Lepton Flavours at the Early LHC Experiments as the Footprints of the Dark Matter Producing Mechanisms

The mSUGRA parameter space corresponding to light sleptons well within the reach of LHC and relatively light squarks and gluinos (mass $\le$ 1 TeV) has three regions consistent with the WMAP data on dark matter relic density and direct mass bounds from LEP 2. Each region can lead to distinct leptonic signatures from squark-gluino events during the early LHC experiments (integrated luminosity $\sim 10 ~fb^{-1}$ or even smaller). In the much studied stau-LSP coannihilation region with a vanishing common trilinear coupling ($A_0$) at the GUT scale a large fraction of the final states contain electrons and / or muons and $e$ - $\mu$ - $\tau$ universality holds to a good approximation. In the not so well studied scenarios with non-vanishing $A_0$ both LSP pair annihilation and stau-LSP coannihilation could contribute significantly to the dark matter relic density for even smaller squark-gluino masses. Our simulations indicate that the corresponding signatures are final states rich in $\tau$-leptons while final states with electrons and muons are suppressed leading to a violation of lepton universality. These features may be observed to a lesser extent even in the modified parameter space (with non-zero $A_0$) where the coannihilation process dominates. We also show that the generic $m$-leptons + $n$-jets+ $\not! E_T$ signatures without flavour tagging can also discriminate among the three scenarios. However, the signals become more informative if the $\tau$ and $b$-jet tagging facilities at the LHC experiments are utilized.