subtraction (dashed lines) as a function of ${\cal T}_0^{cut}$. We show the separate cross sections for $\sigma_{NNLO}({\cal T}_0 > {\cal T}_0^{cut})$ from the double-real and real-virtual phase space integrals and for $\sigma_{NNLO}({\cal T}_0 < {\cal T}_0^{cut})$ from the SCET phase space integrals together with their sum.
• Figure 2: ${\cal T}_0^{cut}$ dependence of the NNLO coefficient for $ZZ$ production with the ${\cal T}_0$ independent $gg\to ZZ$ contribution subtracted. The black dashed line shows the fit of the ${\cal T}_0^{cut}$ dependence of the NNLO coefficient (black data points) to the analytic form in equation \ref{['eq:powercorr']}. The ${\cal T}_0^{cut} \rightarrow 0$ limit is shown as a solid black line with a grey band showing the uncertainty on the fitted parameter. The red line represents the NNLO coefficient reconstructed from the NNLO result obtained in Ref. Cascioli:2014yka.
• Figure 3: Renormalisation and factorisation scale dependence of the $ZZ$ cross section at LO, NLO and NNLO for the central scale choice $\mu_R=\mu_F=m_Z$ and with NNPDF-3.0 PDFs. We also show the NNLO result without the gluon fusion contributions. The thickness of the bands shows the variation in the cross section due to factorisation scale while the slope shows the renormalisation scale dependence. The scale uncertainty was obtained by varying the renormalisation and factorisation scales in the range $0.5m_{Z}<\mu_R,\mu_F<2m_{Z}$ with the constraint $0.5<\mu_F/\mu_R<2$.
• Figure 4: (a) $ZZ$ invariant mass distribution and (b) averaged transverse momentum distribution $\langle p_{T,Z}\rangle$ of the $Z$-bosons computed at LO, NLO and NNLO. In the two sub panels we show respectively the NLO/LO and NNLO/NLO $K$-factors to visualise the size of the higher order effects. The result for the contribution from the loop-induced $gg\to ZZ$ subset of the full NNLO correction is also shown separately. Shaded bands represent the theory uncertainty due to the variation of the factorisation and renormalisation scales.