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One of the most-studied signals for physics beyond the standard model in theproduction of gauge bosons in electron-positron collisions is that due to theanomalous triple gauge boson couplings in the $Z \gamma$ final state. In thiswork, we study the implications of this at the ILC with polarized beams forsignals that go beyond traditional anomalous triple neutral gauge bosoncouplings. Here we report a dimension-8 CP-conserving $Z \gamma Z$ vertex thathas not found mention in the literature. We carry out a systematic study of theanomalous couplings in general terms and arrive at a classification. We thenobtain linear-order distributions with and without CP violation. Furthermore,we place the study in the context of general BSM interactions represented by$e^+e^- Z \gamma$ contact interactions. We set up a correspondence between thetriple gauge boson couplings and the four-point contact interactions. We alsopresent sensitivities on these anomalous couplings, which will be achievable atthe ILC with realistic polarization and luminosity.

New Physics in $e^+e^- \rightarrow Z \gamma$ at the ILC with polarized beams: Explorations beyond conventional anomalous triple gauge boson coupling