Distinguishing Dark Matter Stabilization Symmetries Using Multiple Kinematic Edges and Cusps

Devin G. E. Walker; Doojin Kim; Kaustubh Agashe; Manuel Toharia

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Distinguishing Dark Matter Stabilization Symmetries Using Multiple Kinematic Edges and Cusps

Kaustubh Agashe, Doojin Kim, Manuel Toharia, Devin G. E. Walker

High Energy Physics - Phenomenology · Submitted 4 Mar 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this case, we note that certain decay chain "topologies" of the mother particle which are present for the Z_3 case (but absent for the Z_2 case) generate a "cusp" in the invariant mass distribution of the SM particles.

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arXiv ID1003.0899 (version 2)

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CitationDevin G. E. Walker, Doojin Kim, Kaustubh Agashe, Manuel Toharia. "Distinguishing Dark Matter Stabilization Symmetries Using Multiple Kinematic Edges and Cusps." arXiv:1003.0899 (2010). https://pith.science/paper/P2JI4H2J

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.56 · human participants 0.01 · controlled comparison 0.44 · randomized assignment 0.01 · states quantitative result 0.21 · compares with prior results 0.48 · mentions code or data availability 0.02.

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We emphasize that the stabilizing symmetry for dark matter (DM) particles does not have to be the commonly used parity (Z_2) symmetry. We therefore examine the potential of the colliders to distinguish models with parity stabilized DM from models in which the DM is stabilized by other symmetries. We often take the latter to be a Z_3 symmetry for illustration. We focus on signatures where a single particle, charged under the DM stabilization symmetry decays into the DM and Standard Model (SM) particles. Such a Z_3-charged "mother" particle can decay into one or two DM particles along with the same SM particles. This can be contrasted with the decay of a Z_2-charged mother particle, where only one DM particle appears. Thus, if the intermediate particles in these decay chains are off-shell, then the reconstructed invariant mass of the SM particles exhibits two kinematic edges for the Z_3 case but only one for the Z_2 case. For the case of on-shell intermediate particles, distinguishing the two symmetries requires more than the kinematic edges. In this case, we note that certain decay chain "topologies" of the mother particle which are present for the Z_3 case (but absent for the Z_2 case) generate a "cusp" in the invariant mass distribution of the SM particles. We demonstrate that this cusp is generally invariant of the various spin configurations. We further apply these techniques within the context of explicit models.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We emphasize that the stabilizing symmetry for dark matter (DM) particles does not have to be the commonly used parity (Z_2) symmetry.	background 0.92	0.14	0.14	asserted 0.73
s1	We therefore examine the potential of the colliders to distinguish models with parity stabilized DM from models in which the DM is stabilized by other symmetries.	contribution 0.98	0.59	0.10	hedged possibility 0.64
s2	We often take the latter to be a Z_3 symmetry for illustration.	method 0.72	0.55	0.04	asserted 0.83
s3	We focus on signatures where a single particle, charged under the DM stabilization symmetry decays into the DM and Standard Model (SM) particles.	method 0.56	0.44	0.04	asserted 0.97
s4	Such a Z_3-charged "mother" particle can decay into one or two DM particles along with the same SM particles.	method 0.52	0.32	0.05	asserted 0.75
s5	This can be contrasted with the decay of a Z_2-charged mother particle, where only one DM particle appears.	background 0.60	0.16	0.05	asserted 1.00
s6	Thus, if the intermediate particles in these decay chains are off-shell, then the reconstructed invariant mass of the SM particles exhibits two kinematic edges for the Z_3 case but only one for the Z_2 case.	result 0.90	0.65	0.29	asserted 0.95
s7	For the case of on-shell intermediate particles, distinguishing the two symmetries requires more than the kinematic edges.	limitation 0.63	0.43	0.07	asserted 0.99
s8	In this case, we note that certain decay chain "topologies" of the mother particle which are present for the Z_3 case (but absent for the Z_2 case) generate a "cusp" in the invariant mass distribution of the SM particles.	result 0.51	0.74	0.25	asserted 0.98
s9	We demonstrate that this cusp is generally invariant of the various spin configurations.	result 0.96	0.88	0.13	asserted 1.00
s10	We further apply these techniques within the context of explicit models.	contribution 0.81	0.88	0.05	asserted 0.95

What kind of paper the classifier reports this is: method or tool 0.64 · evidence from proof or derivation 0.66.

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Original abstract

We emphasize that the stabilizing symmetry for dark matter (DM) particles does not have to be the commonly used parity (Z_2) symmetry. We therefore examine the potential of the colliders to distinguish models with parity stabilized DM from models in which the DM is stabilized by other symmetries. We often take the latter to be a Z_3 symmetry for illustration. We focus on signatures where a single particle, charged under the DM stabilization symmetry decays into the DM and Standard Model (SM) particles. Such a Z_3-charged "mother" particle can decay into one or two DM particles along with the same SM particles. This can be contrasted with the decay of a Z_2-charged mother particle, where only one DM particle appears. Thus, if the intermediate particles in these decay chains are off-shell, then the reconstructed invariant mass of the SM particles exhibits two kinematic edges for the Z_3 case but only one for the Z_2 case. For the case of on-shell intermediate particles, distinguishing the two symmetries requires more than the kinematic edges. In this case, we note that certain decay chain "topologies" of the mother particle which are present for the Z_3 case (but absent for the Z_2 case) generate a "cusp" in the invariant mass distribution of the SM particles. We demonstrate that this cusp is generally invariant of the various spin configurations. We further apply these techniques within the context of explicit models.

