Probing anomalous $W^-W^+γ/Z$ couplings in the SMEFT with $e^-e^+ \to W^-W^+ \to 4j/\ell^-\ell^+\slashed{E}$ channel

TL;DR

This work evaluates anomalous $W^-W^+\gamma/Z$ couplings in the SMEFT with the HISZ basis at a future $e^-e^+$ collider operating at $\sqrt{s}=250$ GeV. By analyzing $e^-e^+\to W^-W^+\to 4j$ and $e^-e^+\to \ell^-\ell^++\slashed{E}$ (plus a semileptonic channel), and employing machine learning for WW reconstruction, jet-charge tagging, jet-flavor tagging, and neural-network neutrino reconstruction, the authors build a large set of polarization and spin-correlation observables across eight production-angle bins. A combined MCMC analysis of all three channels yields marginalized 95% CL limits on the five Wilson coefficients $c_{WWW}, c_W, c_B, c_{\widetilde{W}WW}, c_{\widetilde{W}}$, with CP-even and CP-odd observables showing complementary sensitivity and reducing flat directions. The fully hadronic channel provides strongest sensitivity to $c_B$ and $c_{\widetilde{W}}$, while the semi-leptonic channel tightens bounds on $c_{WWW}, c_W, c_{\widetilde{W}WW}$, and the leptonic channel adds complementary information; systematic uncertainties and luminosity determine the ultimate precision, underscoring the value of a multi-channel, ML-assisted SMEFT program for electroweak precision at future $e^-e^+$ colliders.

Abstract

We investigate anomalous charged triple gauge boson couplings induced by $SU(2)_L \times U(1)_Y$ gauge-invariant dimension-6 operators in the HISZ basis through the processes $e^-e^+ \to 4j$ and $e^-e^+ \to \ell^-\ell^+ + \text{missing energy}$ at $\sqrt{s}=250\,$GeV with longitudinally polarized beams. The analysis includes three CP-even operators $(O_{WWW}, O_W, O_B)$ and two CP-odd operators $(\tilde O_{WWW}, \tilde O_W)$, which parameterize deviations in the $W^-W^+γ/Z$ vertex. All leading-order contributions are included, including interference between $W^-W^+$ production and non-resonant amplitudes. In the $e^-e^+ \to 4j$ channel, $W^-W^+$ candidates are selected using boosted decision trees. The $W$-boson charges are reconstructed using a jet-charge observable, and jet flavors from $W$ decays are identified with a dedicated classifier, enabling measurements of vector polarization and correlation asymmetries. In the $e^-e^+ \to \ell^-\ell^+ + \text{missing energy}$ channel, events are selected with cuts on lepton transverse momentum and dilepton mass, and the two neutrino momenta are reconstructed using neural-network regression. Combining total cross sections with spin asymmetries allows constraints on anomalous gauge couplings. The fully hadronic channel provides the strongest sensitivity to $O_B$ and $\tilde O_W$, while the semi-leptonic channel yields tighter limits on $O_{WWW}$, $O_W$, and $\tilde O_{WWW}$. The fully leptonic channel adds complementary sensitivity. Finally, we derive marginalized limits on all five operators using a Markov Chain Monte Carlo analysis for several choices of systematic uncertainties and integrated luminosities.

Figures (18)

• Figure 1: Schematic Feynman diagrams at lowest order for $4j$ events in final state at $e^-e^+$ collider. The top row represents the one/two-resonant $ZZ/\gamma$, and $W^-W^+$ amplitudes with coupling order of $\alpha_{\mathrm{EW}}^2$. The middle row amplitudes represents gluons in the final state of order $\alpha_{\mathrm{EW}}\alpha_S$, and the bottom row contains zero-resonant amplitudes with four quarks in final states with coupling order of $\alpha_{\mathrm{EW}}^2$.
• Figure 2: Schematic representation of Feynman diagrams for $e^-e^+ \to l^-l^+ \slashed{E}$ process at the leading order.
• Figure 3: Schematic representation of polarization and spin-correlation asymmetries, categorized by their CP properties and flavor dependence. Asymmetries shown in red indicate flavor-dependent observables, while those in blue are flavor independent. The symbols labeled with E denote CP-even, and those with O denote CP-odd asymmetries.
• Figure 4: Detector level distribution of number of jets and invariant mass of pair of jets for four different processes at $\sqrt{s}=250$ GeV. The distribution are obtained for $e^-e^+ \to 4j$ process along with di-boson ($W^-W^+, ZZ$) and QCD production. The detector analysis is achieved with simulation with ILC detector implemented in Delphes.
• Figure 5: We show the confusion matrix and ROC curves to highlight the efficiency of network to classify signal events ($W^+W^-$) from the $ZZ$ and QCD backgrounds.