发表机构
Tongji University; Rutgers, the State University of New Jersey（同济大学; 罗格斯大学（新泽西州立大学））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文提出M3R框架，统一分析对撞机事件度量下的流形结构，发现不同度量揭示互补信息，为系统描述事件空间提供新途径。
AI 中文摘要
通过对对撞机事件之间定义相似性概念，度量产生了具有非平凡几何结构的事件流形。理解这些结构及其与基础物理的关系在很大程度上仍未探索，部分原因在于系统比较具有不同度量的空间的挑战。我们引入了多参考相对表示（M3R）框架，该框架提供了一个统一的坐标系，用于在同等条件下分析不同空间。将M3R应用于三种物理动机的事件度量——相空间、谱2-Wasserstein和能量流2-Wasserstein度量——我们研究了单个事件流形以及区分不同物理过程的决策边界。我们发现这些度量解析出不同但部分共享的结构，而流形内和流形间的几何性质表现出定性差异。结合多个度量进一步揭示了可以在统一表示中利用的互补信息。更广泛地说，M3R提供了一种比较和组合不同事件相似性概念的通用语言，为系统描述对撞机事件空间开辟了道路。
英文摘要
By defining notions of similarity between collider events, metrics give rise to event manifolds with nontrivial geometric structure. Understanding these structures and their relation to the underlying physics remains largely unexplored, partly due to the challenge of systematically comparing spaces endowed with distinct metrics. We introduce the multi-reference relative representation (M3R) framework, which provides a unified coordinate system for analyzing different spaces on equal footing. Applying M3R to three physically motivated event metrics---the phase space, spectral 2-Wasserstein, and energy-flow 2-Wasserstein metrics---we study individual event manifolds and the decision boundaries separating different physical processes. We find that these metrics resolve distinct yet partially shared structures, while intra- and inter-manifold geometries exhibit qualitatively different properties. Combining multiple metrics further reveals complementary information that can be exploited within a unified representation. More broadly, M3R provides a general language for comparing and composing different notions of event similarity, opening a path toward a systematic geometric description of collider event space.
Comments37 pages, 8 figures
