Threshold resummation for $Z$-boson pair production at NNLO+NNLL

TL;DR

This work performs threshold resummation for on-shell $Z$-boson pair production at NNLO+NNLL by resumming large soft-gluon logarithms near partonic threshold ($z\to 1$) and matching to NNLO fixed-order results. The authors tackle the process-dependent resummation coefficient $g_0$, which receives two-loop contributions, and extract the necessary coefficients by combining one- and two-loop amplitudes with cross-checks against MATRIX. They present invariant-mass distributions and total cross sections at LHC energies ($13.0$ and $13.6$ TeV) and discuss improvements in precision: NNLO corrections are large, NNLL adds a few percent, and scale uncertainties are reduced from about 3.4% to ~2.6% in high-$Q$ regions. The results are in good agreement with ATLAS and CMS data and provide improved predictions for future high-energy colliders, including a 100 TeV scenario.

Abstract

The production of a pair of on-shell $Z$-bosons is an important process at the Large Hadron Collider. Owing to its large production cross section at the LHC, this process is very useful for SM precision studies, electroweak symmetry breaking sector as well as to unravel the possible new physics. In this work, we have performed the threshold resummation of the large logarithms that arise in the partonic threshold limit $z \to 1$, up to Next-to-Next-to-Leading Logarithmic (NNLL) accuracy. The presence of the two-loop contributions in the process dependent resummation coefficient $g_0$ makes the numerical computation a non-trivial task. After matching the resummed predictions to the Next-to-Next-to-Leading order (NNLO) fixed order results, we present the invariant mass distribution to NNLO+NNLL accuracy in QCD for the current LHC energies. We find that in the high invariant mass region ($Q=1$ TeV), while the NNLO corrections are as large as $83\%$ with respect to the leading order, the NNLL contribution enhances the cross section by additional few percent, about $4\%$ for $13.6$ TeV LHC. In this invariant mass region, the conventional scale uncertainties in the fixed order results get reduced from $3.4\%$ at NNLO to about $2.6\%$ at NNLO+NNLL, and this reduction is expected to be more for higher $Q$ values.

Figures (5)

• Figure 1: Resummed predictions for the $Z$-boson pair invariant mass distribution (upper panel) and the corresponding K-factors(lower panel) up to NNLO+NNLL.
• Figure 2: K-factors for the fixed-order and resummed results for $Z$-boson pair production(see Eq. (\ref{['eq:ratio']}) for details).
• Figure 3: Seven point scale uncertainties for $Z$-boson pair production up to NNLO+NNLL.
• Figure 4: Renormalization(left) and factorization(right) scale uncertainties for $Z$-boson pair production up to NNLO+NNLL.
• Figure 5: K-factors as defined in Eq. (\ref{['eq:ratio']}) but using same NNLO PDFs at various orders in the perturbation theory.