Dark Matter at Colliders: a Model-Independent Approach

Andreas Birkedal; Konstantin Matchev; Maxim Perelstein

REVIEW

Dark Matter at Colliders: a Model-Independent Approach

Andreas Birkedal, Konstantin Matchev, Maxim Perelstein

High Energy Physics - Phenomenology · Submitted 29 Feb 2004 · 10 references

Pith's verdict: A clean, correct leading-order formula for e+e- → 2χ+γ tied to the relic density; the abstract's 'guaranteed' does more work than the body supports.

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arXiv IDhep-ph/0403004 (version 2)

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CitationAndreas Birkedal, Konstantin Matchev, Maxim Perelstein. "Dark Matter at Colliders: a Model-Independent Approach." arXiv:hep-ph/0403004 (2004). https://pith.science/paper/UYVJLOQQ

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Editor's note

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The thing worth knowing: Eq. (9) is a real result. Take detailed balancing, take collinear factorization, and you get a compact prediction for the photon spectrum in e+e- → 2χ+γ in terms of σ_an (fixed by WMAP), M_χ, S_χ, J_0, and κ_e. The derivation is textbook-clean and the threshold scaling (β for s-wave, β^3 for p-wave) comes out right. The check against explicit MSSM points in Fig. 2 is the part I'd point to: they generate exact spectra with CompHEP and show the collinear formula tracks the endpoint. That's a genuine validation, not a hand-wave, and they're honest that it degrades at low E_γ because the v^2 expansion breaks down. Good practice, and they say so themselves rather than hiding it. The s-annihilator case is marginal and they admit that too. The soft spot is the word 'guaranteed' in the abstract. The rate is proportional to κ_e, and cosmology fixes σ_an, not κ_e. The body knows this: Table I says the signal 'scales linearly with κ_e,' and the discussion says 'up to the unknown annihilation fraction.' But the abstract and the 'guaranteed' framing suggest something stronger than what's delivered. The stress-test's helicity-suppression point is right in spirit: for a Majorana s-annihilator, κ_e can be tiny, and the paper's only quantitative statement about typical values is the passing '0.2 to 0.3 in the bulk of mSUGRA.' A short paragraph on the expected range of κ_e across the models they invoke would have made the reach plot far more useful. As it stands, Fig. 3 is a plot in (M_χ, κ_e) with no guidance on where real models sit. Smaller things: the 'model-independent' claim is checked only against MSSM, though the derivation is general enough that this is illustrative rather than load-bearing. Coannihilation and non-standard cosmology are assumed away in one sentence; standard for 2004, but it does mean σ_an isn't as fixed as the abstract implies. None of this breaks the central result. Eq. (9) is valid at leading order and the method is sound. Who it's for: anyone working on WIMP collider signatures or LC physics; it's a standard reference for the relic-density-to-collider-rate logic. Worth a serious referee. The physics is right and the framing issue is a revision, not a rejection.

Referee report

Major objections (3)

[Abstract; Eq. (9); Table I; Discussion] The abstract's claim of 'guaranteed rates' (abstract:s0) is stronger than Eq. (9) supports, since the predicted rate is proportional to κ_e, the annihilation fraction into e+e-, which cosmology does not fix. The Discussion does qualify the claim ('up to the unknown annihilation fraction'), and Table I states that the signal 'scales linearly with κ_e,' but the abstract and Introduction do not carry this qualification. For a Majorana WIMP with s-wave annihilation, κ_e is helicity-suppressed by m_e²/M_χ², so the rate can be arbitrarily small even when the WIMP hypothesis is correct. The paper focuses on p-annihilators (Table I, Fig. 3) but never states this reason. I recommend revising the abstract to state the κ_e dependence explicitly and adding a short paragraph quantifying the range of κ_e expected in realistic models, including the helicity-suppression argument.
[Introduction; Eq. (3); Fig. 1] The entire prediction is anchored to σ_an extracted from WMAP under the assumption of standard thermal freeze-out of a single species. The Introduction acknowledges the coannihilation assumption, but non-thermal production, resonances, and threshold effects are not discussed. Since the 'guaranteed' rate is conditional on this cosmological input, the paper should state the freeze-out assumption explicitly and, if possible, estimate how much σ_an can shift under plausible non-standard cosmologies. This is load-bearing because the connection between cosmology and collider is the paper's central idea.
[Fig. 3; Table I] The reach contours in Fig. 3 include only statistical uncertainty and a 0.3% systematic, but the signal prediction itself carries a theory uncertainty from the collinear approximation and the truncation of the v² expansion. Fig. 2 shows that the approximation works near the endpoint but fails at lower Eγ, yet this is not translated into an uncertainty band on Fig. 3. I recommend estimating the theory uncertainty (e.g., by varying the collinear cutoff or comparing to the exact matrix element at a second √s) and showing its effect on the reach contours.

