  We consider top-quarks produced at large energy in e+e- collisions, and
address the question of what top-mass can be measured from reconstruction. The
production process is characterized by well separated scales: the
center-of-mass energy, Q, the top mass, m, the top decay width, Gamma_t, and
also LambdaQCD; scales which can be disentangled with effective theory methods.
In particular we show how the mass measurement depends on the way in which soft
radiation is treated, and that this can shift the mass peak by an amount of
order Q LambdaQCD/m. We sum large logs for Q >> m >> Gamma_t > LambdaQCD and
demonstrate that the renormalization group ties together the jet and soft
interactions below the scale m. Necessary conditions for the invariant mass
spectrum to be protected from large logs are formulated. Results for the
cross-section are presented at next-to-leading order with next-to-leading-log
resummation, for invariant masses in the peak region and the tail region. Using
our results we also predict the thrust distribution for massive quark jets at
NLL order for large thrust. We demonstrate that soft radiation can be precisely
controlled using data on massless jet production, and that in principle, a
short distance mass parameter can be measured using jets with precision better
than LambdaQCD.
