Indirect measurements of the τ˜-χ˜10 mass difference and Mg˜ in the co-annihilation region of mSUGRA models at the LHC

We study the prospects for the measurement of the τ˜-χ˜10 mass difference (ΔM) and the g˜ mass (Mg˜) in the supersymmetric co-annihilation region of mSUGRA at the LHC using tau leptons. Recent WMAP measurements of the amount of cold dark matter and previous accelerator experiments favor the co-annihilation region of mSUGRA, characterized by a small ΔM (5-15 GeV). Focusing on taus from χ˜20→ττ˜→ττχ˜10 decays in g˜ and q˜ production, we consider inclusive 3τ+jet+E̸T production, with two τ's above a high ET threshold and a third τ above a lower threshold. Two observables, the number of opposite-signed τ pairs minus the number of like-signed τ pairs, and the peak of the di-tau invariant mass distribution, allow for the simultaneous determination of ΔM and Mg˜ for ΔM≳6 GeV. For example, for ΔM=9 GeV and Mg˜=850 GeV with 30 fb−1 of data, we can measure ΔM to 15% and Mg˜ to 6%.