Higgs bosons: discovered and hidden, in extended Supersymmetric Standard Models at the LHC

We investigate an extension of the Minimal Supersymmetric Standard Model (MSSM) containing a $SU(2)$ Higgs triplet of zero hypercharge and a gauge singlet. We focus on a scenario of this model which allows a light pseudoscalar and/or a scalar below $100$ GeV in the spectrum, consistent with the most recent data from the LHC and the earlier data from the LEP experiments. We analyze the exotic decay of the discovered Higgs $(h_{125})$ into two light (hidden) Higgs bosons present in the extension. The latter are allowed by the uncertainties in the Higgs decay $h_{125}\to WW^*$, $h_{125}\to ZZ^*$ and $h_{125}\to \gamma\gamma$. We have searched for such light Higgs bosons in the $2b+2\tau$, $\geq 3\tau$, $2b+2\mu$ and $2\tau+2\mu$ final states at the LHC with 13 and 14 TeV. A region of such parameter space can be explored with an integrated luminosity of 25 fb$^{-1}$ at the LHC.