Amplitude Zeros in $W^\pm Z$ Production

TL;DR

The approximate zero is the combined result of an exact zero in the dominant helicity amplitudes [ital scrM]([plus minus],[minus plus]) and strong gauge cancellations in the remaning amplitudes for nonstandard [ital WWZ] couplings.

Abstract

We demonstrate that the Standard Model amplitude for $f_1 \bar f_2 \rightarrow W^\pm Z $ at the Born-level exhibits an approximate zero located at $\cosθ= (g^{f_1}_{-} + g^{f_2}_{-}) / (g^{f_1}_{-} - g^{f_2}_{-})$ at high energies, where the $g^{f_i}_{-}$ ($i=1,2$) are the left-handed couplings of the $Z$-boson to fermions and $θ$ is the center of mass scattering angle of the $W$-boson. The approximate zero is the combined result of an exact zero in the dominant helicity amplitudes ${\cal M}(\pm,\mp)$ and strong gauge cancelations in the remaining amplitudes. For non-standard $WWZ$ couplings these cancelations no longer occur and the approximate amplitude zero is eliminated.

Figures (4)

• Figure 1: Feynman diagrams contributing to the Born-level subprocess $f_1 \bar{f}_2 \rightarrow W Z$.
• Figure 2: Differential cross section $d\sigma(\lambda_{\rm w}, \lambda_{\rm z})/d\cos\theta$ versus the $W^-$ scattering angle $\theta$ in the center of mass frame for the Born-level processes (a) $e^- \bar{\nu}_e \rightarrow W^-Z$ and (b) $d \bar{u} \rightarrow W^-Z$. The dashed, dotted, and dash-dotted curves are for $(\lambda_{\rm w},\lambda_{\rm z})=(0,0)$, $(+,-)$, and $(-,+)$, respectively. The solid line represents the total (unpolarized) cross section. For comparison, the long dashed curve in (a) shows the $e^+e^-\rightarrow ZZ$ cross section, normalized to the $e^-\bar{\nu}_e \rightarrow W^-Z$ cross section at $\cos\theta=0.9$.
• Figure 3: Differential cross section $d\sigma/d\cos\theta$ versus the $W^-$ scattering angle $\theta$ in the center of mass frame for the Born-level processes (a) $e^- \bar{\nu}_e \rightarrow W^-Z$ and (b) $d \bar{u} \rightarrow W^-Z$. The dotted, dashed, and solid curves are for ${\sqrt{s}=0.2}$, 0.5, and 2 TeV, respectively.
• Figure 4: Differential cross sections for the subprocess $d \bar{u} \rightarrow W^-Z$ at ${\sqrt{s}=500}$ GeV with anomalous couplings as defined in Eq. (\ref{['EQ:LAGRANGE']}). Parts a), b), and c) are for $\lambda = 0.1$, $\Delta g_1 = 0.2$, and $\Delta \kappa = 0.5$, respectively. The solid (dashed) lines give the total differential cross section with (without) anomalous $WWZ$ couplings. The dotted curves show the cross section for the helicity state which produces the largest non-standard contribution for the given anomalous coupling.