A formalism for the resummation of non-factorizable observables in SCET

In the framework of soft-collinear effective theory (SCET), we show how to formulate the resummation for a broad family of final-state, global observables in high-energy collisions in a general way that is suitable for a numerical calculation. Contrary to the standard SCET approach, this results in a method that does not require an observable-specific factorization theorem. We present a complete formulation at next-to-next-to-leading logarithmic order for $e^+e^-$ observables, and show how to systematically extend the framework to higher orders. This work paves the way to automated resummation in SCET for several physical observables within a single framework.