Identifying phase-space boundaries with Voronoi tessellations

Abstract

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.

Singularity variables for missing energy event kinematics

“…The singularity is then found at the two-dimensional surface boundary of the allowed region [16][17][18][19]. In order to maximize the sensitivity, the experimental analysis should target this two-dimensional surface; this can be done either directly [20][21][22] (e.g., using Voronoi tessellations of the data [23,24]) or by means of a suitable one-dimensional singularity coordinate [25].…”

“…The fact that the event number density is in addition singular at that boundary was later emphasized in [18]. 20 The visible momenta p1, p2 and p3 parametrize a 9-dimensional phase space, but the constraints (5.2) are invariant under the 6-parameter Lorentz group, leaving only 3 relevant visible degrees of freedom. singularity locations [18].…”

“…Since the allowed region is three-dimensional, it is difficult to visualize this enhancement unless one looks at two-dimensional slices through the allowed region -such plots can be found in Fig. 8 of [20] and Fig. 12 of [21].…”

“…The differential distribution of ∆ 4 is known analytically. In terms of the unit-normalized variable q ≡ ∆ 4 /∆ max 4 it is given by [20] dN dq = arcsin(…”

Mass Reconstruction for High Multiplicity Final States Using the Boundary of Phase Space

“…For squark decaysq → jl n l fχ 0 proceeding through a cascade of 2-body decays it has already been demonstrated [4] that mass measurement is possible even in the presence combinatoric and simple Standard Model backgrounds by using Voronoi tessellation, as illustrated in fig. 3.…”