Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.

We critically examine the classic endpoint method for particle mass determination, focusing on difficult corners of parameter space, where some of the measurements are not independent, while others are adversely affected by the experimental resolution. In such scenarios, mass differences can be measured relatively well, but the overall mass scale remains poorly constrained. Using the example of the standard SUSY decay chaiñ q →χ 0 2 →˜ →χ 0 1 , we demonstrate that sensitivity to the remaining mass scale parameter can be recovered by measuring the two-dimensional kinematical boundary in the relevant three-dimensional phase space of invariant masses squared. We develop an algorithm for detecting this boundary, which uses the geometric properties of the Voronoi tessellation of the data, and in particular, the relative standard deviation (RSD) of the volumes of the neighbors for each Voronoi cell in the tessellation. We propose a new observable,Σ, which is the average RSD per unit area, calculated over the hypothesized boundary. We show that the location of theΣ maximum correlates very well with the true values of the new particle masses. Our approach represents the natural extension of the one-dimensional kinematic endpoint method to the relevant three dimensions of invariant mass phase space.

The lack of a new physics signal thus far at the Large Hadron Collider motivates us to consider how to look for challenging final states, with large Standard Model backgrounds and subtle kinematic features, such as cascade decays with compressed spectra. Adopting a benchmark SUSY-like decay topology with a four-body final state proceeding through a sequence of two-body decays via intermediate resonances, we focus our attention on the kinematic variable ∆ 4 which previously has been used to parameterize the boundary of the allowed four-body phase space. We highlight the advantages of using ∆ 4 as a discovery variable, and present an analysis suggesting that the pairing of ∆ 4 with another invariant mass variable leads to a significant improvement over more conventional variable choices and techniques.

Phenomenological studies of Flavored Dark Matter (FDM) models often have to assume a near-diagonal flavor structure in the coupling matrix in order to remain consistent with bounds from flavor violating processes. In this paper we show that for Lepton FDM, such a structure can naturally arise from an extra dimensional setup. The extra dimension is taken to be flat, with the dark matter and mediator fields confined to a brane on one end of the extra dimension, and the Higgs field to a brane on the other end. The Standard Model fermion and gauge fields are the zero modes of corresponding bulk fields with appropriate boundary conditions. Global flavor symmetries exist in the bulk and on the FDM brane, while they are broken on the Higgs brane. Flavor violating processes arise due to the misalignment of bases for which the interactions on the two branes are diagonalized, and their size can be controlled by a choice of the lepton profiles along the extra dimension. By studying the parameter space for the model, we show that when relic abundance and indirect detection constraints are satisfied, the rates for flavor violating processes such as µ → eγ remain far below the experimental limits.

The lack of conclusive evidence for new physics in Run I of the LHC suggests that future discoveries may manifest themselves with small numbers of signal events. In this case, it will be crucial to use analysis techniques that extract as much information as possible from a limited number of events. Previously, a technique exploiting correlations in the full multi-particle phase space to efficiently reconstruct intermediate and invisible masses in decay chains has been demonstrated for the case of four final state particles. We review this technique and discuss its generalization to five or more final state particles. We also demonstrate a new technique for implementing a mass finding algorithm based on the same principle in the presence of realistic backgrounds with Voronoi tessellations.