General Analysis of the Charged Higgs Sector of the $Y=0$ Triplet-Singlet Extension of the MSSM at the LHC

We investigate the extended Higgs sectors, specially the charged Higgs sector in a supersymmetric $Y=0$ $SU(2)$ triplet and a Standard Model (SM) gauge singlet extension of SM. We show that in this model the allowed data for the Higgs boson interaction eigenstates tend to group into separate blocks for $SU(2)$ triplet, doublet and singlet. The triplet sector has two degenerate paired states, each pair composed of a mostly-triplet charged Higgs and of a mostly-triplet scalar or pseudoscalar state. The mostly-doublet sector involves a Standard Model like Higgs of 125 GeV and extra mass-degenerate states, composed of a charged, a scalar and a pseudoscalar. The CP-odd component of the singlet scalar, after supersymmetry breaking, takes the role of a pseudo-Nambu-Goldstone mode in the $Z_3$ symmetric case, while the CP-even one becomes decoupled. In a second part of our study we investigate the different decay processes allowed to a charged Higgs boson of this model. Specifically, we search for general signatures of the TNMSSM in order to distinguish among Higgs fields belonging to $SU(2)$ doublet, triplet and singlet representations at the LHC. We also propose few golden plated final state modes carrying the distinctive signatures of this model which could be investigated in collider searches. We also show how in the decoupling limit of the triplet ($|λ_T| \simeq 0$) affects the decays as well as the production channels at the LHC.