Two Photon Background and the Reach of a Linear Collider for Supersymmetry in WMAP Favoured Coannihilation Regions

A neutralino relic density in accord with WMAP measurements can be found inthe minimal supergravity (mSUGRA) model in several regions of parameter space:the stau co-annihilation corridor at low m_0 and the hyperbolic branch/focuspoint (HB/FP) region at large m_0 at the edges of parameter space, and the bulkand Higgs boson funnel regions within. In the regions at the edge, the mass gapbetween the next-to-lightest SUSY particle (NLSP) and the lightest SUSYparticle (LSP) becomes small, and backgrounds from $\gamma\gamma\to f\bar{f}$($f$ is a SM fermion) become important for NLSP detection at an $e^+e^-$ linearcollider. We evaluate these backgrounds from bremsstrahlung and beamstrahlungphotons, and demonstrate that these do not preclude the observability of thesignal for the cases where either the stau or the chargino is the NLSP. We alsodelineate the additional portion of the stau coannihilation region, beyond whatcan be accessed via a search for selectrons and smuons, that can be probed by asearch for di-tau-jet events plus missing energy. The reach of a LC for SUSY inthe HB/FP region is shown for an updated value of $m_t\simeq 180$ GeV asrecently measured by the $D\O$ experiment.Comment: 19 pages including 9 eps figure