Power corrections to the event shape in $e^+e^-$ annihilation

Abstract

We study power corrections to the event shapes in $\e^+\e^--$annihilation in the two jets kinematical region, $e\ll 1$. We argue that for $e \sim \Lambda_{QCD}/Q$ all power corrections of the form $1/\lr{Qe}^n$ have to be taken into account for an arbitrary $n$. This is achieved by introducing a new universal distribution, the shape function, which describes the energy flow in the final state. The event shape differential distributions are given by a convolution of the shape function with perturbatively resummed cross-sections. Choosing a physically motivated ansatz for the shape function, we observe a good agreement of our predictions with available data on the differential thrust, $C$-parameter and heavy-jet mass distributions and their first few moments.