  We review the non-supersymmetric (Extended) Left-Right Symmetric Models
(LRSM) and low energy $E_6$-based models to investigate if they can explain
both the recently detected excess $eejj$ signal at CMS and leptogenesis. The
$eejj$ excess can be explained from the decay of the right-handed gauge bosons
($W_R$) with mass $\sim \rm{TeV}$ in certain variants of the LRSM (with
$g_{L}\neq g_{R}$). However such scenarios can not accommodate high-scale
leptogenesis. Other attempts have been made to explain leptogenesis while
keeping the $W_{R}$ mass almost within the reach of the LHC by considering the
resonant leptogenesis scenario in the context of the LRSM for relatively large
Yukawa couplings. However this may not be feasible due to washout of the lepton
asymmetry by certain processes. Therefore we consider three effective low
energy subgroups of the superstring inspired $E_{6}$ model having a number of
additional exotic fermions which provides a rich phenomenology to be explored.
We however find that these three effective low energy subgroups of $E_6$ too
cannot explain both the $eejj$ excess signal and leptogenesis simultaneously.
