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Identifying Phase Space Boundaries with Voronoi Tessellations
High Energy Physics - Phenomenology · Submitted 8 Jun 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s1 | 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. | background 0.99 | 0.05 | 0.06 | asserted 0.94 |
| s2 | 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. | contribution 0.54 | 0.92 | 0.85 | asserted 1.00 |
| s3 | 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. | interpretation 0.94 | 0.12 | 0.08 | hedged possibility 1.00 |
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The paper
Original 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.
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How the literature uses it
11 arXiv papers cite this in 40 sentences
Papers citing it · 24 sentences without a confident label
Builds on it 2 papers
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In this paper we further develop and refine the Voronoi boundary detection methods from Refs. [ref] .
Finding Wombling Boundaries in LHC Data with Voronoi and Delaunay Tessellations · Introduction · 0.97
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The RSD, $σ̅_i$, is now defined by [equation] where we have normalized by the average volume of the set of neighbors, $N_i$, of the $i$-th cell [equation] Subsequently, in [ref] we showed that this procedure for tagging edge cells can be readily extended to three-dimensional point data, as is the case here.
Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events · Introduction · 0.87
Uses its method or tool 2 papers
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We have tested our Voronoi-based algorithm [ref] for detecting the boundary surface and demonstrated that it can be usefully applied in order to lift the degeneracy along the flat direction.
Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events · Conclusions · 0.93
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For this purpose, Refs. [ref] introduced a parameter $ρ$ which measures the ratio of the event densities $dn/da$ on the two sides of the boundary[Since we are interested in detecting a wombling boundary, the parameter $ρ$ as defined here is more suitable than the more familiar ratio $S/B$ of signal to background inside the signal region $P_SR$.
Finding Wombling Boundaries in LHC Data with Voronoi and Delaunay Tessellations · Simulation Details · 0.84
Cites it as support 3 papers
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As already mentioned, $Δ_4$ has been shown to be a powerful observable for analyzing this decay chain, both for discovery and for mass measurement purposes [ref] .
Applying Machine Learning Techniques To Intermediate-Length Cascade Decays · Review of Phase Space and Kinematic Observables · 0.98
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Second, as shown in [ref] , a uniform background distribution is actually a pretty good approximation to more realistic backgrounds resulting, e.g., from dilepton $tt̅$ events (compare to the results in Section [ref] below).
Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events · A toy study with uniformly distributed background · 0.98
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As it turns out, the latter is a very safe assumption — if anything, $f_NP$ is not only non-vanishing, but often enhanced and even singular on the boundary $∂P_NP$ [ref] .
Finding Wombling Boundaries in LHC Data with Voronoi and Delaunay Tessellations · Introduction · 0.99
Cites it as background 2 papers
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In recent years, several efforts have been made to analyze the global patterns of the collider observations using techniques such as Voronoi and Delaunay tessellations [ref] , network distance metrics [ref] , and machine learning based classifications [ref] .
Intrinsic Geometry of Collider Observations and Forman Ricci Curvature · Introduction · 0.89
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These include traditional bump-hunting methods, edge detection techniques [ref] and recent machine-learning based approaches [ref] .
A Quantum Algorithm for Model-Independent Searches for New Physics · Introduction · 0.91
What it cites · 63 sentences without a confident label
Builds on 1 paper
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While the analysis of Ref. [ref] was limited to data in two dimensions, here we extend the procedure to the three-dimensional case and try to delineate the region, $V_3$, in the phase space of the three variables, $(m_12, m_23, m_13)$.
Edge Detecting New Physics the Voronoi Way · Introduction · 1.00
Uses the method or tool of 3 papers
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Following Ref. [ref] , in order to select “edge" cells in the Voronoi tessellation of the data, we consider the relative standard deviation[In statistics, the RSD is also known as the coefficient of variation (CV).] (RSD), $σ̅_i$, of the volumes of neighboring cells, which is defined as follows.
Edge Detecting New Physics the Voronoi Way · Introduction · 0.91
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The standard approach in the literature is to trade the original variables $m_jℓ_n$ and $m_jℓ_f$ for the ordered pair [ref]
Precise reconstruction of sparticle masses without ambiguities · A realistic example with $tt̅$ background and combinatorics · 0.84
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Events were generated with MadGraph5 [ref] .
MadGraph 5 : Going Beyond · Finding Phase Space Boundaries with Voronoi Tessellations · 1.00
Compares with 1 paper
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If we nevertheless test against a standard SUSY search, e.g. a signature with a same-flavour opposite-sign lepton pair, jets and large missing transverse momentum [ref] , we find a rather low selection efficiency ($1%$), due to the softness of the visible decay products and the tendency of the two final state neutralinos to be back to back, thus reducing the amount of missing transverse energy.] The particles visible in the detector are: a quark jet $v_1=j$, a “near" lepton $v_2=ℓ_n$, and a “far" lepton $v_3=ℓ_f$.
Search for supersymmetry in events containing a same-flavour opposite-sign dilepton pair, jets, and large missing transverse momentum in $\sqrt{s}=8$ TeV $pp$ collisions with the ATLAS detector · Finding Phase Space Boundaries with Voronoi Tessellations · 0.80
Cites as support 1 paper
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This improves on one-dimensional methods, in increasing greatly the amount of information that can be extracted from the data [ref] .[At the same time, this approach avoids the drawbacks of some of the more model-dependent, process-specific, and computationally intensive methods, of which the MEM is perhaps the paradigmatic example.] To be specific, we shall consider the classic SUSY decay chain of three successive two-body decays as shown in Fig. [ref].
Improved mass measurement using the boundary of many-body phase space · Introduction · 0.98
Cites as background 38 papers
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This approach naturally evolved into the so-called “polynomial method” [ref] , where one attempts to solve explicitly for the momenta of the invisible particles in a given event, possibly using additional information from prior measurements of kinematic invariant mass endpoints.
Neutralino Reconstruction at the LHC from Decay-frame Kinematics · Introduction · 0.86
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This approach naturally evolved into the so-called “polynomial method” [ref] , where one attempts to solve explicitly for the momenta of the invisible particles in a given event, possibly using additional information from prior measurements of kinematic invariant mass endpoints.
Missing Momentum Reconstruction and Spin Measurements at Hadron Colliders · Introduction · 0.86
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This approach naturally evolved into the so-called “polynomial method” [ref] , where one attempts to solve explicitly for the momenta of the invisible particles in a given event, possibly using additional information from prior measurements of kinematic invariant mass endpoints.
Accurate Mass Determinations in Decay Chains with Missing Energy · Introduction · 0.86
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