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New Scalar Contributions to $h\to Zγ$

We calculate the Higgs decay rate of $h\to Zγ$ by including the contributions from new scalars with arbitrary quantum numbers of the weak isospin ($T$) and hypercharge ($Y$) in the standard model. We find that our general formula for the decay rate of $h\to Zγ$ matches with that for $h\to γγ$ in the limit of $m_Z=0$, but it is different from those in the literature. To illustrate our result, by taking the current $2σ$ excess of the $h\to γγ$ rate measured by the LHC, we examine the corresponding shift for the $Zγ$ decay channel due to the new scalar. We show that the enhancement or reduction of the $h\to Zγ$ rate only depends on the relative size of $T$ and the absolute value of $Y$. Explicitly, we predict $0.76<R_{Zγ}\equiv Γ(h\to Zγ)/Γ_{SM}(h\to Zγ)<2.05$ by imposing the observed range of $1.5<R_{γγ}\equiv Γ(h\to Zγγ)/Γ_{SM}(h\toγγ)<2$, which is independent of the number of multiplets and the couplings to the Higgs particle as long as the scalars are heavier than 200 GeV. This result provides a clear signature for the future LHC measurements to test physics beyond the standard model.