SUSY signals with small and large trilinear couplings at the LHC 7 TeV runs and neutralino dark matter

We propose the signal $1b+1l+N_j+\text{etslash}$ along with appropriate selection criteria for the LHC 7 TeV run, where the number of jets $(N_j)$ is $\ge$ 2 or 4. These signals can complement the canonical $Jets+\text{etslash}$ signature since they are sensitive to the trilinear soft breaking parameter $(A_0)$ and low values of the parameter tan$\beta$ in the minimal supergravity (mSUGRA) model. A large region of this mSUGRA parameter space within the reach of the ongoing experiments at the LHC is disfavoured by the bound on the lightest Higgs boson mass ($m_h\ge 114.4$ GeV) unless $A_0$ has moderate to large negative values. Interestingly this parameter space with $A_0\mathrm{\ne }0$ is also consistent with the observed dark matter relic density. A natural consequence of large $A_0$ is the existence of a light top squark ($\text{lstop}$). The proposed signals primarily stem from direct $\text{lstop}{\text{lstop}}^{\ast }$ production and/or $\tilde{g}\text{ra}{\tilde{t}}_{1}t$, if all squark-gluino events are considered. A thorough analysis of the signals and the corresponding backgrounds are presented using the event generator Pythia. We finally compare the signal size for $A_0=0$ and $A_0\mathrm{\ne }0$.