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Production of multiple charged Higgs bosons in 3-3-1 models

We undertake the study of the charged Higgs bosons predicted by the model with gauge symmetry $SU(3)_c \otimes SU(3)_L \otimes U(1)_X$. By considering Yukawa mixing couplings between small ($\sim$ GeV) and large ($\sim$ TeV) scales, we show that the hypercharge-one $H_1^{\pm}$ and hypercharge-two $H_2^{\pm}$ Higgs bosons predicted by the model, can be simultaneously produced in $pp$ collisions at different production rates. At low energy, the $H_1^{\pm}$ bosons exhibit the same properties as the charged Higgs bosons from a two Higgs doublet model (2HDM), while $H_2^{\pm}$ are additional like-charged Higgs bosons from the underlying 3-3-1 model. Thus, the identification of multiple like-charged Higgs boson resonances may test the compatibility of theoretical models with experimental data. We study $H_{1,2}^{\pm}$ pair and associated $tbH_{1,2}^{\pm}$ productions at CERN LHC collider. In particular, we obtain that pair production can be as large as the single production in gluon-gluon collisions due to the interchange of a heavy neutral $Z'$ gauge boson predicted by the model. By considering decays to leptons $H_{1,2}^{\pm} \rightarrow τν_τ$, we obtain scenarios where small peaks of $H_{2}^{\pm}$-boson events in transverse mass distributions can be identified over the $H_{1}^{\pm}$ background.