Detection of long-lived staus and gravitinos at the ILC

Supersymmetry (Susy) provides an attractive scenario to account for the amount of dark matter in the universe. If R-parity is conserved, the lightest supersymmetric particle (LSP) is stable and an ideal dark matter candidate. A very interesting option is the spin 3/2 gravitino G̃. The mass of the gravitino is set by the Susy breaking scale F via m3/2 = mG̃ = F/ √ 3 MP , with MP ' 2.4 · 10 GeV the reduced Planck scale. In general m3/2 is a free parameter and may extend over a wide range of O(eV − TeV) for gauge, gaugino and supergravity mediated symmetry breaking. A gravitino LSP may be produced in decays of Susy particles. If the next-to-lightest supersymmetric particle (NLSP) is the scalar tau τ̃ , the dominant process is τ̃ → τ G̃. Since the coupling is gravitational, the lifetime may be very long, ranging from seconds to years. The decay-width Γτ̃ , respectively lifetime τ = Γ −1 τ̃ , of the τ̃ NLSP