Next-to-leading-order electroweak corrections to $pp \to W^+W^-\to$ 4 leptons at the LHC

TL;DR

This work delivers the first complete calculation of next-to-leading-order electroweak corrections to W-pair production at the LHC that includes leptonic W decays and all off-shell effects via a full four-fermion final state. Using the complex-mass scheme and two independent computational approaches, the study benchmarks the full off-shell results against the double-pole approximation across realistic event selections, revealing strong agreement in angular and rapidity observables but notable discrepancies at TeV scales, especially for high-pT distributions where non-resonant backgrounds gain prominence. The results underscore the importance of full off-shell treatment for precise WW backgrounds to Higgs analyses and for high-energy EW measurements, while confirming the DPA’s adequacy for many observables at moderate energies. Photon-induced channels and collinear photon radiation effects are shown to influence the integrated corrections modestly but can significantly shape differential distributions, particularly under different jet-veto scenarios. Overall, the paper provides essential guidance for accurate EW predictions in WW-related Higgs and new-physics searches at the LHC.

Abstract

We present results of the first calculation of next-to-leading-order electroweak corrections to W-boson pair production at the LHC that fully takes into account leptonic W-boson decays and off-shell effects. Employing realistic event selections, we discuss the corrections in situations that are typical for the study of W-boson pairs as a signal process or of Higgs-boson decays $H\to W W^*$, to which W-boson pair production represents an irreducible background. In particular, we compare the full off-shell results, obtained treating the W-boson resonances in the complex-mass scheme, to previous results in the so-called double-pole approximation, which is based on an expansion of the loop amplitudes about the W resonance poles. At small and intermediate scales, i.e. in particular in angular and rapidity distributions, the two approaches show the expected agreement at the level of fractions of a percent, but larger differences appear in the TeV range. For transverse-momentum distributions, the differences can even exceed the 10% level in the TeV range where "background diagrams" with one instead of two resonant W bosons gain in importance because of recoil effects.

Figures (11)

• Figure 1: Generic diagram for virtual factorizable corrections to $\bar{q}q\to\, {\rm W}$ W${\rm W}$ W$\to4\,$leptons appearing in DPA, where the blobs stand for tree-level or one-loop insertions.
• Figure 2: Typical diagrams contributing to the virtual non-factorizable corrections to $\bar{q}q\to\, {\rm W}$ W${\rm W}$ W$\to4\,$leptons appearing in DPA, where the blobs stand for any tree-level subdiagram.
• Figure 3: Individual contributions to the differential cross section with the default ATLAS jet veto of $p_{{{\rm T}},{{\rm jet}}}>25\,{\rm GeV}$ (left) and jet-veto (JV) dependence (right) of the transverse-momentum distribution of the electron in ${\rm p}$ p${\rm p}$ p$\to\nu_\mu\mu^+ {\rm e}$ e$^-\bar{\nu}_{\rm e}$ e$+X$ in the ATLAS WW setup. The lower panels show the relative size of the various corrections.
• Figure 4: Transverse-mass distribution of the four-lepton system (left) and invariant-mass distribution of the charged-lepton system (right) in ${\rm p}$ p${\rm p}$ p$\to\nu_\mu\mu^+ {\rm e}$ e$^-\bar{\nu}_{\rm e}$ e$+X$ in the ATLAS WW setup (upper panels), together with the relative impact of the individual corrections (lower panels). Note that the $\gamma\gamma$ contribution is scaled by a factor of ten only in the upper panels.
• Figure 5: Rapidity distribution of the electron (left) and distribution in the azimuthal-angle separation of the two charged leptons (right) in ${\rm p}$ p${\rm p}$ p$\to\nu_\mu\mu^+ {\rm e}$ e$^-\bar{\nu}_{\rm e}$ e$+X$ in the ATLAS WW setup. The lower panels show the relative impact of the various contributions. Note that the $\gamma\gamma$ contribution is scaled by a factor of hundred only in the upper panels.