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

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