Using $\tau$ Polarization as a Distinctive SUGRA Signature at LHC

In the minimal SUGRA model the lighter tau slepton is expected to be the second lightest superparticle over a large parameter range at large $\tan\beta$. Consequently one expects a viable SUGRA signal at LHC in the tau lepton channel coming from the decay of these tau sleptons. The model predicts the polarization of this tau lepton to be +1 to a very good accuracy. We show how this prediction can be tested by looking at the momentum fraction of the tau-jet, carried by the charged prong, in its 1-prong hadronic decay channel.