The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. 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). 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. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. 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. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.
翻译:研究喷气器内有趣结构的识别对于在对撞机中寻找新物理并探测标准模型至关重要。许多这些结构工具先前已被证明是最优输运问题,特别是能量搬运距离(EMD)。在本文中,我们展示了EMD实际上是比较对撞事件的自然结构,这解释了它在理解事件和喷气器内部结构方面的最近成功。然后,我们提出了一个使用参数能量重建的形状搜索算法(SHAPER),是一种定义和计算基于形状的观测值的通用框架。SHAPER将N-jettiness从点簇推广到任何扩展的、可参数化的形状上。这是通过有效地最小化事件和表示理想形状的能量流参数化流形之间的EMD来完成的,其实现使用了Wasserstein度量的双势Sinkhorn逼近。我们展示了观测量作为流形的几何语言如何用于定义具有内置红外与相干安全性的新观测值。我们通过使用几个新的基于形状的观测值执行经验喷气器内部结构研究,证明了SHAPER框架的功效。