Contributions to $ZZ{V}^{\ast }$ ($V=\gamma ,Z,Z^{\prime }$) couplings from $CP$ violating flavor changing couplings

Abstract

The one-loop contributions to the trilinear neutral gauge boson couplings $ZZ{V}^{\ast }$ ($V=\gamma ,Z,Z^{\prime }$), 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 $Z^{\prime }$. Analytical results are presented in terms of both Passarino-Veltman scalar functions and closed form 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 $t\to Zq$ decays. It is found that in the case of the $ZZ{\gamma }^{\ast }$ vertex the only non-vanishing form factor is $f_5^{\gamma }$, which can be of the order of $10^{-3}$, whereas for the $ZZ{Z}^{\ast }$ 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 $ZZ{Z^{\prime }}^{\ast }$ form factors arising from both diagonal and non-diagonal $Z^{\prime }$ couplings within a few extension models. It is found that in the diagonal case $f_5^{Z^{\prime }}$ 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 $f_4^{Z^{\prime }}$ can reach values as large as $10^{-7}-10^{-8}$, with the largest contributions arising from the $Z^{\prime }tq$ couplings.

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