A Markov Chain Monte Carlo Analysis of the CMSSM

Leszek Roszkowski; Roberto Ruiz de Austri; Roberto Trotta

REVIEW

A Markov Chain Monte Carlo Analysis of the CMSSM

Roberto Ruiz de Austri, Roberto Trotta, Leszek Roszkowski

High Energy Physics - Phenomenology · Submitted 2 Feb 2006 · 104 references

Pith's verdict: A careful, genuinely useful Bayesian MCMC scan of the CMSSM whose headline robustness claim holds; the m0 and σ_SI^p numbers are softer than the abstract's precision suggests, and the authors know it.

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arXiv IDhep-ph/0602028 (version 3)

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CitationLeszek Roszkowski, Roberto Ruiz de Austri, Roberto Trotta. "A Markov Chain Monte Carlo Analysis of the CMSSM." arXiv:hep-ph/0602028 (2006). https://pith.science/paper/T2GPYWOZ

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Editor's note

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Bottom line: this is solid, useful work, and the central claim survives scrutiny. The paper runs a proper Bayesian MCMC over the CMSSM with nuisance SM parameters marginalized, smears hard experimental limits with estimated theoretical errors instead of cutting on them, and — the part that matters — reruns the whole analysis under two prior ranges to test robustness. That last step is what makes the conclusions worth quoting: m1/2, A0 and tanβ come out essentially prior-independent, and m0 does not. The authors say so plainly in the abstract [abstract:s10] and back it with Table 5 and Fig. 4. Credit where due: including α_em(MZ) as a nuisance parameter and finding it moves Ω h2 by ~10% is a real, easily-missed effect, and the focus-point region had not been covered by MCMC before. The correlation maps (BR(Bs→μμ) against BR(B̄→Xsγ) and σ_SI^p) are the kind of thing people will actually use once SUSY is found, or not found. On the stress-test note: it lands, but narrowly, and the paper already concedes the ground. §3.3 states outright that in the FP region the relic-density error is 'almost certainly much larger' and can reach ~100%, while Eq. 3.11 applies a flat 10% everywhere. §4.1 and §4.4 repeat the caveat about the FP location and the ~1.6e-8 pb σ_SI^p band. So the m0 < 2.10 TeV bound and the σ_SI^p 68% interval are quoted at more precision than the likelihood supports — true — but this is a flagged limitation, not a hidden one, and it does not touch the m1/2/A0/tanβ conclusions. Worth noting the classifier's 'limitations: none found' is simply wrong here; the authors are more candid than that. Smaller things: no chains or code shipped (normal for 2006, still a shame), and a 2–3% acceptance rate is low, though they report Gelman–Rubin R−1 < 0.05 and cross-checks between runs. The posterior-versus-quality-of-fit comparison in §4.3 is a good idea, but the claim that the tanβ preference is volume-driven rests on a 2D projection and is stated a bit more firmly than the evidence carries. Who should read it: anyone doing CMSSM phenomenology, dark matter direct detection forecasts, or Bayesian inference in SUSY. Send it to referees — it deserves the time.

Referee report

Significance

The paper is a careful and, for its time, methodologically advanced application of Bayesian MCMC to the CMSSM. Its durable contributions are the systematic treatment of theoretical and experimental uncertainties in the likelihood (section 3.1), the explicit marginalization over Standard Model nuisance parameters including alpha_em(M_Z), the smearing of sharp experimental limits rather than hard cuts, the explicit prior-sensitivity study with two prior ranges, and the honest separation of posterior probability from quality of fit (section 4.3). The reported correlations among BR(B_s -> mu+ mu-), BR(Bbar -> X_s gamma), delta a_mu^SUSY and sigma_p^SI (section 4.5, Fig. 14) are useful and falsifiable, and the observation that the 'WMAP strips' widen under full marginalization (section 4.5, Fig. 15) is a genuine and often-cited point. The convergence diagnostics (Gelman-Rubin R-1 < 0.05, appendix A.2) and the use of publicly available spectrum and relic-density codes make the analysis reproducible in principle. The main caveat is that several headline numbers depend on hand-chosen theoretical error scales, which the authors flag but do not quantify in the focus-point region.

