Phenomenology of power corrections in fragmentation processes in e⁺e^- annihilation

We analyse power corrections to longitudinal and transverse fragmentation processes in e⁺e^- annihilation, based on the assumption of ultraviolet dominance of power corrections. Under this assumption, we determine the dependence of power corrections on the scaling variable x from the infrared renormalon asymptotics of leading power coefficient functions. Our results suggest that the longitudinal and transverse gluon fragmentation coefficient functions receive corrections of order 1/(xQ)². The power expansion breaks down at x < Λ/Q and has to be resummed. This resummation leads to 1/Q corrections to the longitudinal and transverse cross section, which cancel for the total cross section. We provide a simple parametrization of the x dependence of 1/Q² corrections to fragmentation processes and investigate perturbative corrections to the longitudinal cross section in higher orders, in view of a determination of the strong coupling.