Resummation of Next-to-Leading Non-Global Logarithms at the LHC

In cross sections with angular cuts, an intricate pattern of enhanced higher-order corrections known as non-global logarithms arises. The leading logarithmic terms were computed numerically two decades ago, but the resummation of subleading non-global logarithms remained a challenge that we solve in this Letter using renormalization group methods in effective field theory. To achieve next-to-leading logarithmic accuracy, we implement the two-loop anomalous dimension governing the resummation of non-global logarithms into a large-$N_c$ parton shower framework, together with one-loop matching corrections. As a first application, we study the interjet energy flow in $e^+e^-$ annihilation into two jets. We then present, for the first time, resummed predictions at next-to-leading logarithmic accuracy for a gap-between-jets observable at hadron colliders.