  We perform a search for new physics using final states consisting of three
leptons and a large imbalance in transverse momentum resulting from
proton-antiproton collisions at 1.96 TeV center-of-mass energy. We use data
corresponding to 5.8 fb-1 of integrated luminosity recorded by the CDF II
detector at the Tevatron collider. Our main objective is to investigate
possible new low-momentum (down to 5 GeV/c) multi-leptonic final states not
investigated by LHC experiments. Relative to previous CDF analyses, we expand
the geometric and kinematic coverage of electrons and muons and utilize tau
leptons that decay hadronically. Inclusion of tau leptons is particularly
important for supersymmetry (SUSY) searches. The results are consistent with
standard-model predictions. By optimizing our event selection to increase
sensitivity to the minimal supergravity (mSUGRA) SUSY model, we set limits on
the associated production of chargino and neutralino, the SUSY partners of the
electroweak gauge bosons. We exclude cross sections up to 0.1 pb and chargino
masses up to 168 GeV/c^2 at 95% CL, for a suited set of mSUGRA parameters. We
also exclude a region of the two-dimensional space of the masses of the
neutralino and the supersymmetric partner of the tau lepton, not previously
excluded at the Tevatron.
