Collimation of the e^+e^- annihilation event

The collimation $C$ of a hadronic event in the e^+e^- annihilation is defined as the average of $\cos\theta$, $C=<\cos\theta>$, where $\theta$ is the angle of each hadron measured from the thrust axis, and the average is over all the hadrons produced in an event. It is an infrared-stable event-shape parameter. $1-\bar C$, the difference between the unity and the average collimation at a given energy, is proportional to the anomalous dimension of the hadron multiplicity at the leading order in MLLA. Its next-to-leading order corrections are calculated.