Major objections (2)

[Section 3.3, Eq. (3.11); Table 5; Eq. (4.4); Figs. 12 and 13] The relic-density theoretical error is set to a uniform tau(Omega h^2) = 10% at every point of parameter space (Eq. 3.11), while the same section states that in the focus-point region 'the error is almost certainly much larger' and can reach about 100%. The focus-point region is not peripheral to the quoted results: it supplies the large-m_0 tail of the posterior (Figs. 2 and 6) and the distinctive sigma_p^SI ~ 1.6e-8 pb band that Figs. 12 and 13 present as a focus-point signature. Consequently the 68% upper bound m_0 < 2.10 TeV quoted in the abstract (s4) and in Table 5, and the 68% interval 1.0e-10 pb < sigma_p^SI < 1.0e-8 pb of Eq. (4.4), are stated at a precision that the likelihood does not support. The authors acknowledge the issue in the text, so this is not a new finding, but it remains unquantified. I would ask either for one variant run in which tau(Omega h^2) is inflated in the focus-point region (a factor of a few would suffice to demonstrate the direction and magnitude of the effect), or for an explicit statement in the abstract and in Table 5 that the m_0 upper bound and the high-sigma_p^SI band are not robust. This does not undercut the central robustness claim of s10, which already excludes m_0 from the robust set, but it does affect how the abstract's numbers should be read.
[Section 3.3, Eqs. (3.14)-(3.15); Section 4.4; Fig. 13] The hadronic matrix elements entering sigma_p^SI are quoted with their uncertainties (f_Ts^(p) = 0.118 +/- 0.062, i.e. a roughly 50% error, plus the smaller f_Tu, f_Td and mass-ratio errors), and the text correctly notes that f_Ts dominates the cross section. Unlike the Standard Model parameters, however, these are not treated as nuisance parameters and are not marginalized over; a single central set from Ref. [80] is adopted. Since sigma_p^SI is one of the paper's highlighted outputs (Eq. 4.4, Figs. 12 and 13, and the complementarity discussion in section 4.4), the resulting posterior is under-dispersed by an amount that is at least comparable to the spread shown. I would ask the authors either to propagate these form-factor uncertainties as additional nuisance parameters, or to state explicitly in section 4.4 and in the caption of Fig. 13 that the quoted sigma_p^SI intervals do not include hadronic-uncertainty dispersion, and to estimate how much the 68% interval of Eq. (4.4) would widen.

Minor objections (10)

