Dark Matter and Collider Searches in $S_3$-Symmetric 2HDM with Vector Like Leptons

We study the $S_3$-symmetric two Higgs doublet model by adding two generations of vector like leptons (VLL) which are odd under a discrete $Z_2$ symmetry. The lightest neutral component of the VLL acts as a dark matter (DM) whereas the full VLL set belongs to a dark sector with no mixings allowed with the standard model fermions. We analyse the model in light of dark matter and collider searches. We show that the DM is compatible with the current relic density data as well as satisfying all direct and indirect dark matter search constraints. We choose some representative points in the model parameter space allowed by all aforementioned dark matter constraints and present a detailed collider analysis of multi-lepton signal viz. the mono-lepton, di-lepton, tri-lepton and four-lepton along with missing transverse energy in the final state using both the cut-based analysis and multivariate analysis respectively at the high luminosity 14 TeV LHC run.