Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions

Using soft-collinear effective theory (SCET), which provides a unified framework for factorization, resummation of logarithms, and incorporation of universal nonperturbative functions in hard-scattering QCD cross-sections, we present a new prediction of angularity distributions in e+e− annihilation. Angularities τa are an infinite class of event shapes which vary in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter a < 2. We calculate angularity distributions for all a < 1 to next-to-leading order (NLO) in the strong coupling αs and resum large logarithms in these distributions to next-to-leading logarithmic (NLL) accuracy. Our expressions for the NLO partonic jet and soft functions in the factorization theorem for angularity distributions are given for the first time. We employ a model for the nonperturbative soft function with a gap parameter which cancels the renormalon ambiguity in the partonic soft function. We explore the relation between the SCET approach to resummation and past approaches in QCD, and find that the effective theory approach with the inclusion of our NLO results greatly reduces the scale variation of the distributions. In addition, we draw from the NLO calculations of the jet and soft functions an intuitive lesson about how factorization breaks down in the effective theory as a→ 1.