[Table 8] The 95% interval quoted for the lightest neutralino in the no-(g-2)_mu column, (0.57, 0.76) TeV, is inconsistent with the corresponding 68% interval (0.23, 0.60) TeV, since the 95% lower bound cannot lie above the 68% lower bound. This looks like a typographical error for a value near 0.07 TeV; please check and correct.
[Table 9] The 95% intervals for Omega_chi h^2 in both columns are printed as (0.946, 0.157) and (0.949, 0.158), which are evidently missing a leading zero and should read (0.0946, 0.157) and (0.0949, 0.158). Please correct, since these entries are compared directly with the WMAP range.
[Section 4.1, discussion of Fig. 2 and Table 5] The text states that 'the 95% probability region extends up to the upper prior range for m_0', but Table 5 gives the 95% bound as m_0 < 3.66 TeV against a prior edge of 4 TeV. Please reconcile the wording with the table, or state that the posterior is still non-negligible at the prior edge even though the 95% contour closes below it.
[Table 5] The m_0 rows give only upper bounds ('< 1.36', '< 2.10', etc.) without a lower bound. Please state explicitly that the lower end of these intervals is set by the prior edge at 50 GeV rather than by the data, so that the asymmetry with the other parameters is not misread.
[Section 3.3, paragraph on the lightest MSSM Higgs boson] The smearing of the Higgs constraints is described in one sentence as a theoretical uncertainty 'tau of 3%' and in the next as 'tau(m_h) = 3 GeV'. Please clarify which quantity each applies to (presumably 3 GeV for m_h and 3% for zeta_h^2), and make Table 4 consistent with the text.
[Abstract and Section 4.1] The cumulative probabilities quoted in the abstract and in section 4.1 (P(m_gluino < 2.7 TeV) = 78%, P(m_squark_R < 2.5 TeV) = 85%, P(m_chargino_1 < 0.8 TeV) = 65%) should state which prior range they refer to, since the paper's own message is that m_0-dependent quantities are prior-sensitive and these numbers are not obviously prior-independent.
[Section 3.3, list of constraints] The constraint set omits Delta M_s and B -> tau nu, both of which were becoming constraining at large tan beta around the time of this revision. A sentence explaining why they were not included, or a check that adding them does not shift the tan beta preference of Fig. 4, would strengthen the large-tan beta conclusion.
[Section 4.1] Typographical: 'We will come come back to the issue' should read 'We will come back to the issue'.
[References] Reference [84] (the DO search for B_s^0 -> mu+ mu-) appears in the bibliography but does not seem to be cited anywhere in the text; the B_s -> mu+ mu- discussion cites [85], [86] and [87] only. Please either cite it or remove it.
[Appendix A.2] The reported acceptance rate of 2-3% is low, and the posterior contains narrow features such as the light-Higgs funnel at m_1/2 ~ 0.2 TeV visible in Figs. 2 and 4. The authors state that they performed checks with and without the covariance matrix; it would help to report one quantitative check, for example the stability of the relative probability assigned to the funnel region between independent runs, so that readers can judge whether the funnel's weight in the one-dimensional pdf of Fig. 4 is converged.

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The paper

The paper claims

A Markov-chain fit of the constrained MSSM turns collider, cosmological and rare-decay data into probability intervals for the theory's five parameters, and finds that most of the favored superpartner mass range sits within LHC reach.

The reading

The paper asks where in the Constrained Minimal Supersymmetric Standard Model (CMSSM) — the MSSM with common scalar, gaugino and trilinear masses fixed at the unification scale — the existing data actually point. Instead of scanning a fixed grid and discarding points that fail experimental bounds, the authors run a Markov chain Monte Carlo over eight parameters, four of them supersymmetric ($m_0$, $m_{1/2}$, $A_0$, $tan beta$) and four Standard Model nuisance parameters ($M_t$, $m_b(m_b)$, $alpha_em$, $alpha_s$), weighting each sample by a likelihood that folds theoretical and experimental errors together. The output is a posterior probability density rather than a best-fit point, and its 68% intervals are $0.52$ TeV $< m_{1/2} < 1.26$ TeV, $m_0 < 2.10$ TeV, $-0.34$ TeV $< A_0 < 2.41$ TeV and $38.5 < tan beta < 54.6$. Those numbers matter because they translate directly into reach: the paper puts 78% probability on a gluino below 2.7 TeV, 85% on a right-handed squark below 2.5 TeV and 65% on the lightest chargino below 0.8 TeV, and it locates the spin-independent WIMP-proton cross section mostly between $10^{-10}$ and $10^{-8}$ pb. The paper's own headline conclusion is a statement about robustness: $m_{1/2}$, $A_0$ and $tan beta$ barely move when the prior ranges are doubled, while $m_0$ does, because a broad focus-point region at multi-TeV scalar masses reproduces the measured dark-matter abundance just as well.

