Contributions to $$ZZV^*$$ Z Z V ∗ ( $$V=\gamma ,Z,Z'$$ V = γ , Z , Z ′ ) couplings from CP violating flavor changing couplings

Abstract

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