  Resummation and power-corrections play a crucial role in the phenomenology of
event-shape variables like the thrust T. Previous investigations showed that
the perturbative contribution to the average thrust is dominated by gluons of
small invariant mass, of the order of 10% of Q, where Q is the center-of-mass
energy. The effect of soft gluons is also important, leading to a
non-perturbative 1/Q correction. These conclusions are based on renormalon
analysis in the single dressed gluon (SDG) approximation. Here we analyze
higher moments of the thrust distribution using a similar technique. We find
that the characteristic gluon invariant mass contributing to <(1-T)^m>
increases with m. Yet, for m=2 this scale is quite low, around 27% of Q, and
therefore renormalon resummation is still very important. On the other hand,
the power-correction to <(1-T)^2> from a single soft gluon emission is found to
be highly suppressed: it scales as 1/Q^3. In practice, <(1-T)^2> and higher
moments depend also on soft gluon emission from configurations of three hard
partons, which may lead to alpha_s(Q^2)/Q power-corrections. This issue is yet
to be investigated.