What carries the argument

The load-bearing device is the likelihood construction. Experimental upper and lower limits are not applied as step functions; instead each 95% confidence bound is convolved with a Gaussian of width $tau$ representing the theoretical uncertainty of the mapping from parameters to observables, which smears the edge of the allowed region over the scale $tau$ (their Eq. 3.5). Positive measurements are treated as Gaussians with experimental and theoretical errors added in quadrature. Around this likelihood sits a Metropolis sampler that alternates updates of the SUSY block and the nuisance block, proposes steps along directions drawn from the eigenvectors of an estimated posterior covariance matrix, and is monitored with the Gelman-Rubin statistic until $R-1 < 0.05$ across 24 to 32 chains. The spectra come from SOFTSUSY, the relic density from an exact coannihilation calculation, and the rare decays from next-to-leading-order and one-loop treatments with large-$tan beta$ corrections.

Extended reading notes

Core claim

The central claim is that a Bayesian global fit of the CMSSM, with all relevant uncertainties carried explicitly, yields well-defined and mostly prior-independent probability intervals, and that these intervals can be converted into concrete expectations for the LHC and for WIMP direct detection. Concretely, the authors report 68% ranges of $0.52$ TeV $< m_{1/2} < 1.26$ TeV, $m_0 < 2.10$ TeV, $-0.34$ TeV $< A_0 < 2.41$ TeV and $38.5 < tan beta < 54.6$, with $m_{1/2}$, $A_0$ and $tan beta$ stable under a change of prior range while $m_0$ is not. Two secondary findings carry weight. First, the narrow 'WMAP strips' familiar from fixed-grid scans widen into a large region once every parameter is allowed to vary and the others are marginalized, so the relic-density constraint is less restrictive than it had appeared. Second, high posterior probability and good quality of fit are not the same thing: the posterior prefers large $tan beta$, but acceptable fits exist down to $tan beta$ around 15, a discrepancy the authors say only better data can settle. The paper also maps correlations among observables, most usefully between $BR(B_s to mu^+ mu^-)$ and both $BR(bar{B} to X_s gamma)$ and $sigma_p^{SI}$, which it proposes as a handle for distinguishing the CMSSM from other supersymmetric models once a signal is found.

Load-bearing premise

The quoted intervals are only as wide as the hand-chosen theoretical error bars fed into the likelihood, above all a single 10% error on the dark-matter relic abundance applied everywhere and a flat 5% error on every superpartner mass, even though the authors say the relic-density error in the focus-point region is almost certainly much larger.

Editorial extensions

If this is right

The LHC should cover a large share of the favored region: the paper quotes 78% probability for $m_{gluino} < 2.7$ TeV, 85% for $m_{squark_R} < 2.5$ TeV and 65% for $m_{chargino} < 0.8$ TeV.
Direct WIMP detection has a 68% probability of landing between $10^{-10}$ and $10^{-8}$ pb, with a nearly $tan beta$-independent band at about $1.6 times 10^{-8}$ pb produced by the focus-point region and expected to be probed first.
A Tevatron measurement of $BR(B_s to mu^+ mu^-)$ above roughly $2 times 10^{-8}$ would strongly disfavor large $m_0$, including the focus-point region.
Removing the $(g-2)_mu$ measurement from the likelihood relaxes the constraint on $m_0$ almost entirely and shifts the predicted $BR(B_s to mu^+ mu^-)$ and $sigma_p^{SI}$ downward, lowering the chance that sleptons and squarks fall inside LHC reach.
Because the posterior and the quality of fit disagree, a Bayesian preference for large $tan beta$ should not be read as a statement that the best-fitting points live there.

