Classification of Energy Flow Observables in Narrow Jets

We present a classification of energy flow variables for highly collimated jets. Observables are constructed by taking moments of the energy flow and forming scalars of a suitable Lorentz subgroup. The jet shapes are naturally arranged in an expansion in both angular and energy resolution, allowing us to derive the natural observables for describing an N-particle jet. We classify the leading variables that characterize jets with up to 4 particles. We rediscover the familiar jet mass, angularities, and planar flow, which dominate the lowest order substructure variables. We also discover several new observables and we briefly discuss their physical interpretation.