Abstract
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.
Highlights
Perturbation theory is one of the most widely used techniques to make predictions for interacting quantum field theories
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
In fixed order (FO) perturbation theory, one expands the physical observables in powers of the coupling constants of the theory, where leading order (LO) predictions describe a given process to lowest order, while higher order corrections are suppressed by additional powers of αi = gi2/4π
Summary
Perturbation theory is one of the most widely used techniques to make predictions for interacting quantum field theories. Using the thrust observable as a case study, in [48] it was shown how these two formulations of resummation can be combined into a hybrid method This approach proceeds by defining a simpler version of thrust, defined in order to obey a simple factorization theorem that can be handled using the standard SCET formalism. We briefly touch on all aspects of the derivation: we introduce a generic and fully differential factorization approach derived from SCET, from which any observable can be calculated, define the simple observable and how it can be resummed using SCET and finish by an SCET definition of the transfer function.
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