Phenomenology of an $E_6$ inspired extension of Standard Model (I): Higgs sector

We investigate a variant of Left-Right symmetric model based on $E_6$ inspired $SU(3)_C \otimes SU(2)_L \otimes U(1)_L \otimes SU(2)_R \otimes U(1)_R$ gauge group $(32121)$. Spontaneous breaking of $32121$ down to the Standard Model (SM) gauge group, requires a bi-doublet under $SU(2)_L \otimes SU(2)_R$, a right-handed doublet scalar under $SU(2)_R$ along with a $SU(2)$ singlet scalar boson. Symmetry breaking leads to several neutral and charged massive gauge bosons apart from the SM $W$ and $Z$. The Large Hadron Collider (LHC) results for the search of heavy gauge bosons can be used to constrain the vacuum expectation values responsible for giving masses to these extra heavy gauge bosons. Physical spectrum of the scalar bosons contains several neutral CP-even and CP-odd states and a couple of charged scalars apart from the SM-like Higgs boson. We have put constraints on the masses of some of these scalars from the existing LHC data. The possible decay rates and production cross-sections of these scalars have been investigated in some details. Production cross-sections for some of the scalars look promising at 14 TeV and 27 TeV run of the LHC with high luminosity option. As the model stems from Grand Unified group $E_6$, we keep all the fermions present in the $27$-dimensional fundamental representation of $E_6$. Mass limit of one such exotic lepton has also been derived from present LHC data. It is noted that some of these neutral exotic lepton or neutral scalar bosons of this model can serve the purpose of a cold dark matter.