Threshold Resummed and Approximate NNLO results for W+W- Pair Production at the LHC

TL;DR

The paper enhances precision for W+W- production at the LHC by combining NLO QCD with NNLL threshold resummation and by constructing an approximate NNLO cross section using SCET. It employs pair-invariant-mass kinematics to resumm soft-gluon threshold logarithms and matches to fixed-order results to deliver accurate differential and total cross sections with controlled uncertainties. The NNLL resummation increases the invariant-mass distribution peak by about 3–4% at 8 and 14 TeV, while the combined NLO+NNLL and approximate NNLO cross sections modestly exceed the NLO predictions, with approximate NNLO exhibiting reduced scale variation. Overall, the results provide the most precise WW predictions to date, improving the reliability of WW backgrounds in Higgs analyses and tests of electroweak dynamics.

Abstract

The next-to-leading order (NLO) QCD radiative corrections to W+W- production at hadron colliders are well understood. We combine NLO perturbative QCD calculations with soft-gluon resummation of threshold logarithms to find a next-to-next-to leading logarithmic (NNLL) prediction for the total cross section and the invariant mass distribution at the LHC. We also obtain approximate next-to-next-to-leading order (NNLO) results for the total W+W- cross section at the LHC which includes all contributions from the scale dependent leading singular terms. Our result for the approximate NNLO total cross section is the most precise theoretical prediction available. Uncertainties due to scale variation are shown to be small when the threshold logarithms are included. NNLL threshold resummation increases the W+W- invariant mass distribution by ~ 3-4% in the peak region for both \sqrt{S}=8 and 14 TeV. The NNLL threshold resummed and approximate NNLO cross sections increase the NLO cross section by 0.5-3% for \sqrt{S}=7, 8, 13, and 14 TeV.

Figures (7)

• Figure 1: Feynman diagrams for the (a) $s$-channel and (b) $t$-channel contributions to $q\bar{q}\rightarrow W^+W^-$.
• Figure 2: (a) The ratio of the NNLL-resummed invariant mass distribution evaluated with only the $\mathcal{O}(\alpha_s)$ piece of the soft function, $(d\sigma^{NNLL}/dM_{WW})_{\alpha_s}$, to the NNLL-resummed distribution evaluated with only the LO piece of the soft function, $(d\sigma^{NNLL}/dM_{WW})_0$, at $\sqrt{S}=8$ TeV and various values of $M_{WW}$. (b) The minimum value of $\mu_s/M_{WW}$ at $\sqrt{S}=8$ TeV (solid) and $\sqrt{S}=14$ TeV (dashed) as a function of $\tau$.
• Figure 3: Ratio of the contribution of the leading singularity to the fixed order NLO cross section at $\sqrt{S}=8$ and $14$ TeV using MSTW2008 PDFs. NNLO (NLO) PDFs are used for the NNLL leading contribution (fixed order NLO contribution).
• Figure 4: (a) Invariant mass distribution and factorization scale dependence of fixed order and matched differential cross sections at $\sqrt{S}=14$ TeV using MSTW2008 PDFs. The dash-dot-dot curves have $\mu_f=M_W$ and the dashed curves have $\mu_f=4M_W$. (b) Ratio of the NLO+NNLL matched and NLO invariant mass distribution for $\sqrt{S}=8$ and $14$ TeV with the NLO cross section with NLO PDFs (solid) and NNLO PDFs (dashed). The factorization scale is fixed to $\mu_f=2 M_W$.
• Figure 5: Factorization scale dependence of (a) NNLL resummed and NLO leading singularity, and (b) NLO and matched NNLL invariant mass distributions at $\sqrt{S}=14$ TeV using MSTW2008 PDFs. The dash-dot-dot curves have $\mu_f=M_W$ and the dashed curves have $\mu_f=4M_W$.