Edge Detecting New Physics the Voronoi Way

TL;DR

This paper introduces Voronoi tessellation-based algorithms to detect kinematic edges in high energy physics data, enhancing the analysis of potential signals beyond the standard model.

Contribution

It presents novel geometric results and algorithms for identifying kinematic edges using Voronoi tessellations, with improvements through Lloyd's relaxation.

Findings

Voronoi methods effectively identify kinematic edges.

Adding Lloyd's relaxation improves detection efficiency.

Applicable to high energy physics data analysis.

Abstract

We point out that interesting features in high energy physics data can be determined from properties of Voronoi tessellations of the relevant phase space. For illustration, we focus on the detection of kinematic "edges" in two dimensions, which may signal physics beyond the standard model. After deriving some useful geometric results for Voronoi tessellations on perfect grids, we propose several algorithms for tagging the Voronoi cells in the vicinity of kinematic edges in real data. We show that the efficiency is improved by the addition of a few Voronoi relaxation steps via Lloyd's method. By preserving the maximum spatial resolution of the data, Voronoi methods can be a valuable addition to the data analysis toolkit at the LHC.