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Probing CP Violation in $h \to Zγ$ with Background Interference

We show that the parity of the $h Zγ$ vertex can be probed by interference between the gluon fusion Higgs production, $gg \to h \to γZ \to γ\ell^+\ell^-$, and the background, $gg \to γZ \to γ\ell^+\ell^-$, amplitudes. In the presence of a parity violating $hZγ$ vertex, this interference alters the kinematic distribution of the leptons and photon compared to Standard Model (SM) expectations. For a Higgs with SM-sized width and couplings, we find that the size of the effect enters at most at the $10^{-2}$ level. Such a small effect cannot be seen at the LHC, even with futuristic high luminosities. Should there exist other broader scalar particles with larger production cross-section times branching ratio to $Zγ$, then the parity structure of their $Zγ$ couplings can be probed with this technique.