Minor objections (7)

[Eq. (4)] The printed form of Eq. (4) is difficult to parse; please state explicitly the placement of the spin-degeneracy factors (2S_χ+1)² and (2S_X+1)² and the identical-particle factor of 2, and confirm that the convention is consistent with Eq. (6).
[Table I; Fig. 1] The paper does not explain why p-annihilators give larger signals than s-annihilators. The reason is that the p-wave band in Fig. 1 lies above the s-wave band, because a larger σ_an is required to achieve the same relic density when annihilation is p-wave suppressed. A sentence in the text would help the reader interpret Table I.
[Fig. 1 caption] The caption lists three spin values but does not identify which band corresponds to which spin; please label the bands or add a legend.
[Table I caption] The background cross section is non-monotonic in M_χ (peaking near 175 GeV) because the cuts in Eq. (10) depend on M_χ. A sentence in the caption would clarify this.
[Title] The title 'Model-Independent' is slightly overstated, since the result depends on J0, S_χ, M_χ, and κ_e. Consider qualifying it, or at least making the abstract precise about the residual parameters.
[Ref. [7]] The detailed-balancing relation is cited to a 1966 textbook; a more modern reference (e.g., Griest & Seckel, or a review of dark matter) would be more useful to readers.
[Background discussion] The paper states that e+e- → νν̄γ is the main irreducible background but does not give the cross section formula or the cut efficiency. A sentence on how the background is computed would help.

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The paper

The paper claims

Cosmology alone fixes how often dark matter should show up at a lepton collider, if dark matter is a WIMP.

The reading

The paper asks whether cosmology by itself can tell us how often dark matter particles should be produced at a particle collider, without committing to any particular model of what the dark matter is. The authors answer yes for a weakly interacting massive particle: the same annihilation cross section that sets the present relic abundance also, through detailed balancing, fixes the rate at which a pair of such particles is produced in electron-positron collisions. Because a WIMP pair is invisible in the detector, they attach a photon emitted soft or collinear with the beams, and use factorization theorems to tie the photon-tagged rate back to the invisible one. The resulting formula needs only a few inputs: the WIMP mass and spin, whether annihilation is dominated by s-wave or p-wave, and the fraction of annihilations that end in electrons. If the reasoning holds, a 500 GeV lepton collider acquires a quantitative target to aim at before any WIMP model has been specified.

What carries the argument

Two standard tools are chained together. The first is detailed balancing, which relates the spin-averaged cross sections for $chi chi$ to $X_i bar{X}_i$ and its inverse up to a ratio of spin-degeneracy factors and a velocity factor, so that a quantity measured by cosmology becomes a production cross section at a collider. The second is soft/collinear factorization, which says that the rate for $e^+e^-$ to two WIMPs plus a photon factors into a universal collinear radiator $F(x, cos heta) = (alpha/pi), [(1+(1-x)^2)/x], [1/sin^2 heta]$ times the WIMP-pair cross section evaluated at the reduced energy $hat{s} = (1-x)s$. The bridge between the two is the annihilation fraction $kappa_i = sigma_i^{(J_0)}/sigma_an$, the share of annihilations going into a given Standard Model final state, which sums to one over all channels and is the one continuous parameter that collider data would have to supply.

Extended reading notes

Core claim

The central claim is Eq. (9): a differential cross section for $e^+e^-$ to two WIMPs plus a collinear photon, written entirely in terms of quantities fixed either by cosmology or by a small discrete menu of WIMP properties. The overall normalization is the annihilation cross section $s$-wave coefficient $s_an$ (denoted $s_an$ in the paper), which the WMAP relic abundance $Omega_dm h^2 = 0.112 pm 0.009$ pins down as a function of the WIMP mass for s-wave and p-wave annihilators and for spins 0, 1/2, and 1. The model dependence collapses into the mass $M_chi$, the spin $S_chi$, the dominant partial wave $J_0$, and the annihilation fraction $kappa_e$ into electrons. The authors check the formula against explicit MSSM points tuned to the measured relic density at $M_chi = 100, 150, 200, 225$ GeV and find the photon spectrum near the kinematic endpoint reproduced well, with the agreement degrading at lower photon energies where the relative motion of the WIMP pair becomes relativistic and higher-order terms in the velocity expansion matter. They then translate the formula into reach contours for a 500 GeV collider with 500 fb$^{-1}$, showing that p-wave annihilators with a sizeable $kappa_e$ are discoverable over a broad mass range, while s-wave annihilators are at best marginal because the rate carries an extra suppression from the p-wave-like velocity factor.

