Higher-order non-global logarithms from jet calculus

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.

33 pages, 5 figures, code repository: https://github.com/non-global/gnole

References in corpus (16)

• A simple shower and matching algorithm
• Super-leading logarithms in non-global observables in QCD?
• Super-leading logarithms in non-global observables in QCD: Colour basis independent calculation
• On jet mass distributions in Z+jet and dijet processes at the LHC
• Non-global Logarithms at 3 Loops, 4 Loops, 5 Loops and Beyond
• Spin correlations in final-state parton showers and jet observables
• Jet vetoing at the LHC
• The Analytic Structure of Non-Global Logarithms: Convergence of the Dressed Gluon Expansion
• Non-Global Logarithms in Filtered Jet Algorithms
• Non-global logarithms in hadron collisions at $N_c=3$
• NLL${}^{\prime }$ resummation of jet mass
• Factorization for the light-jet mass and hemisphere soft function
• Resummation of Super-Leading Logarithms
• The Asymptotic Form of Non-Global Logarithms, Black Disc Saturation, and Gluonic Deserts
• Non-global and rapidity logarithms in narrow jet broadening
• Jet mass distribution in Higgs/vector boson + jet events at hadron colliders with $k_t$ clustering

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