  We study perturbative and non-perturbative aspects of the distribution of the
C parameter in e+e- annihilation using renormalon techniques. We perform an
exact calculation of the characteristic function, corresponding to the C
parameter differential cross section for a single off-shell gluon. We then
concentrate on the two-jet region, derive the Borel representation of the
Sudakov exponent in the large-beta_0 limit and compare the result to that of
the thrust T. Analysing the exponent, we distinguish two ingredients: the jet
function, depending on Q^2C, summarizing the effects of collinear radiation,
and a function describing soft emission at large angles, with momenta of order
QC. The former is the same as for the thrust upon scaling C by 1/6, whereas the
latter is different. We verify that the rescaled C distribution coincides with
that of 1-T to next-to-leading logarithmic accuracy, as predicted by Catani and
Webber, and demonstrate that this relation breaks down beyond this order owing
to soft radiation at large angles. The pattern of power corrections is also
similar to that of the thrust: corrections appear as odd powers of Lambda/(QC).
Based on the size of the renormalon ambiguity, however, the shape function is
different: subleading power corrections for the C distribution appear to be
significantly smaller than those for the thrust.
