Higher-order non-global logarithms from jet calculus

TL;DR

This paper advances the resummation of non-global QCD observables beyond leading order by numerically solving non-linear equations at next-to-leading logarithmic accuracy, significantly improving theoretical predictions for jet-related measurements.

Contribution

It provides the first complete NLL resummation for non-global observables using a numerical solution of derived evolution equations in the large-N_c limit.

Findings

NLL corrections are substantial.

Inclusion of NLL reduces scale uncertainties.

The method is applicable to various non-global problems.

Abstract

Non-global QCD observables are characterised by a sensitivity to the full angular distribution of soft radiation emitted coherently in hard scattering processes. This complexity poses a challenge to their all-order resummation, that was formulated at the leading-logarithmic order about two decades ago. In this article we present a solution to the long-standing problem of their resummation beyond this order, and carry out the first complete next-to-leading logarithmic calculation for non-global observables. This is achieved by solving numerically the recently derived set of non-linear differential equations which describe the evolution of soft radiation in the planar, large-$N_c$ limit. As a case study we address the calculation of the transverse energy distribution in the interjet rapidity region in $e^+e^-\to$ dijet production. The calculation is performed by means of an algorithm that we formulate in the language of jet-calculus generating functionals, which also makes the resummation technique applicable to more general non-global problems, such as those that arise in hadronic collisions. We find that NLL corrections are substantial and their inclusion leads to a significant reduction of the perturbative scale uncertainties for these observables. The computer code used in the calculations is made publicly available.