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

TL;DR

The paper addresses precise QCD predictions for on-shell $W^+W^-$ production at the LHC in the threshold region. It implements NNLO QCD corrections together with NNLL threshold resummation by factorizing soft-virtual contributions and performing Mellin-space resummation of the SV terms. Key results include a $\sim 6.3\%$ NNLO$+$NNLL enhancement at $Q=2500$ GeV and a reduction of seven-point scale uncertainties from about $6.8\%$ to $4.1\%$, with PDF uncertainties around $3\%$ at high $Q$. These computations extend fixed-order precision for WW production and provide robust benchmarks for current LHC analyses and future hadron colliders.

Abstract

We present results for threshold resummation of the invariant mass distribution, for on-shell production of a pair of $W$-bosons at next-to-next-to-leading order + next-to-next-to-leading logarithmic (NNLO+NNLL) accuracy in QCD. Owing to its sensitivity to the self-interactions between gauge bosons, this process is important to investigate at the energies of the Large Hadron Collider (LHC). We achieve this resummation by exploiting the factorization properties of the soft and virtual parts of the partonic cross-section. Our analysis has been carried out for the invariant mass distribution up to $Q$ = 2500 GeV. At this highest $Q$ we find that, for 13.6 TeV LHC, the NNLL resummation enhances the NNLO cross-sections by about $6.3\%$ and reduces the conventional scale uncertainties from 6.8\% at NNLO to 4.1\% at NNLO+NNLL. We also estimate the intrinsic uncertainties due to the non-perturbative parton distribution functions at the highest perturbative order, for both fixed-order and resummed results, to be around 3\% for $Q \sim$ 2000 GeV.

Figures (4)

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