O(αS2) contributions to the longitudinal fragmentation function in e+e− annihilation

We present the order αS2 contributions to the coefficient functions corresponding to the longitudinal fragmentation function FL(x, Q>2). A comparison with the leading order αS result for FL(x, Q2) shows that the corrections are large and vary from 44% to 67% in the region 0.01 < x < 0.9 at Q2 = MZ2. Our calculations also reveal that the ratio of the longitudinal and total cross section σLσtot amounts to 0.054. This number is very close to the most recent value obtained by the OPAL collaboration which obtained 0.057 ± 0.005.