Reading between the lines

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

The two-branch structure of the $BR(B_s to mu^+ mu^-)$ versus $sigma_p^{SI}$ plane gives a clean experimental discriminator: a joint signal (or joint null) in a rare-decay measurement and a direct-detection experiment would test whether the focus-point branch is really populated, which no single measurement can do.
If the focus-point reading is correct, a null result near $10^{-8}$ pb in the next direct-detection round would not kill the model but would push the preferred region toward lower $m_0$, where sleptons are more accessible to the LHC, so the two searches cover each other's blind spots in a way that could be planned for deliberately.
The gap between posterior preference and best-fit quality for $tan beta$ is a warning about how global-fit results get quoted generally: a parameter can look pinned by a Bayesian scan purely because the allowed volume shrinks, and the check is to report the profile likelihood alongside the marginal posterior.
The authors' own admission that the relic-density error in the focus-point region may reach order unity suggests the honest test is not a better central value but a propagated error band on $Omega_chi h^2$ computed region by region; that would sharpen or dissolve the large-$m_0$ tail that drives the high-$sigma_p^{SI}$ prediction.

Original abstract

We perform a comprehensive exploration of the Constrained MSSM parameters using a Markov Chain Monte Carlo technique and a Bayesian analysis. We compute superpartner masses and other collider observables as well as a cold dark matter abundance, and compare them with experimental data. We include uncertainties arising from theoretical approximations as well as from residual experimental errors on relevant SM parameters. We delineate probability distributions of the CMSSM parameters, the collider and cosmological observables as well as a dark matter direct detection cross section. The 68% probability intervals of the CMSSM parameters are: 0.52 TeV < m_{1/2} < 1.26 TeV, m_0 <2.10 TeV, -0.34 TeV < A_0 < 2.41 TeV and 38.5< tan(beta) <54.6. Generally, large fractions of high probability ranges of the superpartner masses will be probed at the LHC. We highlight a complementarity between LHC and WIMP dark matter searches in exploring the CMSSM parameter space. We further expose a number of correlations among the observables, in particular between BR(B_s \to \mu^+ \mu^-) and BR({\bar B}\to X_s\gamma) or sigma_p^{SI}. Once SUSY is discovered, this and other correlations may prove helpful in distinguishing the CMSSM from other supersymmetric models. The robustness of our results is investigated in terms of the assumed ranges of CMSSM parameters and the effect of the (g-2)_mu anomaly which shows some tension with the other observables. We find that the results for m_0, and the observables which strongly depend on it, are sensitive to our assumptions, while our conclusions for the other variables are robust.

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, 8,447 input tokens, $0.0004 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.95 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We perform a comprehensive exploration of the Constrained MSSM parameters using a Markov Chain Monte Carlo technique and a Bayesian analysis. We compute superpartner masses and other collider observables as well as a cold dark matter abundance, and compare them with experimental data. We include uncertainties arising from theoretical approximations as well as from residual experimental errors on relevant SM parameters. We delineate probability distributions of the CMSSM parameters, the collider and cosmological observables as well as a dark matter direct detection cross section. The 68% probability intervals of the CMSSM parameters are: 0.52 TeV < m_{1/2} < 1.26 TeV, m_0 <2.10 TeV, -0.34 TeV < A_0 < 2.41 TeV and 38.5< tan(beta) <54.6. Generally, large fractions of high probability ranges of the superpartner masses will be probed at the LHC. We highlight a complementarity between LHC and WIMP dark matter searches in exploring the CMSSM parameter space. We further expose a number of correlations among the observables, in particular between BR(B_s \to \mu^+ \mu^-) and BR({\bar B}\to X_s\gamma) or sigma_p^{SI}. Once SUSY is discovered, this and other correlations may prove helpful in distinguishing the CMSSM from other supersymmetric models. The robustness of our results is investigated in terms of the assumed ranges of CMSSM parameters and the effect of the (g-2)_mu anomaly which shows some tension with the other observables. We find that the results for m_0, and the observables which strongly depend on it, are sensitive to our assumptions, while our conclusions for the other variables are robust.

