Two-loop anomalous dimension for the resummation of non-global observables

Abstract

The soft radiation emitted in jet cross sections can resolve the directions and colors of individual hard partons, leading to a complicated pattern of logarithmically enhanced terms in the perturbative series. Starting from a factorization theorem and solving the renormalization group equations for its ingredients, these large logarithms can be resummed. In this paper, we extract the two-loop anomalous dimension governing the resummation of subleading logarithms in jet cross sections and other non-global observables. This anomalous dimension can be obtained by considering soft limits of hard amplitudes, but the presence of collinear singularities in intermediate expressions makes its extraction delicate. As a consistency check, we use our results to predict the known subleading non-global logarithms in the two-jet cross section.

53 pages, 3 figures, v2: journal version

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• Colour Evolution and Infrared Physics
• Glauber Phases in Non-Global LHC Observables: Resummation for Quark-Initiated Processes
• QCD anatomy of photon isolation
• Non-global logarithms up to four loops at finite-N${}_c$ for V/H+jet processes at hadron colliders