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CP-odd contributions to the $ZZ^\astγ$, $ZZγ^\ast$, and $ZZZ^\ast$ vertices induced by nondiagonal charged scalar boson couplings

In models with extended scalar sectors with several Higgs multiplets, such as Higgs triplet models, the $Z$ gauge boson can have nondiagonal couplings to charged Higgs bosons. In a model-independent way, we study the potential contributions arising from such theories to the CP-violating trilinear neutral gauge boson couplings $ZZ^*γ$, $ZZγ^*$, and $ZZZ^*$, which are parametrized by four form factors: $h^Z_{1,2}$, $f_4^γ$, and $f_4^Z$, respectively. Such form factors can only be induced if there are at least two nondegenerate charged Higgs scalars and an imaginary phase in the coupling constants. For the masses of the charged scalar bosons we consider values above 300 GeV and find that the form factors can reach the following orders of magnitude: $|h_1^Z|\sim 10^{-5}-10^{-4}$, $|h_2^Z|\sim 10^{-7}-10^{-6}$, $|f_4^γ|\sim 10^{-5}-10^{-3}$ and $|f_4^Z|\sim 10^{-6}-10^{-5}$, though there could be an additional suppression factor arising from the coupling constants. We also find that the form factors decouple at high energies and are not very sensitive to a change in the masses of the charged scalar bosons. Apart from a proportionality factor, our results for the $f_4^Z$ form factor, associated with the $ZZZ^*$ vertex, is of the same order of magnitude than that induced via nondiagonal neutral scalar boson couplings in the framework of a two-Higgs doublet model.