The one-loop contributions to the trilinear neutral gauge boson couplings \(ZZV^*\) (\(V=\gamma ,Z,Z'\)), parametrized in terms of one CP-conserving \(f_5^{V}\) and one CP-violating \(f_4^{V}\) form factors, are calculated in models with CP-violating flavor changing neutral current couplings mediated by the Z gauge boson and an extra neutral gauge boson \(Z'\). Analytical results are presented in terms of Passarino-Veltman scalar functions. Constraints on the vector and axial couplings of the Z gauge boson \(\left| g_{{VZ}}^{tu}\right| < 0.0096\) and \(\left| g_{{VZ}}^{tc}\right| <0.011\) are obtained from the current experimental data on the \(t\rightarrow Z q\) decays. It is found that in the case of the \(ZZ\gamma ^*\) vertex the only non-vanishing form factor is \(f_5^{\gamma }\), which can be of the order of \(10^{-3}\), whereas for the \(ZZZ^*\) vertex both form factors \(f_5^{Z}\) and \(f_4^{Z}\) are non-vanishing and can be of the order of \(10^{-6}\) and \(10^{-5}\), respectively. Our estimates for \(f_5^{\gamma }\) and \(f_5^{Z}\) are smaller than those predicted by the standard model, where \(f_4^{Z}\) is absent up to the one loop level. We also estimate the \(ZZ{Z'}^{*}\) form factors arising from both diagonal and non-diagonal \(Z'\) couplings within a few extension models. It is found that in the diagonal case \(f_{5}^{Z'}\) is the only non-vanishing form factor and its real and imaginary parts can be of the order of \(10^{-1}\)–\(10^{-2}\) and \( 10^{-2}\)–\(10^{-3}\), respectively, with the dominant contributions arising from the light quarks and leptons. In the non-diagonal case \(f_{5}^{Z^\prime }\) can be of the order of \(10^{-4}\), whereas \(f_4^{Z'}\) can reach values as large as \(10^{-7}\)–\(10^{-8}\), with the largest contributions arising from the \(Z'tq\) couplings.

对三线性中性规范玻色子耦合\（ZZV ^ * \）（\（V = \ gamma，Z，Z'\））的单环贡献是根据一个CP守恒\（f_5 ^ {V} \）和一个CP -violating \（F_4 ^ {V} \）的形状因子，在模型计算与CP -violating风味改变由介导的中性电流联轴器ž规范玻色子和一个额外的中性规范玻色子\（Z'\）。分析结果以Passarino-Veltman标量函数表示。Z规格玻色子\（\ left | g _ {{VZ}} ^ {tu} \ right | <0.0096 \）的矢量和轴向耦合的约束，\（\ left | g _ {{VZ}} ^ {tc} \ right | <0.011 \）是从\（t \ rightarrow Z q \）衰减的当前实验数据获得的。发现在\（ZZ \ gamma ^ * \）顶点的情况下，唯一不消失的形状因子是\（f_5 ^ {\ gamma} \），其大小可能约为\（10 ^ { -3} \），而对于\（ZZZ ^ * \）顶点，形状因数\（f_5 ^ {Z} \）和\（f_4 ^ {Z} \）都不会消失，并且可以为\（10 ^ {-6} \）和\（10 ^ {-5} \）。我们对\（f_5 ^ {\ gamma} \）和\（f_5 ^ {Z} \）的估计小于标准模型所预测的值，在标准模型中，直到一个循环级别都没有\（f_4 ^ {Z} \）。我们还估计了一些扩展模型中对角和非对角\（Z'\）耦合产生的\（ZZ {Z'} ^ {*} \）形状因数。发现在对角线情况下\（f_ {5} ^ {Z'} \）是唯一不消失的形状因数，其实部和虚部可以为\（10 ^ {-1} \ ） – \（10 ^ {-2} \）和\（10 ^ {-2} \） – \（10 ^ {-3} \），分别由轻夸克和轻子产生。在非对角情况下，\（f_ {5} ^ {Z ^ \ prime} \）的数量级为\（10 ^ {-4} \），而\（f_4 ^ {Z'} \）可以达到\（10 ^ {-7} \） – \（10 ^ {-8} \）大的值，\（Z'tq \）耦合产生的最大贡献。