  We study the dynamics of a tagged particle in a glassy system under shear.
The recently developed integration through transients approach based on mode
coupling theory, is continued to arrive at the equations for the tagged
particle correlators and the mean squared displacements. The equations are
solved numerically for a two dimensional system, including a nonlinear
stability analysis of the glass solution, the so called beta-analysis. We
perform Brownian Dynamics simulations in 2-D and compare with theory. After
switch on, transient glassy correlation functions show strong fingerprints of
the stress overshoot scenario, including, additionally to previously studied
superexponential decay, a shoulder-like slowing down after the overshoot. We
also find a new type of Taylor dispersion in glassy states which has intriguing
similarity to the known low density case. The theory qualitatively captures
most features of the simulations with quantitative deviations concerning the
shear induced timescales. We attribute these deviations to an underestimation
of the overshoot scenario in the theory.
