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 ∝ E⁵, 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.

在标准模型有效理论中，直到6维算子都没有中性三元规联轴器（nTGC），但是它可能来自8维算子。在这项工作中，我们研究了8维的纯规范算子，这些算子对nTGC有所贡献，并且与涉及希格斯二重峰的8维算子无关。我们表明，纯规范运营商产生既ZγZ*和Zγγ*顶点与快速的能量依赖性α ë ⁵，它可以通过灵敏的反应来探测ë ⁺ ë ^- → Zγ。我们表明，通过反应测量nTGCs ë ⁺ ë ^- → Zγ紧接着\（Z \ rightarrow q \ bar {q} \）衰变可以在CEPC，FCC-ee和ILC对撞机上探测8维纯量规算子的新物理尺度，最高可达（1-5）TeV范围。\（\ sqrt {s} =（0.25-1）\） TeV，并在CLIC上使用\（\ sqrt {s} =（3-5）\） TeV达到（10–16）TeV 。每种情况的综合发光度均为5 ab ^-1。我们将这些敏感性与涉及希格斯双峰的8维nTGC算子和有助于e ⁺ e ^- Zγ顶点的8维铁离子接触算子的相应探针进行了比较。