From NNLO Soft Functions to NNLL Resummations
Soft-Collinear Effective Theory (SCET) formally disentangles the effects of hard, soft, and collinear radiation at the level of the QCD lagrangian, and thereby permits the derivation of effective factorization theorems composed of largely process-independent functions. For example, in processes with two hard, colored partons (e.g. one-jet production in DIS, e+e- -> 2j, or p p -> 0j), the effects of unoriented soft radiation can be parameterized into a perturbatively calculable 'dijet soft function.' After briefly sketching this factorization for a simple e+e- event shape, I will demonstrate how otherwise tough two-loop calculations for soft functions can be reduced to master integrals requiring only a few input functions. I will then discuss their numerical implementation and present results for a host of both lepton and hadron collider observables, including a novel calculation of the NNLO soft anomalous dimension for the e+e- event shape 'angularities', which we have used to resum its large logarithms to NNLL(') accuracy. I will then motivate a precision extraction of the strong coupling constant from our theory distributions after showing comparisons with LEP data. To conclude, I will discuss the future extension of our numerical approach in the soft sector to fully automated resummations in SCET.