On the infrared sensitivity of the longitudinal cross section in e{sup +}e{sup {minus}} annihilation

The authors have calculated the contributions proportional to {beta}{sub 0}{sup n}{alpha}{sub s}{sup n+1} to the longitudinal fragmentation function in e{sup +}e{sup {minus}} annihilation to all orders of perturbation theory. They use this result to estimate higher-order perturbative corrections and nonperturbative corrections to the longitudinal cross section {sigma}{sub L} and discuss the prospects of determining {alpha}{sub s} from {sigma}{sub L}. 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/(x{sup 2}Q{sup 2}), whereas the total cross section has a larger, 1/Q correction. This correction arises from very large longitudinal distances and is related to the behavior of the Borel integral for the cross section with fixed x at large values of the Borel parameter