Precise predictions for joint polarisation fractions in WZ production at the LHC

TL;DR

The paper delivers the first combined $NNLO$ QCD and $NLO$ EW predictions for fully leptonic, doubly polarised $WZ$ production at the LHC, using the double-pole approximation to define intermediate boson polarisations. It demonstrates sizeable higher-order corrections across polarisation states, emphasizes the importance of including photon-induced contributions, and provides a detailed comparison of MHOU estimation methods (scale variations and theory-nuisance-parameters). The results include fiducial cross sections, differential distributions, and joint polarisation fractions within ATLAS-like selections, highlighting a TT-dominated cross section and stable LL fractions under higher orders. The work establishes a new state-of-the-art fixed-order baseline for polarised diboson production and offers a framework for future matching to parton showers and for robust MHOU assessments in polarisation observables.

Abstract

We achieve for the first time NNLO QCD + NLO EW accuracy for doubly polarised WZ inclusive production at the LHC, in the case of fully leptonic decays. Additionally, we provide estimates for missing higher-order uncertainties in QCD associated with doubly polarised differential cross sections and joint polarisation fractions, obtained both with standard scale variations and with a theory-nuisance-parameter approach. The study is carried out in the fiducial setup of a recent ATLAS analysis of Run-2 data.

Figures (3)

• Figure 1: Distributions in the transverse-momentum of the muon--antimuon system (a) and the rapidity separation between the positron and the muon--antimuon system (b) in the fiducial ATLAS setup ATLAS:2022oge. Upper panels: absolute differential cross sections at NNLO$^{(+)}$ accuracy, namely combining additively NNLO QCD and NLO EW corrections according to Eq. \ref{['eq:mult_add']}. Middle panels: ratios between NNLO and NLO QCD distributions. Lower panels: ratio of NNLO$^{(+)}$ distributions including (solid) and excluding (dashed) photon-induced contributions over the NNLO QCD ones. Colour key: full off-shell (black), unpolarised (grey), ${\mathrm{L}}{\mathrm{L}}$ (red), ${\mathrm{L}}{\mathrm{T}}$ (yellow), ${\mathrm{T}}{\mathrm{L}}$ (green), and ${\mathrm{T}}{\mathrm{T}}$ (blue), where the first (second) polarisation label is associated with the $\text{W}\xspace\,(\text{Z}\xspace)$ boson.
• Figure 2: Differential QCD $K$-factors ($\mathrm d\sigma^{\rm QCD}_{\rm NNLO}/\mathrm d\sigma^{\rm QCD}_{\rm NLO}$) in the transverse-momentum of the muon--antimuon system (a) and the rapidity separation between the positron and the muon--antimuon system (b) in the fiducial ATLAS setup ATLAS:2022oge. The NLO (NNLO) results are shown in blue (red) colour for the LL, LT, TL, and TT polarisation states, from top down. The MHOU QCD uncertainties are computed with seven-point scale variations ("7pSV", dashed boundary lines) and with the theory nuisance parameter approach ("TNP", shaded bands).
• Figure 3: Differential polarisation fractions $f_{\lambda\lambda'}$ ($=\mathrm d\sigma_{\lambda\lambda'}/\mathrm d\sigma_{\rm unp}$) in the transverse-momentum of the muon--antimuon system (a) and the rapidity separation between the positron and the muon--antimuon system (b) in the fiducial ATLAS setup ATLAS:2022oge. The NLO (NNLO) QCD fractions are shown in blue (red) colour for the LL, LT, TL, and TT states, from top down. The MHOU QCD uncertainties are computed with correlated seven-point scale variations ("7pSV", dashed boundary lines) and with the theory nuisance parameter approach ("TNP", shaded bands).