Light scalar top quark at $e^{+}$$e^{\mathrm{-}}$ colliders

We examine the production and decay of a supersymmetric scalar top t${̃}_1$ at $e^{+}$$e^{\mathrm{-}}$ colliders such as TRISTAN at KEK, the Stanford Linear Collider, and LEP at CERN, based on supersymmetric models with soft breaking. Existing bounds for supersymmetric particles imply that t${̃}_1$ in the energy range of these colliders would be lighter than other scalar quarks and than the top quark. We make a careful study of available t${̃}_1$ decay modes in this scenario. The flavor-changing decay t${̃}_1$→cγ̃ is found to proceed through the misalignment of the scalar-quark and quark mixing matrices. If the three-body decay t${̃}_1$→${\mathrm{bl}}^{+}$ν̃ is kinematically accessible it dominates the two-body decay. The decay t${̃}_1$→bνl${̃}^{+}$ is even larger due to different chirality structure, but is likely to suffer from a large phase-space suppression. Four-body decays are negligible. The t${̃}_1$ pair production cross section including the γ and Z contribution and the left-right mixing is presented.