Two-body decays of the lightest stop in minimal supergravity with and without R-parity

We study the decays of the lightest top squark in supergravity models with and without R-parity. Using the simplest model with an effective explicit b ilinear breaking of R-parity and radiative electroweak symmetry breaking we show that, below the threshold for decays into charginos (t) over tilde(1) --> b<(chi)over tilde>(+)(1), the lightest stop decays mainly into third g eneration fermions, (t) over tilde 1 --> b tau instead of the R-parity cons erving mode (t) over tilde(1) --> c<(chi)over tilde>(0)(1), even for tiny t au-neutrino mass values. Moreover we show that, even above the threshold fo r decays into charginos, the decay (t) over tilde(1) --> b tau may be domin ant. We study the role played by the universality of the boundary condition s on the soft supersymmetry breaking terms. This new decay mode (t) over ti lde(1) --> b tau as well as the cascades originated by the conventional (t) over tilde(1) --> c<(chi)over tilde>(0)(1) decay followed by the R-parity violating neutralino decays can provide new signatures for stop production at LEP and the Tevatron. (C) 2000 Elsevier Science B.V. All rights reserved .