Electroweak corrections to doubly polarised WZ scattering at the LHC

TL;DR

This paper provides the first exact NLO electroweak corrections to a doubly polarised $WZ$ vector-boson scattering process in association with two jets at the LHC, using a pole-approximation framework to define polarised intermediate bosons in a gauge-invariant way. The authors implement an on-shell projection and helicity-state separation to extract polarised amplitudes, carefully handling potential overlaps with triply resonant contributions via a fudge-factor regularisation, and apply realistic Run-3 fiducial cuts. Their results show large negative NLO EW corrections (approximately $-15\%$ to $-20\%$ in most channels, with the TT state strongest) and a TT-dominated unpolarised cross section, while off-shell and interference effects remain small (of order a few percent) in most observables. The work provides crucial theoretical templates for disentangling the spin structure of VBS in LHC data and outlines paths for incorporating future NLO QCD corrections in polarised $WZ$ scattering analyses.

Abstract

We present a calculation of next-to-leading-order electroweak corrections to the vector-boson scattering (VBS) process resulting in leptonically decaying W and Z bosons in association with two jets at the LHC. The VBS process is computed for both polarised and unpolarised intermediate bosons, exploiting the pole approximation and the separation of helicity states in tree-level and one-loop amplitudes. A phenomenological analysis is carried out for a realistic fiducial setup at a 13.6 TeV LHC collision energy, highlighting different patterns for the various polarisation states both at integrated and at differential level. This study provides theoretical predictions that are necessary to perform a sound characterisation of the spin structure of VBS processes with full LHC data.

Figures (7)

• Figure 1: Tree-level SM diagrams contributing to the $\text{W}\xspace^+\text{Z}\xspace\rightarrow\text{W}\xspace^+\text{Z}\xspace$ scattering process.
• Figure 2: Tree-level total cross sections in the SM and in its real-singlet extension (RxSM) for the on-shell $\text{W}\xspace\text{Z}\xspace\rightarrow\text{W}\xspace_{\lambda}\text{Z}\xspace_{\lambda'}$ scattering, as functions of the di-boson CM energy. The two initial bosons are unpolarised, while the final ones are either longitudinal (${\mathrm{L}}$) or transverse (${\mathrm{T}}$). Numerical results have been obtained with Recola2 Denner:2017wsf for the SM and for the $\mathcal{Z}_2$-symmetric RxSM with $\sin\alpha=0.22,\,M_\text{H}\xspace\xspace =125\,\text{GeV}\xspace$, and $M_{\rm S}=2\,\text{TeV}\xspace$. Note that the curves for TL and LT are on top of each other.
• Figure 3: Distributions in the reconstructed invariant mass (left) and the transverse mass (right) of the $\text{W}\xspace\text{Z}\xspace$ system for $\text{W}\xspace^+\text{Z}\xspace$ scattering at the LHC in the fiducial setup described in Section \ref{['sec:ATLASfid']}. The invariant mass is obtained through the neutrino-reconstruction algorithm of Ref. Aaboud:2019gxl, while the transverse mass is defined in Eq. \ref{['eq:MTWZ']}. The structure reads (from the top down): absolute NLO EW distributions, normalised NLO EW distributions (to have unit integral), ratios over the unpolarised DPA results (at NLO EW accuracy), NLO EW corrections relative to LO. The colour key is as follows: full off-shell (black), unpolarised (grey), LL (red), LT (yellow), TL (green), TT (blue), and interference (magenta). The first/second polarisation label refers to the $\text{W}\xspace^+\!/\text{Z}\xspace$ boson.
• Figure 4: Distributions in the transverse momentum of the muon--antimuon pair (left) and of the tagging-jet system (right) for $\text{W}\xspace^+\text{Z}\xspace$ scattering at the LHC in the fiducial setup described in Section \ref{['sec:ATLASfid']}. Same structure as in Figure \ref{['fig:first']}.
• Figure 5: Distributions in the cosine of the reconstructed positron decay angle in the $\text{W}\xspace$-boson rest frame (left) and in the azimuthal-angle separation between the positron and the neutrino (right) for $\text{W}\xspace^+\text{Z}\xspace$ scattering at the LHC in the fiducial setup described in Section \ref{['sec:ATLASfid']}. The $\text{W}\xspace$-boson kinematics is obtained through the neutrino-reconstruction algorithm of Ref. Aaboud:2019gxl. Same structure as in Figure \ref{['fig:first']}.