Principles of general final-state resummation and automated implementation

TL;DR

The paper addresses the challenge of performing precise final-state resummations for arbitrary observables by deriving a master NLL resummation formula that relies on clearly defined observable characteristics. It introduces recursive infrared and collinear safety (rIRC) and continuous globalness as core applicability conditions, enabling a universal, automated resummation approach. The CAESAR framework automates the extraction of these observable properties from a subroutine and computes the resummed predictions, including an analytic master formula and a Monte Carlo–based evaluation of the single-logarithmic F factor. The work demonstrates the thrust as a worked example and discusses rIRC-unsafety cases and convergence issues, while outlining Extensions to more complex Born topologies and outgoing/incoming leg configurations. This methodology offers a scalable path toward systematic, perturbative, and automated resummations across a broad class of high-energy processes, with implications for precision QCD phenomenology and matching to fixed-order results.

Abstract

Next-to-leading logarithmic final-state resummed predictions have traditionally been calculated, manually, separately for each observable. In this article we derive NLL resummed results for generic observables. We highlight and discuss the conditions that the observable should satisfy for the approach to be valid, in particular continuous globalness and recursive infrared and collinear safety. The resulting resummation formula is expressed in terms of certain well-defined characteristics of the observable. We have written a computer program, CAESAR, which, given a subroutine for an arbitrary observable, determines those characteristics, enabling full automation of a large class of final-state resummations, in a range of processes.