Probing New Physics in Dimension-8 Neutral Gauge Couplings at $e^+e^-$ Colliders

TL;DR

The paper shows that dimension-8 pure-gauge operators in SMEFT can induce neutral triple gauge couplings (nTGCs) absent at lower orders, with the operator O_G+ generating ZγZ^* and Zγγ^* vertices that scale as E^5. By studying e^+e^- → Zγ with hadronic Z decays and exploiting angular observables, the authors derive strong sensitivity to the new physics scale Λ, outperforming Higgs-related and fermionic dim-8 operators in many collider scenarios. Hadronic Z decays offer substantially enhanced reach, pushing Λ into the multi-TeV regime (and up to ~10–16 TeV for CLIC-type energies), especially when polarization and high luminosity are employed. The work provides a comprehensive framework for constraining nTGCs at future e^+e^- colliders and highlights the complementary role of high-dimension operators in probing UV physics beyond the SM.

Abstract

Neutral triple gauge couplings (nTGCs) are absent in the standard model effective theory up to dimension-6 operators, but could arise from dimension-8 effective operators. In this work, we study the pure gauge operators of dimension-8 that contribute to nTGCs and are independent of the dimension-8 operator involving the Higgs doublet. We show that the pure gauge operators generate both $ZγZ^*$ and $Zγγ^*$ vertices with rapid energy dependence $\propto E^5$, which can be probed sensitively via the reaction $e^+e^- \to Zγ$. We demonstrate that measuring the nTGCs via the reaction $e^+e^- \to Zγ$ followed by $Z \to q\bar{q}$ decays can probe the new physics scales of dimension-8 pure gauge operators up to the range $(1-5)$TeV at the CEPC, FCC-ee and ILC colliders with $\sqrt{s}=(0.25-1)$TeV, and up to the range $(10-16)$TeV at CLIC with $\sqrt{s}=(3-5)$TeV, assuming in each case an integrated luminosity of 5/ab. We compare these sensitivities with the corresponding probes of the dimension-8 nTGC operators involving Higgs doublets and the dimension-8 fermionic contact operators that contribute to the $e^+e^-Zγ$ vertex.

Figures (7)

• Figure 1: Kinematical structure of the reaction $\,e^+e^-\!\!\rightarrow Z\gamma\,$ followed by the hadronic decays $\,Z\!\rightarrow q\bar{q}\,$, in the $\,e^+e^-$ collision frame.
• Figure 2: Feynman diagrams that contribute to the reaction $e^-e^+\!\!\rightarrow\! \gamma\,q\bar{q}$ . Type (a) provides the signals via the nTGC vertex $Z^*Z\gamma$ or $\gamma^*Z\gamma$, arising from the relevant dimension-8 operator, while types (b) and (c) give the SM backgrounds. Diagram (b) together with a similar $u$-channel diagram for $\,e^-e^+\!\!\rightarrow\! Z\gamma\!\rightarrow\!\gamma q \bar{q}$ presents an irreducible background. Diagram (c) has the $s$-channel gauge-boson exchange and final-state $\gamma$ radiation, providing a reducible background. Diagram (d) arises from the contact vertex $eeZ\gamma$ which is generated by the relevant dimension-8 fermion-bilinear operator.
• Figure 3: Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\rightarrow Z\gamma$ followed by $Z\!\rightarrow d\bar{d}$ decays, as generated by $\,\mathcal{O}_{G+}^{}$ at the collision energies $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$ TeV, respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{\cal O}(\Lambda^{-4})$, and the quadratic term of $\,{\cal O}(\Lambda^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.
• Figure 4: Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\rightarrow Z\gamma$ followed by $Z\!\rightarrow\! d\bar{d}$ decays, as generated by $\,\mathcal{O}_{G-}^{}$ at collision energies $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$ TeV, respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${O}(\Lambda^{-4})$, and the quadratic term of ${O}(\Lambda^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.
• Figure 5: Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\rightarrow\! Z\gamma$ followed by $Z\!\rightarrow d\bar{d}$ decays, as generated by $\,\mathcal{O}_{\widetilde{B}W}^{}$ at the collision energies $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$ TeV, respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{O}(\Lambda^{-4})$, and the quadratic term of $\,{O}(\Lambda^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\,\delta=0.2\,$ for illustration.