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

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.

💡 Research Summary

The paper presents a state‑of‑the‑art QCD prediction for the production of an on‑shell Z‑boson pair at the Large Hadron Collider, combining fixed‑order calculations at next‑to‑next‑to‑leading order (NNLO) with threshold resummation at next‑to‑next‑to‑leading logarithmic (NNLL) accuracy, i.e. NNLO+NNLL. The authors start by motivating the importance of ZZ production for precision tests of the Standard Model, electroweak symmetry breaking, and searches for new physics. They note that while leading‑order (LO), next‑to‑leading order (NLO) and even NNLO QCD results are available, the high‑invariant‑mass region (Q ≳ 1 TeV) suffers from large logarithmic corrections of the form lnⁿ(1‑z) that arise when the partonic scaling variable z = Q²/s approaches unity (the partonic threshold).

In the threshold limit the partonic cross section factorises into a soft‑virtual (SV) piece containing all singular distributions (δ(1‑z) and plus‑distributions D_i =