Load-bearing premise

The chain from cosmology to collider rate assumes the WIMP relic abundance is set entirely by ordinary thermal freeze-out of a single species, with no coannihilation with other exotic particles and no non-standard cosmology, an assumption the paper states explicitly in the introduction.

Editorial extensions

If this is right

A 500 GeV electron-positron collider with 500 fb$^{-1}$ can probe p-wave annihilating WIMPs with sizeable electron fraction over a wide mass range using only photons near the endpoint of the spectrum plus missing energy.
The search strategy is fixed in advance by cosmology: the energy window in Eq. (10) depends only on the assumed WIMP mass, so the analysis can be optimized before any model is chosen.
Beam polarization raises the signal-to-background ratio substantially, by factors of order 5 for electron polarization alone and about 18.5 for combined electron and positron polarization in the helicity-conserving case, because the dominant $W$-exchange background is left-handed while the WIMP coupling need not be.
A detected signal would measure $kappa_e$, the electron annihilation fraction, giving a collider handle on the same quantity that governs WIMP annihilation in the early universe and in indirect-detection targets.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the prediction is a lower-bound-style guarantee rather than an upper bound, the test is asymmetric: a signal confirms the WIMP hypothesis, but a null result cannot exclude it, since an unmeasured small $kappa_e$ or a suppressed partial wave can hide the rate.
If coannihilation, thresholds, or non-thermal production contribute to the relic abundance, the cosmologically inferred $sigma_an$ shifts and the quoted rate moves with it, so the same machinery could be inverted to bound how much of the abundance comes from ordinary thermal freeze-out.
The endpoint-only strategy makes the method's statistical reach a function of photon energy resolution near the kinematic edge, which suggests that the practical sensitivity is set by detector energy resolution as much as by luminosity.
The factorization step is indifferent to what the invisible pair is, so the same template could in principle be reused for any neutral stable particle whose abundance is independently known, not only for WIMPs.

Original abstract

Assuming that cosmological dark matter consists of weakly interacting massive particles, we use the recent precise measurement of cosmological parameters to predict the guaranteed rates of production of such particles in association with photons at electron-positron colliders. Our approach is based on general physical principles such as detailed balancing and soft/collinear factorization. It leads to predictions that are valid across a broad range of models containing WIMPs, including supersymmetry, universal extra dimensions, and many others. We also discuss the discovery prospects for the predicted experimental signatures.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,579 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Assuming that cosmological dark matter consists of weakly interacting massive particles, we use the recent precise measurement of cosmological parameters to predict the guaranteed rates of production of such particles in association with photons at electron-positron colliders. Our approach is based on general physical principles such as detailed balancing and soft/collinear factorization. It leads to predictions that are valid across a broad range of models containing WIMPs, including supersymmetry, universal extra dimensions, and many others. We also discuss the discovery prospects for the predicted experimental signatures.

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	Assuming that cosmological dark matter consists of weakly interacting massive particles, we use the recent precise measurement of cosmological parameters to predict the guaranteed rates of production of such particles in association with photons at electron-positron colliders.	contribution 0.96	0.77	0.46	asserted 0.87
s1	Our approach is based on general physical principles such as detailed balancing and soft/collinear factorization.	method 1.00	0.51	0.05	asserted 1.00
s2	It leads to predictions that are valid across a broad range of models containing WIMPs, including supersymmetry, universal extra dimensions, and many others.	interpretation 0.41	0.81	0.23	asserted 1.00
s3	We also discuss the discovery prospects for the predicted experimental signatures.	contribution 0.73	0.71	0.07	unclear 0.68

What kind of paper the classifier reports this is: theoretical result 0.91 · evidence from proof or derivation 0.77.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Values of the quantity

**Figure 3.** FIG. 3: The reach of a 500 GeV unpolarized electron-positron

Showing 2 of the paper's 3 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0403004 by the authors.

