Signatures of the anomalous Zγ and ZZ production at the lepton and hadron Colliders

The possible form of New Physics (NP) interactions affecting the ZZZ, $ZZ \gamma$ and $Z\gamma \gamma$ vertices, is critically examined. Their signatures and the possibilities to study them, through ZZ and $Z\gamma$ production, at the e^-e^+ Colliders LEP and LC and at the hadronic Colliders Tevatron and LHC, are investigated. Experimental limits obtained or expected on each coupling are collected. A simple theoretical model based on virtual effects due to some heavy fermions is used for acquiring some guidance on the plausible forms of these NP vertices. In such a case specific relations among the various neutral couplings are predicted, which can be experimentally tested and possibly used to constrain the form of the responsible NP structure.