  The resummation for the event-shape variable jet broadening is extended to
next-to-next-to-leading logarithmic accuracy by computing the relevant jet and
soft functions at one-loop order and the collinear anomaly to two-loop
accuracy. The anomaly coefficient is extracted from the soft function and
expressed in terms of polylogarithmic as well as elliptic functions. With our
results, the uncertainty on jet-broadening distributions is reduced
significantly, which should allow for a precise determination of the strong
coupling constant from the existing experimental data and provide a consistency
check on the extraction of alpha_s from higher-log resummations of thrust.