References

Works cited (10)

[1]

G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. 267, 195 (1996) [hep-ph/9506380]

View on Pith Pith review arXiv 1996
[2]

G. Servant and T. Tait, Nucl. Phys. B 650, 391 (2003) [hep-ph/0206071]; H. C. Cheng, J. Feng and K. Matchev, Phys. Rev. Lett. 89, 211301 (2002) [hep-ph/0207125]

View on Pith Pith review arXiv 2003
[3]

A. Birkedal and J. Wacker, Phys. Rev. D 69, 065022 (2004) [hep-ph/0306161]

View on Pith Pith review arXiv 2004
[4]

We assume that χ and ¯χ are identical; the only modiﬁ- cation required to lift this assumption is the insertion of appropriate factors of two to undo the identical-particle factors implicit in our formulas

View on Pith
[5]

The expansion fails in the presence of nearby thresholds or s-channel poles, see K. Griest and D. Seckel, Phys. Rev. D 43, 3191 (1991). However neither of these cases 5 is generic, as they require some ﬁne-tuning of the masses

View on Pith 1991
[6]

D. N. Spergel et al., Astrophys. J. Suppl. 148, 175 (2003) [astro-ph/0302209]

View on Pith Pith review arXiv 2003
[7]

W. Frazer, “Elementary Particles” (Prentice-Hall, 1966)

View on Pith 1966
[8]

J. A. Aguilar-Saavedra et al. [ECF A/DESY LC Physics Working Group Collaboration], hep-ph/0106315

View on Pith Pith review arXiv
[9]

The photon spectra were computed using the CompHEP package; see A. Pukhov et al. , hep-ph/9908288

View on Pith Pith review arXiv
[10]

The relic density was estimated using the DarkSUSY package; see P. Gondolo et. al., astro-ph/0406204

View on Pith Pith review arXiv

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How later papers used it

82 later papers cite it

Evidence: substantial. 72 of the citing papers share no author with it, and 13 of those carry a confident label from Pith's citation classifier.

Pith read 25 of the 122 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

5 later papers by other authors are listed below: 2 used its method or tool, 1 used its data or values, 1 compared its own results with it and 1 cited it as support. 1 more paper by the same authors is listed: 1 built on it.

Builds on it 1 of 2 papers with this label · 1 by the same authors

By the same authors

Extended this paper's formalism into the region away from the endpoint of the photon energy spectrum.

Shedding Light on the Dark Sector with Direct WIMP Production (2009) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

Uses its method or tool 2 of 7 papers with this label

Related the WIMP pair-production process to radiative WIMP pair production for soft or collinear photons through this paper.

Detection of WIMP-like dark matter in some extensions of the Standard Model (2011) · 0.89 · paraphrased: the licence does not allow quoting
Related the WIMP pair-production process to radiative WIMP pair production for soft or collinear photons through this paper.

Determining the WIMP mass using the complementarity between direct and indirect searches and the ILC (2008) · 0.96 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 3 papers with this label

Used this paper's value of a_tot = 0.81±0.09 pb, required by the WMAP dark matter abundance, assuming its dark matter candidate makes up all dark matter.

A Unified Dark Matter Model in sUED (2008) · 0.80 · paraphrased: the licence does not allow quoting

Compares with it 1 of 4 papers with this label

Evaluated cross sections for different masses of hidden-sector gauge bosons at 500 GeV to compare with the background and WIMPs signal calculated in this paper.

Prospects for detecting $SU(2)_L$ hidden sector bosons at ILC (2019) · 0.95 · paraphrased: the licence does not allow quoting

Cites it as support 1 of 3 papers with this label

Said that the collinear approximation works well, also supported by a similar analysis in this paper.

Unitarisation of EFT Amplitudes for Dark Matter Searches at the LHC (2016) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

81 arXiv papers cite this in 121 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 · 80 sentences without a confident label

Builds on it 2 papers

Our main results are as follows: * We extended the formalism of Ref. [ref] into the region away from the endpoint of the photon energy spectrum.

Shedding Light on the Dark Sector with Direct WIMP Production · Conclusions · 1.00
The study which we shortly outline here [ref] , is a model specific application of the model independent study to search for WIMP Dark Matter at the ILC [ref] , for further details see Ref. [ref] .

Measurement of radiative neutralino production · Experimental analysis · 0.93

Uses its method or tool 7 papers

In this case, the two processes are related through [ref] : [equation] where $x = 2E_γ/√(s)$, $θ$ is the angle between the photon direction and the direction of the incoming electron beam, $σ̃$ is the WIMP pair-production cross-section produced at the reduced center of mass energy $s̃=(1-x)s$, and $F$ is defined as: [equation]

Detection of WIMP-like dark matter in some extensions of the Standard Model · The Approach · 0.89
A model independent description of ISR associated WIMP pair production can be derived as in [ref] .

Model independent WIMP Searches in full Simulation of the ILD Detector · Dark Matter and WIMPs · 0.82
In this case, the two processes are related through [ref] : [equation] where $x = 2E_γ/√(s)$, $θ$ is the angle between the photon direction and the direction of the incoming electron beam, $σ̃$ is the WIMP pair-production cross-section produced at the reduced center of mass energy $s̃=(1-x)s$, and $F$ is defined as: [equation]

Determining the WIMP mass using the complementarity between direct and indirect searches and the ILC · The Approach · 0.96

Uses its data or values 3 papers

The background cross section at the ILC ($√(S)$=500 GeV) with no polarization was provided in Ref. [ref] , which is treated as the function of the DM mass, and has a rather large value.

