Extended Higgs sector of 2HDM with real singlet facing LHC data

We study the phenomenology of the two Higgs doublet model with a real singlet scalar $S$ (2HDMS). The model predicts three CP-even Higgses $h_{1,2,3}$, one CP-odd $A^0$ and a pair of charged Higgs. We discuss the consistency of the 2HDMS with theoretical as well as with all available experimental data. In contrast with previous studies, we focus on the scenario where $h_2$ is the Standard Model (SM) 125 GeV Higgs, while $h_1$ is lighter than $h_2$ which may open a window for Higgs to Higgs decays. We perform an extensive scan into the parameter space of 2HDMS of type I and explore the effect of the singlet-doublet admixture. We found that a large singlet-doublet admixture is still compatible with the recent Higgs data from LHC. Moreover, we show that $h_1$ could be quasi-fermiophobic and would decay dominantly into two photons. We also study in details the consistency of the non-detected decay of $h_2\to h_1 h_1$ with LHC data followed by $h_1\to \gamma \gamma$ which leads to four photons final state at LHC: $pp\to h_2\to h_1 h_1\to 4\gamma$. Using the results of null searches of multi-photons carried by the ATLAS collaboration, we have found that a large area of the parameter space is still allowed. We also demonstrate that various neutral Higgs of the 2HDMS could have several exotic decays.