Extended Higgs sectors in the context of supersymmetry at the LHC

We studied the extension of Standard Model (SM) Higgs sector with $SU(2)$ triplet and SM gauge singlet in the context of supersymmetry. For a $Z_3$ symmetric superpotential where the singlet field generates the bi-linear Higgs mixing term between two Higgs doublets dynamically. Models like this often have a very light pseudoscalar as pseudo-Nambu Goldstone model of an extra $U(1)$ symmetry. We investigate the possibility of such light hidden Higgs boson with the data of the discovered Higgs boson around 125 GeV. Along with the neutral sector, the charged Higgs bosons in the triplet extended case are really interesting as the triplet charged Higgs bosons give rise to new decay mode to $Z W^\pm$ along with $ a_1 W^\pm$ due to the existence of light pseudoscalar. These new modes can be looked for at the LHC in the search for the Higgs bosons in other representations of $SU(2)$.