Jet observables without jet algorithms

We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet clustering algorithm, they incorporate a jet radius parameter and a transverse momentum cut. Three of the ubiquitous jet-based observables - jet multiplicity, summed scalar transverse momentum, and missing transverse momentum - have event shape counterparts that are closely correlated with their jet-based cousins. Due to their local computational structure, these jet-like event shapes could potentially be used for trigger-level event selection at the LHC. Intriguingly, the jet multiplicity event shape typically takes on non-integer values, highlighting the inherent ambiguity in defining jets. By inverting jet multiplicity, we show how to characterize the transverse momentum of the n-th hardest jet without actually finding the constituents of that jet. Since many physics applications do require knowledge about the jet constituents, we also build a hybrid event shape that incorporates (local) jet clustering information. As a straightforward application of our general technique, we derive an event-shape version of jet trimming, allowing event-wide jet grooming without explicit jet identification. Finally, we briefly mention possible applications of our method for jet substructure studies.