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References

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Cited by 9 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Guide to transverse projections and mass-constraining variables
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Semi-annihilation and cross-sector annihilation can change the dark matter relic density by factors of a few in minimal Z3 and Z4 scalar models, as shown by micrOMEGAs implementations with explicit benchmark points.

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Semi-annihilation of Z3-charged dark matter, not just standard annihilation, is what brings the predicted relic density of this radiative neutrino mass model into agreement with the observed value.
Dark Discrete Gauge Symmetries
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A broken dark U(1) gauge symmetry can leave a Z_N remnant that stabilizes dark matter, and for composite N it can stabilize several species simultaneously, giving distinctive nuclear recoil spectra and Higgs decay patterns.
A Review of the Mass Measurement Techniques proposed for the Large Hadron Collider
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The paper is a structured review of kinematic mass measurement techniques for LHC events with invisible particles, organized by decay topology and paired with their assumptions and known limitations.

How the literature uses it

32 arXiv papers cite this in 59 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 48 sentences without a confident label

Builds on it 1 paper

Since earlier work [ref] only studied measurements of the visible part of a single mother decay, here we focussed on using the information from both mother decays, including the missing energy in the event which is shared between the two decay chains (or sides).

Using M_T2 to Distinguish Dark Matter Stabilization Symmetries · Conclusions and Outlook · 0.80

Uses its method or tool 1 paper

Based on the method developed in Refs. [ref] , the two symmetries can be potentially discriminated by using multiple kinematical edges and cusps.

Radiative Neutrino Mass with $Z_3$ Dark matter: From Relic Density to LHC Signatures · Signatures for $χ_L$ DM · 1.00

Compares with it 2 papers

Solving the above-given two equations, we obtain both mother and DM masses [The upper edge from SM$_ 2 2$ provides redundant information, but of course can be a cross-check.]: M = 2/3√( C_ E2 )(4C_ E2 -C_ E3 ) m_DM = 2/3√(C_E2)√((4C_ E2 -C_ E3 )(C_ E2 -C_ E3 )) This situation is somewhat like the double-edge signal for single mother decay studied in reference [ref] , where it was again possible to obtain mother and DM masses from the two edges in invariant mass distribution of visible/SM final state.

Using M_T2 to Distinguish Dark Matter Stabilization Symmetries · One Visible/SM Particle in Each Decay Chain · 0.93
In particular, Refs. [ref] used the endpoints of kinematic distributions to probe the stabilization symmetry of the DM, whereas our method relies quite directly on peak measurements and only marginally on endpoint measurements.

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The idea that the baryon asymmetry and dark matter in the Universe may have common origin, is of considerable interest [ref] .

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Even then, the signal distribution $f_NP$ often exhibits some special features[In general, such kinematic singularities arise in the course of projecting the full phase space onto a lower-dimensional space of observables [ref] .], e.g., kinematic endpoints [ref] , kinematic boundaries [ref] , kinks [ref] and cusps [ref] , which are absent in the background distribution $f_SM$.

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Various techniques involving kinematic variables have also been proposed for the purpose of determining decay topologies [ref] .

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What it cites · 39 sentences without a confident label

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To this end, we take a “toy" limit of the model discussed in reference [ref] .

Dark Matter Stabilization Symmetries from Spontaneous Symmetry Breaking · Stabilization Symmetries from Spontaneous Symmetry Breaking · 0.80

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The differential distribution $1/Γ ∂Γ/∂m_ac^2$ that we want to study can be obtained for this “new” topology easily by noting that the differential distribution $1/Γ ∂^2 Γ/∂u∂v$ must be flat, where the variables are defined as follows u=1-cosθ_c DM^(C)/2 and v=1-cosθ_ca^(B)/2, with $θ_ca^(B)$ being the angle between $c$ and $a$ in the rest frame of $B$, and $θ_c DM^(C)$ being the angle between $c$ and DM in the rest frame of $C$ [ref] .

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In figure [ref] we show the distribution (again obtained with Madgraph [ref] ) for the same decay chain as in Figure [ref], but where the chiral structure of some couplings has been modified from before.

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A consensus picture of the nature of such a particle is provided by a host of astrophysical, cosmological and direct detection experiments: A viable DM candidate must be electrically neutral and colorless, non-relativistic at redshifts of $z ∼3000$ and generate the measured relic abundance of $h^2 Ω_DM = 0.1131 ±0.0034$ [ref] .

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Cites as support 2 papers

Similarly, the constraints from direct detection of DM can be satisfied: see Fig. 7 of reference [ref] and Fig. 3 of reference [ref] and related discussion.

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Similarly, the constraints from direct detection of DM can be satisfied: see Fig. 7 of reference [ref] and Fig. 3 of reference [ref] and related discussion.

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Cites as background 3 papers

With this background, in reference [ref] , a model was introduced in which a $SU(N)$ gauge group is spontaneously broken to the $Z_N$ center.

Dark Matter Stabilization Symmetries from Spontaneous Symmetry Breaking · Stabilization Symmetries from Spontaneous Symmetry Breaking · 0.99
This model is based on the framework of a warped extra dimension with the SM fields propagating in it which can address both the Planck-weak and flavor hierarchy problems of the SM [ref] .

Warped 5-Dimensional Models: Phenomenological Status and Experimental Prospects · Warped GUT · 0.89
There is compelling evidence for the existence of dark matter (DM) in the universe [ref] .

Particle Dark Matter: Evidence, Candidates and Constraints · Introduction · 0.87

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