Dark Matter perspective of Left-Right symmetric gauge model

We consider an incarnation of left-right symmetric model with a local gauge symmetry of $SU(3)_C \otimes SU(2)_L \otimes U(1)_L \otimes SU(2)_R \otimes U(1)_R$. Heavy scalars and fermions present in the {\bf 27} of $E_6$ are included in the matter sector along with the Standard Model fermions. Two such colour singlet fermions, $N$ and $l_S$, transforming as bi-doublet and singlet under $SU(2)$s respectively, can be potential candidates for Dark Matter (DM). Assignment of $U(1)$ charges for the matter fields restricts some of the exotic fermions to interact with the SM fermions. We study in some details the prospect of such fermionic dark matters by calculating relic densities and direct detection cross-sections by treating these particles as stand alone relic particles in turn. $N$, when treated as relic particle, would produce a direct-detection cross-section very high compared to the experimental upper limits. However, the interaction rate of $N$ can be controlled by introducing a dimension-6 operator involving two $N$ fields and two SM fermions and appropriately choosing the coupling constant. This in turn, makes the interaction rate of $N$ very high and yields a small relic density. On the other hand, $l_S$ for some chosen mass window, can give us right amount of relic, but its direct detection cross-section is too small. Keeping these in mind, we propose two-component model of DM, where both $N$ and $l_S$ contribute to the relic density, albeit with unequal proportion while the direct detection cross-section limits can be satisfied mainly by $N$ in presence of an extra dimension-6 interaction. We derive limits on such an interaction from XENON experiment.