Explaining the CMS $eejj$ and $e\ \rm{missing}\ p_T \ jj$ excess and
  leptogenesis in superstring inspired $E_6$ models
  We show that superstring inspired $E_6$ models can explain both the recently
detected excess $eejj$ and $e\ \rm{missing}\ p_T \ jj$ signals at CMS, and also
allow for leptogenesis. Working in a R-parity conserving low energy
supersymmetric effective model, we show that the excess CMS events can be
produced via the decay of exotic sleptons in Alternative Left-Right Symmetric
Model of $E_6$, which can also accommodate leptogenesis at a high scale. On the
other hand, either the $eejj$ excess or the $e\ \rm{missing}\ p_T \ jj$ excess
can be produced via the decays of right handed gauge bosons, but some of these
scenarios may not accommodate letptogenesis as there will be strong $B-L$
violation at low energy, which, along with the anomalous fast electroweak $B+L$
violation, will wash out all baryon asymmetry. Baryogenesis below the
electroweak scale may then need to be implemented in these models.
