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.
Supersymmetric (SUSY) models, even those described by relatively few parameters, generically allow many possible SUSY particle (sparticle) mass hierarchies. As the sparticle mass hierarchy determines, to a great extent, the collider phenomenology of
a model, the enumeration of these hierarchies is of the utmost importance. We therefore provide a readily generalizable procedure for determining the number of sparticle mass hierarchies in a given SUSY model. As an application, we analyze the gravity-mediated SUSY breaking scenario with various combinations of GUT-scale boundary conditions involving different levels of universality among the gaugino and scalar masses. For each of the eight considered models, we provide the complete list of forbidden hierarchies in a compact form. Our main result is that the complete (typically rather large) set of forbidden hierarchies among the eight sparticles considered in this analysis can be fully specified by just a few forbidden relations involving much smaller subsets of sparticles.
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.
We present a general procedure for measuring the tensor structure of the coupling of the scalar Higgs-like boson recently discovered at the LHC to two Z bosons, including the effects of interference among different operators. To motivate our concern
with this interference, we explore the parameter space of the couplings in the effective theory describing these interactions and illustrate the effects of interference on the differential dilepton mass distributions. Kinematic discriminants for performing coupling measurements that utilize the effects of interference are developed and described. We present projections for the sensitivity of coupling measurements that use these discriminants in future LHC operation in a variety of physics scenarios.
The importance of the H -> ZZ -> 4l golden channel was shown by its major role in the discovery, by the ATLAS and CMS collaborations, of a Higgs-like boson with mass near 125 GeV. We analyze the discrimination power of the matrix element method both
for separating the signal from the irreducible ZZ background and for distinguishing various spin and parity hypotheses describing a signal in this channel. We show that the proper treatment of interference effects associated with permutations of identical leptons in the four electron and four muon final states plays an important role in achieving the best sensitivity in measuring the properties of the newly discovered boson. We provide a code, MEKD, that calculates kinematic discriminants based on the full leading order matrix elements and which will aid experimentalists and phenomenologists in their continuing studies of the H -> ZZ -> 4l channel.
We have recently examined a large number of points in the parameter space of the phenomenological MSSM, the 19-dimensional parameter space of the CP-conserving MSSM with Minimal Flavor Violation. We determined whether each of these points satisfied e
xisting experimental and theoretical constraints. This analysis provides insight into general features of the MSSM without reference to a particular SUSY breaking scenario or any other assumptions at the GUT scale. This study opens up new possibilities for SUSY phenomenology both in colliders and in astrophysical experiments. Here we shall discuss the implications of this analysis relevant to the study of dark matter.
