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We determine the O(alpha_s^2) corrections to the partonic hemisphere softfunction relevant for thrust and jet mass distributions in e+e- annihilation inthe dijet limit. In this limit the distributions can be described by afactorization theorem that sums large logarithmic terms and separatesperturbative from nonperturbative effects. Using the known O(alpha_s^2)contributions of the jet functions and the hard coefficients in thefactorization theorem, constraints from renormalization group evolution andnonabelian exponentiation, and results from numerical integration ofO(alpha_s^2) QCD matrix elements, the O(alpha_s^2) corrections of the softfunction can be determined unambiguously. We study the impact of subtractingcontributions related to the O(Lambda_QCD) renormalon in the partonic thresholdusing the soft function gap proposed recently by Hoang and Stewart, and wediscuss the importance to account for the renormalization group evolution ofthe gap parameter. As a byproduct we also present the previously unknownnext-to-next-to-leading logarithmic anomalous dimensions for the hardcoefficient that appear in the factorization theorem for the doubledifferential invariant mass distribution for heavy quark pair production athigh energies in the resonance region proven by Fleming etal.

Hemisphere Soft Function at O(alpha_s^2) for Dijet Production in e+e- Annihilation