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

TL;DR

This paper calculates one-loop contributions to $ZZV^*$ couplings from $CP$-violating flavor-changing neutral currents involving $Z$ and $Z'$ bosons, providing analytical results and estimating form factors within various models.

Contribution

It presents the first detailed analytical calculations of $CP$-violating $ZZV^*$ couplings from flavor-changing neutral currents mediated by $Z$ and $Z'$ bosons, including constraints and estimates.

Findings

$f_5^{ ext{γ}}$ can be of order $10^{-3}$

$f_5^{Z}$ and $f_4^{Z}$ are of order $10^{-6}$ and $10^{-5}$

$f_5^{Z'}$ can reach order $10^{-1}$ to $10^{-2}$

Abstract

The one-loop contributions to the trilinear neutral gauge boson couplings $ZZV^\ast$ ($V=\gamma,Z,Z'$), 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 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 $t\rightarrow Z q$ 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 $ZZZ^\ast$ 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 $ZZ{Z'}^{*}$ 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.