We introduce a new event shape observable - event isotropy - that quantifies how close the radiation pattern of a collider event is to a uniform distribution. An intuitive, semi-analytic estimation technique clarifies why this is the case and assists with the interpretation of the distributions. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.Įvent isotropy $$ $$ I sph, λ max ) plane. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric.

SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover's Distance (EMD). PDF Shaper's clean, intuitive interface allows users to become productive in just a few minutes.The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. The software is optimized for low CPU resource usage and operates in batch mode, allowing users to process multiple PDF files while doing other work on their computers. PDF Shaper is a set of feature-rich PDF tools that makes it simple to split, merge, watermark, sign, protect, optimize, convert, encrypt and decrypt your PDF documents.

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