$WZ$ Production at Hadron Colliders: Effects of Non-Standard $WWZ$ Couplings and QCD Corrections

TL;DR

This paper provides a comprehensive ${\cal O}(\alpha_s)$ calculation of hadronic $WZ$ production with leptonic decays, general ${C}$ and ${P}$ conserving $WWZ$ couplings, and form-factor unitarization. It demonstrates that NLO QCD corrections dramatically reshape key distributions at the LHC, reducing sensitivity to anomalous couplings unless a jet veto (0-jet channel) is applied, while corrections at the Tevatron are more modest. The work also analyzes amplitude-zero signatures through rapidity correlations and cross-section ratios, highlighting their utility as complementary probes albeit challenging to observe in practice. Overall, the study provides critical guidance for extracting $WWZ$ vertex information from $WZ$ production at the Tevatron and LHC, including how to optimize observables and event selections to mitigate QCD effects. These results inform experimental strategies for testing the SM and constraining new physics in the weak-boson sector.

Abstract

The process $p\,\pbar \rightarrow W^{\pm}Z + X \rightarrow \ell^\pm_1 ν_1 \ell_2^+ \ell_2^- + X$ is calculated to ${\cal O}(α_s)$ for general $C$ and $P$ conserving $WWZ$ couplings. At the Tevatron center of mass energy, the QCD corrections to $WZ$ production are modest. At Large Hadron Collider (LHC) energies, the inclusive QCD corrections are large, but can be reduced significantly if a jet veto is imposed. Sensitivity limits for the anomalous $WWZ$ couplings are derived from the next-to-leading order $Z$ boson transverse momentum distribution for Tevatron and LHC energies. Unless a jet veto is imposed, next-to-leading order QCD corrections decrease the sensitivity to anomalous $WWZ$ couplings considerably at LHC energies, but have little influence at the Tevatron. We also study, at next-to-leading order, rapidity correlations between the $W$ and $Z$ decay products, and the $ZZ/WZ$ and $WZ/Wγ$ cross section ratios. These quantities are found to be useful tools in searching for the approximate zero present in the Standard Model $WZ$ helicity amplitudes. The prospects for observing the approximate amplitude zero at the Tevatron and the LHC are critically assessed.

Figures (21)

• Figure 1: Feynman rule for the general $WWZ$ vertex. The factor $g_{WWZ}=e\cot\theta_{\rm W}$ is the $WWZ$ coupling strength and $Q_W$ is the electric charge of the $W$ boson. The vertex function $\Gamma_{\beta \mu \nu}(k,k_1,k_2)$ is given in Eq. (\ref{['EQ:NSMCOUPLINGS']}).
• Figure 2: The inclusive differential cross section for the reconstructed $WZ$ mass in the reaction ${p \bar{p} \to W^+Z + X \to\ell_1^+\nu_1\ell_2^+\ell_2^- + X}$ at ${\sqrt{s} = 1.8}$ TeV; a) in the Born approximation and b) including NLO QCD corrections. The curves are for the SM (solid lines), $\lambda^0 = -0.5$ (dashed lines), $\Delta\kappa^0 = -1.0$ (dotted lines), and $\Delta g_1^0 = -0.5$ (dot-dashed lines). The cuts imposed are summarized in Sec. IIIB.
• Figure 3: The inclusive differential cross section for the reconstructed $WZ$ mass in the reaction ${p \bar{p} \to W^+Z + X \to\ell_1^+\nu_1\ell_2^+\ell_2^- + X}$ at ${\sqrt{s} = 3.5}$ TeV; a) in the Born approximation and b) including NLO QCD corrections. The curves are for the SM (solid lines), $\lambda^0 = -0.5$ (dashed lines), $\Delta\kappa^0 = -1.0$ (dotted lines), and $\Delta g_1^0 = -0.5$ (dot-dashed lines). The cuts imposed are summarized in Sec. IIIB.
• Figure 4: The inclusive differential cross section for the reconstructed $WZ$ mass in the reaction ${pp \to W^+Z + X \to\ell_1^+\nu_1\ell_2^+\ell_2^- + X}$ at ${\sqrt{s} = 14}$ TeV; a) in the Born approximation and b) including NLO QCD corrections. The curves are for the SM (solid lines), $\lambda^0 = -0.25$ (dashed lines), $\Delta\kappa^0 = -1.0$ (dotted lines), and $\Delta g_1^0 = -0.25$ (dot-dashed lines). The cuts imposed are summarized in Sec. IIIB.
• Figure 5: The inclusive NLO differential cross section for the reconstructed $WZ$ mass in the reaction a) ${p\bar{p} \to W^+Z + X \to\ell_1^+\nu_1\ell_2^+\ell_2^- + X}$ at ${\sqrt{s} = 1.8}$ TeV and b) ${pp \to W^+Z + X}$${\to\ell_1^+\nu_1\ell_2^+\ell_2^- + X}$ at ${\sqrt{s} = 14}$ TeV. The curves are for the SM with reconstructed invariant mass (solid lines) and non-standard $WWZ$ couplings (dotted, dashed, and dot-dashed curves) as listed on the figure. The lower (upper) lines apply for positive (negative) anomalous couplings. The dash-double-dotted line shows the true SM $WZ$ invariant mass distribution. The cuts imposed are summarized in Sec. IIIB.