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 sig
nal 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 Lloyds 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.
Thus far the LHC experiments have yet to discover beyond-the-standard-model physics. This motivates efforts to search for new physics in model independent ways. In this spirit, we describe procedures for using a variant of the Matrix Element Method t
o search for new physics without regard to a specific signal hypothesis. To make the resulting variables more intuitive, we also describe how these variables can be flattened, which makes the resulting distributions more visually meaningful.
The prevalence of null results in searches for new physics at the LHC motivates the effort to make these searches as model-independent as possible. We describe procedures for adapting the Matrix Element Method for situations where the signal hypothes
is is not known a priori. We also present general and intuitive approaches for performing analyses and presenting results, which involve the flattening of background distributions using likelihood information. The first flattening method involves ranking events by background matrix element, the second involves quantile binning with respect to likelihood (and other) variables, and the third method involves reweighting histograms by the inverse of the background distribution.
