对撞机事件的度量空间：地球移动者距离与事件相似性的探索

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"对撞机事件的度量空间" 在粒子物理学领域，对撞机实验是探索宇宙基本粒子和力的重要工具。对撞机事件是指在高能粒子碰撞时产生的复杂现象，这些事件包含了丰富的物理信息。然而，如何比较和衡量两个不同的对撞机事件之间的相似性或差异性一直是一个挑战。"对撞机事件的度量空间"这篇论文提出了一种新的方法来解决这一问题。标题中的"对撞机事件的度量空间"指的是一个数学框架，用于量化和比较对撞机实验中的事件。这个框架引入了一个名为“推土机距离”的度量标准，它类似于地理学中计算两个地形分布相似性的方法。在这个度量下，"推土机距离"表示将一个事件的辐射模式（即粒子发射的方向和能量分布）转换成另一个事件所需的最小“工作量”。描述中提到的"功"是指在重排辐射模式过程中需要的能量或努力，这可以看作是事件之间的"距离"。这种度量方法考虑了事件的所有粒子分布，不仅关注单个高能粒子，而是整体的辐射模式，从而提供了更全面的事件比较。论文还探讨了这个度量与红外和共线安全可观测量的联系。红外（IR）和共线（Collinear）安全意味着这些可观测量不受软光子或近似平行粒子发射的影响，这是粒子物理中处理辐射修正的关键概念。通过这个度量，研究人员可以更好地理解这些可观测量如何反映对撞机事件的内在性质，并评估因强子化、堆积效应（pileup）以及探测器响应等实验因素导致的事件变化。此外，这种方法为分析和可视化对撞机数据提供了新工具，不再依赖于特定的可观测量选择。这意味着科学家可以更自由地探索数据，发现潜在的新物理现象，或者更准确地测试现有理论。更广泛地说，这一框架开启了数据驱动的粒子物理现象学的新时代，使得研究能够更加依赖于实际实验数据，而不是仅依赖于理论预测。 "对撞机事件的度量空间"的研究为理解和比较高能粒子碰撞事件提供了一种创新且实用的方法，它强化了我们在实验数据中寻找新物理信号的能力，并推动了粒子物理领域的进一步发展。

Metric Space of Collider Events

Patrick T. Komiske,

Eric M. Metodiev,

†

and Jesse Thaler

‡

Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

(Received 15 February 2019; published 26 July 2019)

When are two collider events similar? Despite the simplicity and generality of this question, there is no

established notion of the distance between two events. To address this question, we develop a metric for the

space of collider events based on the earth mover’s distance: the “work” required to rearrange the radiation

pattern of one event into another. We expose interesting connections between this metric and the structure

of infrared- and collinear-safe observables, providing a novel technique to quantify event modifications due

to hadronization, pileup, and detector effects. We showcase how this metrization unlocks powerful new

tools for analyzing and visualizing collider data without relying upon a choice of observables. More

broadly, this framework paves the way for data-driven collider phenomenology without specialized

observables or machine learning models.

DOI: 10.1103/PhysRevLett.123.041801

High-energy particle collisions produce a tremendous

number of intricately correlated particles, especially when

energetic quarks and gluons are involved. Behind this

apparent complexity, however, the overall flow of energy

in an event is a robust memory of its simpler partonic

origins [1–8]. Surprisingly, no definition of the similarity

between events presently exists that sharply captures this

correspondence. In the absence of a metric, efforts typically

fall back upon ad hoc methods such as comparing specific

observables [9–13] or matching the pixels of calorimeter

images [13–17]. These approaches suffer from significant

pathologies: disparate event topologies can give rise to

identical observable values, while pixels lack stability

under small perturbations. A theoretically and experimen-

tally robust definition of the “distance” between events

would profoundly expand our ability to explore the

structure of collider data and unlock entirely new ways

to probe events.

In this Letter, we advocate for the earth (or energy)

mover’s distance (EMD) [18–22] as a metric for the space

of collider events. We propose a variant of the EMD,

inspired by Refs. [21,22], that allows events with different

total energies to be sensibly compared. The EMD is the

minimum “work” required to rearrange one event E into

the other E

by movements of energy f

from particle i in

one event to particle j in the other:

EMDðE; E

Þ¼ min

≥0g



−



;

≤ E

;

≤ E

;

¼ E

min

; ð1Þ

where i and j index particles in events E and E

, respec-

tively, E

is the particle energy, θ

is an angular distance

FIG. 1. The optimal movement to rearrange one top jet (red)

into another (blue). Particles are shown as points in the rapidity-

azimuth plane with areas proportional to their transverse mo-

menta. Darker lines indicate more transverse momentum move-

ment. The energy mover’s distance in Eq. (1) is the total “work”

required to perform this rearrangement.

Published by the American Physical Society under the terms of

the Creative Commons Attribution 4.0 International license.

Further distribution of this work must maintain attribution to

the author(s) and the published article’s title, journal citation,

and DOI. Funded by SCOAP

PHYSICAL REVIEW LETTERS 123, 041801 (2019)

Editors' Suggestion Featured in Physics

0031-9007=19=123(4)=041801(7) 041801-1 Published by the American Physical Society

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