  We report a study on the measurement of the SUSY breaking scale sqrt(F) in
the framework of gauge-mediated supersymmetry breaking (GMSB) models at the
LHC. The work is focused on the GMSB scenario where a stau is the
next-to-lightest SUSY particle (NLSP) and decays into a gravitino with lifetime
c*tau_NLSP in the range 0.5 m to 1 km. We study the identification of
long-lived sleptons using the momentum and time of flight measurements in the
muon chambers of the ATLAS experiment. A realistic evaluation of the
statistical and systematic uncertainties on the measurement of the slepton mass
and lifetime is performed, based on a detailed simulation of the detector
response. Accessible range and precision on sqrt(F) achievable with a counting
method are assessed. Many features of our analysis can be extended to the study
of different theoretical frameworks with similar signatures at the LHC.
