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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.