Probing the Scale of New Physics in the $ZZγ$ Coupling at $e^+e^-$ Colliders

TL;DR

The paper analyzes how dimension-8 SMEFT operators generate neutral triple gauge couplings ZZγ/Zγγ and how future $e^+e^-$ colliders can probe the associated new-physics scale Λ via the process $e^+e^-\to Zγ$ with $Z$ decaying to leptons or invisibles. It identifies the unique CP-even dim-8 operator ${\mathcal O}_{\widetilde{B}W}$ as the source of nTGCs and develops a fully gauge-invariant framework to study the $Zγ$ final state, including detailed angular observables and the role of beam polarization for background suppression. The authors quantify sensitivities across CEPC, FCC-ee, ILC, and CLIC, showing that Λ can be probed in the multi-TeV range and that including ${\cal O}(\Lambda^{-8})$ terms significantly improves reach at higher energies. They demonstrate robust strategies combining leptonic and invisible $Z$ decays and explore polarized beams to maximize significance, providing guidance for experimental studies at forthcoming lepton colliders.

Abstract

The $ZZγ$ triple neutral gauge couplings are absent in the Standard Model (SM) at the tree level. They receive no contributions from dimension-6 effective operators, but can arise from effective operators of dimension-8. We study the scale of new physics associated with such dimension-8 operators that can be probed by measuring the reaction $e^+e^-\to Zγ$, followed by $Z \to \ell\bar{\ell},ν\barν$ decays, at future $e^+e^-$ colliders including the ILC, CEPC, FCC-ee and CLIC. We demonstrate how angular distributions of the final state mono-photon and leptons can play a key role in suppressing SM backgrounds. We further show that using electron/positron beam polarizations can significantly improve the signal sensitivities. We find that the dimension-8 new physics scale can be probed up to the multi-TeV region at such lepton colliders.

Figures (6)

• Figure 1: Illustration of the kinematical structure of the reaction $\,e^+e^-\!\!\rightarrow Z\gamma\,$ followed by the leptonic decay $\,Z\!\rightarrow \ell^+\ell^-$ in the laboratory frame ($\,e^-e^+$ collision frame).
• Figure 2: Normalized angular distributions in the polar scattering angle $\theta$ in the laboratory frame for different collision energies,$\sqrt{s}=(250\,\text{GeV}, 500\,\text{GeV}, 1\,\text{TeV}, 3\,\text{TeV})$. In each plot, the black, red and blue curves denote the contributions from the SM, the ${\cal O}(\Lambda^{-4})$ and ${\cal O}(\Lambda^{-8})$ terms, respectively. We use a polar angle cut $\,\delta=0.2\,$ for illustration.
• Figure 3: Normalized angular distribution in the polar angle $\theta_*^{}$ in the $Z$ decay frame for different collision energies,$\sqrt{s}=(250\,\text{GeV}, 500\,\text{GeV}, 1\,\text{TeV}, 3\,\text{TeV})$. In each plot, the black, red and blue curves denote the contributions from the SM, the ${\cal O}(\Lambda^{-4})$ and ${\cal O}(\Lambda^{-8})$ terms, respectively, where the red and blue curves exactly overlap. We use a laboratory polar angle cut $\delta=0.2$ for illustration.
• Figure 4: Normalized angular distribution in the azimuthal angle $\phi_*^{}$ for different collision energies,$\sqrt{s}=(250\,\text{GeV}, 500\,\text{GeV}, 1\,\text{TeV}, 3\,\text{TeV})$. In each plot, the black, red and blue curves denote the contributions from the SM, the ${\cal O}(\Lambda^{-4})$ and ${\cal O}(\Lambda^{-8})$ terms, respectively, where the blue and black curves nearly overlap. We use a laboratory polar angle cut $\delta=0.2$ for illustration.
• Figure 5: Analysis of the significance $\mathcal{Z}_{4}^{}\!=S/\Delta_B^{}$. Plot (a) depicts $\mathcal{Z}_{4}^{}$ as a function of $\,\delta$ . Plot (b) presents $\,\mathcal{Z}_{4}^{}$ for $\,\delta=\delta_{\text{m}}^{}$ as a function of the new physics scale $\Lambda$ . For illustration, we choose the collision energy$\sqrt{s\,}=3\,\text{TeV}$and the integrated luminosity$\,\mathcal{L}=2\,\text{ab}^{-1}$.