[Paper Review] Discovering New Physics with Voronoi Tessellations

Dipsikha Debnath, James S. Gainer+2 more|arXiv (Cornell University)|Nov 9, 2015

Particle physics theoretical and experimental studies24 references3 citations

TL;DR

This paper proposes a Voronoi tessellation-based method to detect kinematic edges in high-energy physics data—features that may signal physics beyond the Standard Model. By analyzing Voronoi cell properties such as area and neighbor count, and enhancing accuracy with Lloyd’s relaxation, the method identifies edges in sparse, high-dimensional phase space without assuming prior knowledge of the underlying distributions, significantly improving edge detection sensitivity in both toy models and a supersymmetry benchmark scenario.

ABSTRACT

High energy experimental data can be viewed as a sampling of the relevant phase space. We point out that one can apply Voronoi tessellations in order to understand the underlying probability distributions in this phase space. Interesting features in the data can then be discovered by studying the properties of the ensemble of Voronoi cells. For illustration, we demonstrate the detection of kinematic "edges" in two dimensions, which may signal physics beyond the standard model. We motivate the algorithm with some analytical results derived for perfect lattices, and show that the method is further improved with the addition of a few Voronoi relaxation steps via Lloyd's method.

Motivation & Objective

• To address the challenge of detecting kinematic edges in sparse, high-dimensional particle physics data where traditional methods fail due to unknown background forms and detector effects.
• To develop a model-independent, non-parametric approach for identifying structural features in phase space that may indicate new physics beyond the Standard Model.
• To improve edge detection sensitivity in multivariate data by leveraging geometric properties of Voronoi cells and iterative refinement via Lloyd’s method.
• To demonstrate the method’s effectiveness on both synthetic data with known edges and a realistic supersymmetry benchmark at the 13 TeV LHC.

Proposed method

• Construct a Voronoi tessellation of the phase space data, where each event is a generator point and each Voronoi cell represents the region closest to that event.
• Compute geometric attributes of each Voronoi cell, such as area, perimeter, and number of neighboring cells, to form discriminating variables.
• Apply Lloyd’s relaxation algorithm iteratively to reposition generator points toward cell centroids, reducing noise and sharpening edge features.
• Use a variable based on the standard deviation of cell attributes across multiple tiers of neighboring cells to enhance edge contrast.
• Flag candidate edge cells using a threshold on the discriminating variable and validate using ROC curve analysis and the Gini coefficient.
• Evaluate performance via AUROC and Gini index to quantify detection efficiency and robustness across varying density contrasts and data sparsity.

Experimental results

Research questions

• RQ1 Can Voronoi tessellations effectively detect kinematic edges in two-dimensional phase space when the underlying probability distribution is unknown?
• RQ2 How does the addition of Lloyd’s relaxation improve the sensitivity and accuracy of edge detection in sparse data?
• RQ3 To what extent can Voronoi cell attributes such as area and neighbor count serve as robust, model-independent variables for identifying new physics signatures?
• RQ4 How does the method perform in realistic high-energy physics scenarios, such as supersymmetric cascade decays with combinatorial ambiguities?
• RQ5 What is the optimal number of Lloyd iterations and neighbor tiers to maximize edge detection power without overfitting?

Key findings

• The Voronoi-based method successfully detects the true kinematic edge in a 2D toy model with a density contrast of ρ=6, achieving high signal efficiency and low background contamination.
• Lloyd’s relaxation significantly improves detection performance, with the Gini coefficient rising sharply in the first few iterations and plateauing after 3–5 steps.
• Including up to 5 tiers of neighboring Voronoi cells reduces fluctuations and sharpens the edge, enhancing the discriminating power of the test variable.
• In the supersymmetry benchmark, the method clearly identifies the kinematic endpoint in the (m²ℓℓ, (m²jℓℓ−m²ℓℓ)/6) plane, even with combinatorial ambiguity and SM background.
• The ROC curve analysis shows that the method’s performance improves with higher density contrast, and the Gini index reaches a maximum of approximately 0.85 after optimal relaxation and neighbor inclusion.
• The method remains effective even when the analytical form of the signal and background distributions is unknown, making it suitable for model-independent searches.