Abstract
We examine the standard and the new physics (NP) contributions to the $ZZZ,$ $\mathrm{ZZ}\ensuremath{\gamma},$ and $Z\ensuremath{\gamma}\ensuremath{\gamma}$ neutral gauge couplings. At the one-loop level, if we assume that there is no $\mathrm{CP}$ violation contained in NP beyond the standard model (SM) one, we find that only $\mathrm{CP}$ conserving neutral gauge couplings are generated, either from the standard quarks and leptons, or from possible new physics fermions. Bosonic one-loop diagrams never contribute to these couplings, while the aforementioned fermionic contributions satisfy ${h}_{3}^{Z}\ensuremath{\simeq}\ensuremath{-}{f}_{5}^{\ensuremath{\gamma}},$ ${h}_{4}^{Z}{=h}_{4}^{\ensuremath{\gamma}}=0.$ We also study examples of two-loop NP effects that could generate nonvanishing ${h}_{4}^{\ensuremath{\gamma},Z}$ couplings. We compare quantitative estimates from SM, minimal supersymmetric standard model (MSSM), and some specific examples of NP contributions, and we discuss their observability at future colliders.
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