New angles on energy correlation functions

Jet substructure observables, designed to identify specific features within jets, play an essential role at the Large Hadron Collider (LHC), both for searching for signals beyond the Standard Model and for testing QCD in extreme phase space regions. In this paper, we systematically study the structure of infrared and collinear safe substructure observables, defining a generalization of the energy correlation functions to probe n-particle correlations within a jet. These generalized correlators provide a flexible basis for constructing new substructure observables optimized for specific purposes. Focusing on three major targets of the jet substructure community boosted top tagging, boosted W/Z/H tagging, and quark/gluon discrimination - we use power-counting techniques to identify three new series of powerful discriminants: M-i, N-i, and U-i. The Mi series is designed for use on groomed jets, providing a novel example of observables with improved discrimination power after the removal of soft radiation. The N-i series behave parametrically like the N-subjettiness ratio observables, but are defined without respect to subjet axes, exhibiting improved behavior in the unresolved limit. Finally, the U-i series improves quark/gluon discrimination by using higher-point correlators to simultaneously probe multiple emissions within a jet. Taken together, these observables broaden the scope for jet substructure studies at the LHC.