Loop induced $h \rightarrow γγ, Zγ, gg$ decays in 3-Higgs doublet models

In this paper, we analyze the loop induced decays of neutral Higgs boson $h$ into pairs of photons, gluons, and Z$γ$ in 3-Higgs Doublet Models (3HDMs), where all the doublets have non-zero vacuum expectation values. In the 3HDM, there are contributions to these decays from loops of charged scalars $H^{\pm}_{1,2}$ that are not present in the Standard Model. We find an enhancement in the channel $h\rightarrow Zγ$ with respect to the Standard Model prediction in some parameter region while respecting constraints from the measurements of $h\rightarrow γγ$ at the LHC. The charged Higgs bosons $H^{\pm}_{1,2}$ lead to the enhancement of $Zγ$ decay mode in some part of the parameter space of the 3HDM. Then, we discuss the correlations between the decay modes $h\rightarrow Zγ$ and $h\rightarrow γγ$. Moreover, we study Type-I and Type-Z of 3HDMs and find that these types of 3HDMs can be distinguished via only the gluonic decays, since the contributions of the $H^{\pm}_{1,2}$ loops are dominant to those of fermion loops. We also investigate the effects of the model parameters on these loop induced decays. As an interesting phenomenological consequence, the 3HDM is dominantly governed by the parameters: two ratios of vacuum expectation values (VEVs); $\tanγ,~\tanβ$ and the mixing angles of the CP-even Higgs bosons, $α_{1,2}~ \text{and}~θ$.

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