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

TL;DR

This paper calculates the second-order QCD corrections to the hemisphere soft function in e+e- dijet production, improving theoretical precision for event shape distributions and exploring renormalon effects.

Contribution

It provides the first unambiguous determination of O(alpha_s^2) corrections to the hemisphere soft function and introduces new NNLL anomalous dimensions for heavy quark production.

Findings

O(alpha_s^2) corrections to the soft function are now precisely known.

The impact of the renormalon subtraction on the soft function is analyzed.

New NNLL anomalous dimensions for heavy quark invariant mass distributions are presented.

Abstract

We determine the O(alpha_s^2) corrections to the partonic hemisphere soft function relevant for thrust and jet mass distributions in e+e- annihilation in the dijet limit. In this limit the distributions can be described by a factorization theorem that sums large logarithmic terms and separates perturbative from nonperturbative effects. Using the known O(alpha_s^2) contributions of the jet functions and the hard coefficients in the factorization theorem, constraints from renormalization group evolution and nonabelian exponentiation, and results from numerical integration of O(alpha_s^2) QCD matrix elements, the O(alpha_s^2) corrections of the soft function can be determined unambiguously. We study the impact of subtracting contributions related to the O(Lambda_QCD) renormalon in the partonic threshold using the soft function gap proposed recently by Hoang and Stewart, and we discuss the importance to account for the renormalization group evolution of the gap parameter. As a byproduct we also present the previously unknown next-to-next-to-leading logarithmic anomalous dimensions for the hard coefficient that appear in the factorization theorem for the double differential invariant mass distribution for heavy quark pair production at high energies in the resonance region proven by Fleming etal.