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 perform a comprehensive exploration of the Constrained MSSM parameters using a Markov Chain Monte Carlo technique and a Bayesian analysis.	method 0.51	0.97	0.04	asserted 0.99
s1	We compute superpartner masses and other collider observables as well as a cold dark matter abundance, and compare them with experimental data.	contribution 0.68	0.96	0.05	asserted 0.99
s2	We include uncertainties arising from theoretical approximations as well as from residual experimental errors on relevant SM parameters.	method 0.90	0.88	0.02	asserted 0.99
s3	We delineate probability distributions of the CMSSM parameters, the collider and cosmological observables as well as a dark matter direct detection cross section.	contribution 0.58	0.95	0.08	asserted 1.00
s4	The 68% probability intervals of the CMSSM parameters are: 0.52 TeV < m_{1/2} < 1.26 TeV, m_0 <2.10 TeV, -0.34 TeV < A_0 < 2.41 TeV and 38.5< tan(beta) <54.6.	result 1.00	0.95	0.21	asserted 1.00
s5	Generally, large fractions of high probability ranges of the superpartner masses will be probed at the LHC.	interpretation 0.85	0.78	0.13	hedged possibility 0.65
s6	We highlight a complementarity between LHC and WIMP dark matter searches in exploring the CMSSM parameter space.	interpretation 0.55	0.86	0.18	asserted 1.00
s7	We further expose a number of correlations among the observables, in particular between BR(B_s \to \mu^+ \mu^-) and BR({\bar B}\to X_s\gamma) or sigma_p^{SI}.	result 0.98	0.93	0.07	asserted 1.00
s8	Once SUSY is discovered, this and other correlations may prove helpful in distinguishing the CMSSM from other supersymmetric models.	interpretation 0.91	0.24	0.07	hedged possibility 1.00
s9	The robustness of our results is investigated in terms of the assumed ranges of CMSSM parameters and the effect of the (g-2)_mu anomaly which shows some tension with the other observables.	limitation 0.33	0.91	0.06	asserted 0.91
s10	We find that the results for m_0, and the observables which strongly depend on it, are sensitive to our assumptions, while our conclusions for the other variables are robust.	result 0.69	0.96	0.24	asserted 1.00

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 0.99.

What was examined, and what was not

sources read

arXiv listing abstract v3

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.** An illustration of the likelihood function p(σ, ξlim|θ, τ) used for a quantity for which only a lower bound is available, including the theoretical uncertainty τ and setting the experimental error σ = 0. The dashed green line is the sharp 95% CL bound (ξlim = 1), the solid red curve includes the theoretical uncertainty of τ = 0.05 which smears out the limit. confidence limit only, without the possibility of deriving a form of the likelihood analogous to (3.5). In the absence of fuller information about the experimental value of σ, we can take in (3.5) the limit σ ≪ τ and simply use…

**Figure 2.** The 2–dimensional probability densities in the planes spanned by the CMSSM parameters: m1/2, m0, A0 and tan β for the “4 TeV range” analysis (see

**Figure 3.** The 2–dimensional relative probability densities as in

**Figure 4.** The 1–dimensional relative probability densities p(θi |d) for each of the CMSSM parameter, θi = m0, m1/2, A0 and tan β. All other parameters have been marginalized over. The two curves compare the results for two different prior ranges (see

**Figure 6.** The 2–dim relative probability density p(Ωχh 2 , θi |d), where θi = m0, m1/2 and tan β. Note that the measured value of Ωχh 2 , Eq. (3.10), has been included in computing the relative probability density. m0 (TeV) δ aSUSY µ × 1010 1 2 3 4 0 10 20 30 m1/2 (TeV) 0.5 1 1.5 2 0 10 20 30 tanβ 20 40 60 0 10 20 30 Relative probability density 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

**Figure 10.** An illustration of the tensions between different observables. While for mb(mb)MS and Ωχh 2 the likelihood and the posterior pdf agree very well (top panels), for sin2 θeff and δaSUSY µ (bottom panel) they exhibit a substantial discrepancy. The latter case is a clear sign that the other constraints are strongly pulling away the posterior pdf from the value preferred by the anomalous magnetic moment measurement. rameters in the problem after we have seen the data and given our choice of priors, as we have explained in some detail in section 2.1. It is important to remark that regions

