Abstract
An outstanding problem in QCD and jet physics is the factorization and resummation of logarithms that arise due to phase space constraints, so-called non-global logarithms (NGLs). In this paper, we show that NGLs can be factorized and resummed down to an unresolved infrared scale by making sufficiently many measurements on a jet or other restricted phase space region. Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors. To connect with the NGLs of more inclusive measurements, we present a novel perturbative expansion which is controlled by the volume of the allowed phase space for unresolved emissions. Arbitrary accuracy can be obtained by making more and more measurements so to resolve lower and lower scales. We find that even a minimal number of measurements produces agreement with Monte Carlo methods for leading-logarithmic resummation of NGLs at the sub-percent level over the full dynamical range relevant for the Large Hadron Collider. We also discuss other applications of our factorization theorem to soft jet dynamics and how to extend to higher-order accuracy.
Highlights
A fundamental problem in QCD and collider physics is the identification of hierarchical scales in a system defined by some number of observations made on that system
Resummation is accomplished by renormalization group evolution of the objects in the factorization theorem and anomalous dimensions can be calculated to any perturbative accuracy and with any number of colors
In this paper we have presented a novel approach to the resummation of non-global logarithms (NGLs)
Summary
A fundamental problem in QCD and collider physics is the identification of hierarchical scales in a system defined by some number of observations made on that system Ratios of these scales appear in logarithms at every order of the perturbative expansion of the cross section, and can become large in the soft or collinear regions of phase space. In the case just discussed, the soft function could not be further factorized because no measurement was done on the jet to isolate the region of phase space where the NGLs are important. By measuring several observables on a jet we are able to identify the region of phase space where the NGLs live, refactorize the soft function, and resum the NGLs by renormalization group evolution of the now-factorized soft function
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