Stau Coannihilation, Compressed Spectrum and SUSY Discovery at the LHC

The lack of observation of supersymmetry thus far implies that the weak supersymmetry scale is larger than what was thought before the LHC era. This observation is strengthened by the Higgs boson mass measurement at $\sim 125$ GeV which within supersymmetric models implies a large loop correction and a weak supersymmetry scale lying in the several TeV region. In addition if neutralino is the dark matter, its relic density puts further constraints on models often requiring coannihilation to reduce the neutralino relic density to be consistent with experimental observation. The coannihilation in turn implies that the mass gap between the LSP and the NLSP will be small leading to softer final states and making the observation of supersymmetry challenging. In this work we investigate stau coannihilation models within supergravity grand unified models and the potential of discovery of such models at the LHC in the post Higgs boson discovery era. We utilize a variety of signal regions to optimize the discovery of supersymmetry in the stau coannihilation region. In the analysis presented we impose the relic density constraint as well as the constraint of the Higgs boson mass. The range of sparticle masses discoverable up to the optimal integrated luminosity of the HL-LHC is investigated. It is found that the mass difference between the stau and the neutralino does not exceed $\sim 20$ GeV over the entire mass range of the models explored. Thus the discovery of a supersymmetric signal arising from the stau coannihilation region will also provide a measurement of the neutralino mass. The direct detection of neutralino dark matter is analyzed within the class of stau coannihilation models investigated. The analysis is extended to include multi-particle coannihilation where stau along with chargino and the second neutralino enter in the stau coannihilation process.