On New Physics Contributions to the Higgs Decay to $Z\gamma$

We explore models of new physics that can give rise to large (100% or more) enhancements to the rate of Higgs decay to $Z\gamma$ while still being consistent with other measurements. We show that this is impossible in simple models with one additional multiplet and also in well motivated models such as the MSSM and folded SUSY. We do find models with several multiplets that carry electroweak charge where such an enhancement is possible, but they require destructive interference effects. We also show that kinematic measurements in Higgs decay to four leptons can be sensitive to such models. Finally we explore the sensitivity of four lepton measurements to supersymmetric models and find that while the measurement is difficult with the high luminosity LHC, it may be possible with a future high energy hadron collider.