A numerical formulation of resummation in effective field theory

TL;DR

This paper develops a numerical formulation for resummation within Soft-Collinear Effective Theory (SCET), enabling automated Monte Carlo implementations and connecting it with existing resummation approaches like CAESAR/ARES.

Contribution

It introduces a novel numerical method for resummation in SCET, bridging it with automated resummation techniques and facilitating higher-order calculations.

Findings

Resummation of thrust distribution at NLL in e+e- collisions.

Framework adaptable to complex observables and higher logarithmic orders.

Establishes a connection between SCET resummation and CAESAR/ARES methods.

Abstract

In this article we show how the resummation of infrared and collinear logarithms within Soft-Collinear Effective Theory (SCET) can be formulated in a way that makes it suitable for a Monte-Carlo implementation. This is done by applying the techniques developed for automated resummation using the branching formalism, which have resulted in the general resummation approach CAESAR/ARES. This work builds a connection between the two resummation approaches, and paves the way to automated resummation in SCET. As a case study we consider the resummation of the thrust distribution in electron-positron collisions at next-to-leading logarithm (NLL). However, the results presented here are easily generalizable to more complicated observables and processes as well as to higher orders in the logarithmic accuracy.