Probing the Structure of Jets: Factorized and Resummed Angularity Distributions in SCET

Using the framework of soft-collinear effective theory (SCET), we factorize and calculate $e^+e^-$ angularity distributions, including perturbative resummation and the incorporation of a universal model for the nonperturbative soft function. Angularities $\tau_a$ are a class of event shapes varying in their sensitivity to the substructure of jets in the final state, controlled by a continuous parameter $a<2$. We calculate the jet and soft functions in factorized angularity distributions for all $a<1$ to first order in the strong coupling $\alpha_s$ and resum large logarithms to next-to-leading logarithmic (NLL) accuracy. We employ a universal model for the nonperturbative soft function with a gap parameter which cancels the renormalon ambiguity in the partonic soft function.