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

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 ∝ E$^{5}$, which can be probed sensitively via the reaction e$^{+}$e$^{−}$ → Zγ. We demonstrate that measuring the nTGCs via the reaction e$^{+}$e$^{−}$ → Zγ followed by $Z\rightarrow q\bar{q}$ 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$^{−1}$. 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.