Associated production of a photon with dark matter pair at the ILC within the Littlest Higgs model with T-parity · Discussions and conclusions · 0.97
The present dark matter abundance from WMAP collaboration, $0.096 < Ω h^2< 0.122 (2σ)$, requires $a_tot = 0.81±0.09 pb$ [ref] [ref] , assuming the dark matter candidate in our model can make up all the dark matter.

A Unified Dark Matter Model in sUED · Annihilation, Co-annihilation and Relic Abundance · 0.80
For concreteness, we shall use one of the low energy supersymmetry study points from Ref. [ref] , namely, the one with neutralino mass of $M_χ=225$ GeV.

Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression · Data generated with Madgraph · 1.00

Compares with it 4 papers

We evaluated the cross-section with different values of mass of hidden-sector gauge bosons at center of mass $√(s)=500$ GeV to compare with the background and the WIMPs signal calculated in [ref] .

Prospects for detecting $SU(2)_L$ hidden sector bosons at ILC · Results · 0.95
As we will see, this gives a substantially better sensitivity than the model-independent search of [ref] .

Shedding Light on the Dark Sector with Direct WIMP Production · The Signature · 0.96
Our effective field theory description of dark matter is largely model independent, but differs in important ways from previous model-independent analyses [ref] .

Maverick dark matter at colliders · Introduction · 0.95

Cites it as support 2 papers

The absence of a robust handle to distinguish events with direct WIMP production from the large SM background makes it virtually impossible to study this channel at the LHC [ref] .

Shedding Light on the Dark Sector with Direct WIMP Production · Introduction · 0.96
Thus the collinear approximation works well, which is also supported by a similar analysis in Ref. [ref] .

Unitarisation of EFT Amplitudes for Dark Matter Searches at the LHC · Validity of Collinear Approximation · 1.00

Cites it as background 21 papers

This idea was first explored in a model independent approach for the International Linear Collider (Ilc) using mono-photons in a non-relativistic approximation [ref] .

Illuminating Dark Matter at the ILC · Introduction · 0.90
Previous studies at colliders often use effective approach for discussing the prospects for discovery of WIMPs dark matter [ref] .

Prospects for detecting $SU(2)_L$ hidden sector bosons at ILC · Discussion and conclusions · 0.92
Recently, there has been a lot of theoretical effort directed at testing the dark matter hypothesis at the LHC [ref] and the future International Linear Collider (ILC) [ref] .

Dark Matter Particle Spectroscopy at the LHC: Generalizing MT2 to Asymmetric Event Topologies · Introduction · 0.98

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. 267, 195 (1996) [hep-ph/9506380]

View on Pith Pith review arXiv 1996

[2] [2]

G. Servant and T. Tait, Nucl. Phys. B 650, 391 (2003) [hep-ph/0206071]; H. C. Cheng, J. Feng and K. Matchev, Phys. Rev. Lett. 89, 211301 (2002) [hep-ph/0207125]

View on Pith Pith review arXiv 2003

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A. Birkedal and J. Wacker, Phys. Rev. D 69, 065022 (2004) [hep-ph/0306161]

View on Pith Pith review arXiv 2004

[4] [4]

We assume that χ and ¯χ are identical; the only modiﬁ- cation required to lift this assumption is the insertion of appropriate factors of two to undo the identical-particle factors implicit in our formulas

View on Pith

[5] [5]

The expansion fails in the presence of nearby thresholds or s-channel poles, see K. Griest and D. Seckel, Phys. Rev. D 43, 3191 (1991). However neither of these cases 5 is generic, as they require some ﬁne-tuning of the masses

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D. N. Spergel et al., Astrophys. J. Suppl. 148, 175 (2003) [astro-ph/0302209]

View on Pith Pith review arXiv 2003

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W. Frazer, “Elementary Particles” (Prentice-Hall, 1966)

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J. A. Aguilar-Saavedra et al. [ECF A/DESY LC Physics Working Group Collaboration], hep-ph/0106315

View on Pith Pith review arXiv

[9] [9]

The photon spectra were computed using the CompHEP package; see A. Pukhov et al. , hep-ph/9908288

View on Pith Pith review arXiv

[10] [10]

The relic density was estimated using the DarkSUSY package; see P. Gondolo et. al., astro-ph/0406204

View on Pith Pith review arXiv