**Figure 11.** The quality of fit in the planes spanned by the CMSSM parameters: m1/2, m0, A0 and tan β for the “4 TeV range” scan. This figure should be compared with

**Figure 13.** Top panel: the 2–dimensional relative probability density p(mχ, σSI p |d), with the contours containing 68% and 95% probability also marked. Bottom panel: the mean quality of fit (likelihood) with the same 68% and 95% probability contours as in the top panel to facilitate the comparison. Current 90% experimental upper limits are also shown. be the first to be probed by DM search experiments. Finally, after marginalizing over all other parameters, we obtain the following 1– – 33 –

**Figure 14.** The 2–dimensional relative probability density p(ξi , ξj |d) for the pairs of observables marked along horizontal and vertical axes. dimensional regions encompassing 68% and 95% of the total probability: 1.0 × 10−10 pb < σSI p < 1.0 × 10−8 pb (68% region), 0.5 × 10−10 pb < σSI p < 3.2 × 10−8 pb (95% region). (4.4) Currently running experiments (most notably CDMS–II but also Edelweiss–II and ZEPLIN–II) should be able to reach down to a few ×10−8 pb, on the edge of exploring the FP region. A future generation of “one–tonne” detectors are expected to reach down to σ SI p ∼ > 10−10 pb,…

**Figure 15.** Values of mh (upper left), Ωχh 2 (upper right), σ SI p (lower left) and δaSUSY µ (lower right) in the (m1/2, m0) plane for samples uniformly selected from our MC chains. While σ SI p and δaSUSY µ show a clear correlation with the values of (m1/2, m0), the CDM abundance Ωχh 2 can take any value within the 2σ WMAP range in the plane. Narrow “WMAP strips” in the (m1/2, m0) plane for fixed values of tan β and A0 thus disappear when these parameters are allowed to vary and all other parameters are correctly marginalized over. The values of σ SI p (bottom left panel of

**Figure 16.** The 1–dimensional relative posterior pdf’s as in

**Figure 18.** The probability for the superpartner masses to lie below a given mass. All other parameters have been marginalized over. marized in

Showing 12 of the paper's 18 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0602028 by the authors.

References

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hep-ph 2014-06 conditional novelty 5.0 of 10

In synthetic ton-scale detector data, the full 11-parameter dark matter-nucleon effective theory recovers both the dark matter mass and the correct interaction operator in only about 5 of 27 benchmark scenarios.
Dark matter and collider signatures of the MSSM
hep-ph 2013-06 conditional novelty 5.0 of 10

In a nine-parameter MSSM scan, neutralino dark matter consistent with muon g-2 and not yet excluded by LHC electroweak searches sits between 200 and 500 GeV, and the XENON100 bound weakens once a new pion-nucleon sigm...
Gluino-driven Radiative Breaking, Higgs Boson Mass, Muon $\mathbf{g-2}$, and the Higgs Diphoton Decay in SUGRA Unification
hep-ph 2013-04 conditional novelty 5.0 of 10

A Bayesian fit of a SUGRA model with a heavy gluino reproduces the 125 GeV Higgs mass and the muon g-2 anomaly while keeping B_s to mu mu at its Standard Model value, and post-dicts a 20 percent Higgs diphoton excess.
The Constrained NMSSM with a 126 GeV Higgs boson: A global analysis
hep-ph 2012-11 conditional novelty 5.0 of 10

A global Bayesian scan of the Constrained NMSSM shows the 126 GeV Higgs is best fit as the lightest CP-even scalar in the stau-coannihilation region, while next-to-lightest-Higgs interpretations are disfavored by dark...
Bayesian Fit of Exclusive $b \to s \bar\ell\ell$ Decays: The Standard Model Operator Basis
hep-ph 2012-05 conditional novelty 5.0 of 10

