A reassessment of the O(αs2) three-jet cross section for e+e− annihilation

Results of a new evaluation of the O(α_s²) dressed three-jet cross section for e⁺e^? annihilation are summarized. For vanishing cutoffs, the different results in published three-jet cross section formulae are due to differing definitions of resolvable four-jet events. Subleading terms which were ignored in previous calculations are evaluated and found to be sizeable in the phase space region where three-jet events become more two-jet-like. A simple calculation demonstrates that α_s values determined according to the three-jet cross section formulae of Gutbrod, Kramer and Schierholz are systematically too large.