Abstract
We have calculated the contributions proportional to β0nαsn+1 to the longitudinal fragmentation function in e+e− annihilation to all orders of perturbation theory. We use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section σL and discuss the prospects of determining αs from σL. The structure of infrared renormalons in the perturbative expansion suggests that the longitudinal cross section for hadron production with fixed momentum fraction x receives nonperturbative contributions of order 1/(x2Q2), whereas the total cross section has a larger, 1/Q correction. This correction arises from very large longitudinal distances and is related to the behaviour of the Borel integral for the cross section with fixed x at large values of the Borel parameter.
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