The significance of new physics appearing in the loop-induced decays of
neutral Higgs bosons into pairs of di-bosons $\gamma\gamma$ and $Z\gamma$ will
be discussed in the framework of the 3-3-1 models based on a recent work
[arXiv:1604.01948] where the Higgs sector were considered as an extension of
that from the well-known Two Higgs Doublet models (2HDM). For large $SU(3)_L$
scale $v_3\simeq10$ TeV, dominant one-loop contributions to the amplitudes of
the two decays arise from only the single charged Higgs boson predicted by the
2HDM, leading to that experimental constraint on the signal strength
$\mu^{331}_{\gamma\gamma}$ of the Standard model like Higgs boson decay
$h\rightarrow \gamma\gamma$ will result in a strict upper bound on the signal
strength $\mu^{331}_{Z\gamma}$ of the decay $h\rightarrow\, Z\gamma$. For a
particular model with lower $v_3$ around 3 TeV, contributions from heavy
charged gauge and Higgs bosons may have the same order. Therefore, their
destructive or constructive correlations may affect significantly on the two
signal strengths. In particularly, a deviation from the SM prediction
$|\mu^{331}_{\gamma\gamma}-1| \le 0.04$ still allows $|\mu^{331}_{Z\gamma}-1|$
to reach values near 0.1. We also show that there exists an CP-even neutral
Higgs boson $h^0_3$ predicted by the 3-3-1 models, but beyond the 2HDM, has an
interesting property that the branching ratio Br$(h^0_3\rightarrow
\gamma\gamma)$ is very sensitive to the parameter $\beta$ used to distinguish
different 3-3-1 models.

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HEPPhenoPapers:
Neutral Higgs decays $H \rightarrow Z \gamma,\gamma\gamma$ in 3-3-1 models. https://t.co/D2qbhywEgx