  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.
