Abstract
We present a new framework for computing resummed and matched distributions in processes with many hard QCD jets. The intricate color structure of soft gluon emission at large angles renders resummed calculations highly non-trivial in this case. We automate all ingredients necessary for the color evolution of the soft function at next-to-leading-logarithmic accuracy, namely the selection of the color bases and the projections of color operators and Born amplitudes onto those bases. Explicit results for all QCD processes with up to $2\to 5$ partons are given. We also devise a new tree-level matching scheme for resummed calculations which exploits a quasi-local subtraction based on the Catani-Seymour dipole formalism. We implement both resummation and matching in the Sherpa event generator. As a proof of concept, we compute the resummed and matched transverse-thrust distribution for hadronic collisions.
Highlights
Sections are available for pure QCD processes and electroweak (W ±, Z and Higgs) boson production in association with up to five jets [18,19,20,21]
Event shapes in electron-positron, electron-proton and hadron-hadron collisions have been studied for a long time and a general framework for resumming event shapes at next-to-leading logarithmic (NLL) accuracy was developed in refs. [47,48,49,50]
Multi-jet physics is central in the physics program of the LHC
Summary
The main aim of this work is to define and implement NLL resummation for processes with an arbitrary number of hard partons. The construction and implementation of an algorithm addressing all three items represents the core of this paper This problem is closely related to the color decomposition of QCD amplitudes [101], which is typically written in the form. While the number of orderings and the related color coefficients change with the color basis [102,103,104], the partial amplitudes are unique, gauge-invariant objects depending only on the particle momenta. They are given by sums of planar diagrams computed in the large-NC limit [105].
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