Nonzero trilinear parameter in the minimal supergravity model: Dark matter and collider signals at the Fermilab Tevatron and CERN LHC

Phenomenologically viable and interesting regions of parameter space in the minimal supergravity (mSUGRA) model with small $m_0$ and small $m_{1/2}$ consistent with the WMAP data on dark matter relic density and the bound on the mass of the lightest Higgs scalar $m_h>114\mathrm{GeV}$ from the Linear Electron Positron Collider open up if the rather ad hoc assumption $A_0=0$, where $A_0$ is the common trilinear soft breaking parameter, employed in most of the existing analyses is relaxed. Since this region corresponds to relatively light squarks and gluinos which are likely to be probed extensively in the very early stages of the LHC experiments, the consequences of moderate or large negative values of $A_0$ are examined in detail. We find that in this region several processes including lightest supersymmetric particle (LSP) pair annihilation, LSP—lighter tau slepton (${\tilde{\tau }}_1$) coannihilation and LSP—lighter top squark (${\tilde{t}}_1$) coannihilation contribute to the observed dark matter relic density. The possibility that a ${\tilde{t}}_1$ that can participate in coannihilation with the lightest neutralino to satisfy the WMAP bound on relic density and at the same time be observed at the current experiments at the Tevatron is wide open. At the LHC a large number of squark-gluino events lead to a very distinctive semi-inclusive signature ${\tau }^{\pm }+X_{\tau }$ (anything without a tau lepton) with a characteristic size much larger than $e^{\pm }+X_e$ or ${\mu }^{\pm }+X_{\mu }$ events.