Finding Wombling Boundaries in LHC Data with Voronoi and Delaunay Tessellations

TL;DR

This paper introduces a novel method using Voronoi and Delaunay tessellations to identify wombling boundaries in point data, such as LHC event samples, by evaluating the total gradient flux to detect potential new physics signals.

Contribution

It proposes an alternative approach that simultaneously forms and assesses the significance of all possible boundaries based on total gradient flux, improving boundary detection in noisy data.

Findings

Effective boundary detection in toy examples with varying signal levels.

Method can identify both straight and curved boundaries.

Reduces noise in boundary estimation compared to traditional algorithms.

Abstract

We address the problem of finding a wombling boundary in point data generated by a general Poisson point process, a specific example of which is an LHC event sample distributed in the phase space of a final state signature, with the wombling boundary created by some new physics. We discuss the use of Voronoi and Delaunay tessellations of the point data for estimating the local gradients and investigate methods for sharpening the boundaries by reducing the statistical noise. The outcome from traditional wombling algorithms is a set of boundary cell candidates with relatively large gradients, whose spatial properties must then be scrutinized in order to construct the boundary and evaluate its significance. Here we propose an alternative approach where we simultaneously form and evaluate the significance of all possible boundaries in terms of the total gradient flux. We illustrate our method with several toy examples of both straight and curved boundaries with varying amounts of signal present in the data.