A full Bayesian fit of the Wilson coefficients C7, C9 and C10 to exclusive rare B decays finds a Standard-Model-like and a sign-flipped solution with roughly equal posterior weight, and no evidence requiring new physics.
Constrained Supersymmetry after two years of LHC data: a global view with Fittino
hep-ph 2012-04 conditional novelty 5.0 of 10

Combining LHC 5 fb^-1 SUSY searches with precision, flavour and dark matter data, the constrained MSSM fits poorly and cannot comfortably host a 126 GeV Higgs boson.
Complementarity of Dark Matter Direct Detection Targets
astro-ph.CO 2010-12 accept novelty 5.0 of 10

Combining xenon, germanium and argon data roughly doubles the information on WIMP mass and cross-section compared with one target, and can self-calibrate the local circular velocity to about 238 plus or minus 22 km/s.
THE TOOLS AND MONTE CARLO WORKING GROUP Summary Report from the Les Houches 2009 Workshop on TeV Colliders
hep-ph 2010-03 conditional novelty 5.0 of 10

The Les Houches 2009 Tools and Monte Carlo group specifies updated event-file, flavour-observable and NLO runtime interfaces, and reports that the major LHC simulation chains agree in shape within roughly 20 to 50 percent.
A novel determination of the local dark matter density
astro-ph.CO 2009-07 conditional novelty 5.0 of 10

Fitting a Milky Way mass model to updated dynamical data gives a local dark matter density of 0.385 to 0.389 GeV/cm3 with roughly 7% statistical uncertainty, tighter than the usual factor-of-two-to-three range.
The impact of priors and observables on parameter inferences in the Constrained MSSM
hep-ph 2008-09 conditional novelty 5.0 of 10

Current data leave Constrained MSSM parameters prior-dependent: the WMAP relic abundance supplies roughly 80 to 95 percent of all constraining power, and the muon g-2 preference for light superpartners conflicts with ...
An Updated Analysis of Inert Higgs Doublet Model in light of the Recent Results from LUX, PLANCK, AMS-02 and LHC
hep-ph 2013-10 conditional novelty 4.0 of 10

Combining PLANCK relic density, LUX direct detection, Fermi-LAT and AMS-02 indirect searches and LHC monojet data, the Inert Higgs Doublet Model survives best with dark matter between roughly 50 and 100 GeV, peaking n...
GUT-scale constrained SUSY in light of E989 muon g-2 measurement
hep-ph 2021-04 conditional novelty 3.0 of 10

The minimal GUT-scale supersymmetric model cannot explain the new muon g-2 anomaly without violating LHC, Higgs, and flavor constraints, but a gluino-heavy variant can.
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astro-ph 2007-11 conditional novelty 3.0 of 10

The paper defines ten necessary tests for a dark matter candidate and grades sixteen proposed particles against them, concluding that most survive while charged CHAMPs and the first Kaluza-Klein graviton do not.

How later papers used it

74 later papers cite it

Evidence: substantial. 52 of the citing papers share no author with it, and 22 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 129 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: 4 used its method or tool and 1 used its data or values. 4 more papers by the same authors are listed: 4 used its method or tool.

Uses its method or tool 8 of 29 papers with this label · 4 by the same authors

Used the Markov Chain Monte Carlo routines of Superbayes from this paper, which generate Markov chains by means of the Metropolis algorithm, in its FORTRAN code.

A novel determination of the local dark matter density (2009) · 1.00 · paraphrased: the licence does not allow quoting
Accounted for positive measurements with a Gaussian likelihood and implemented upper limits as described in this paper.

Explaining the Fermi Galactic Centre Excess in the CMSSM (2015) · 1.00 · paraphrased: the licence does not allow quoting
Followed this paper's approach for 95% CL exclusion limits, formulating a likelihood that is a step function at the observed limit smeared by a 5% gaussian uncertainty.

Disfavouring Electroweak Baryogenesis and a hidden Higgs in a CP-violating Two-Higgs-Doublet Model (2016) · 1.00 · paraphrased: the licence does not allow quoting
Constructed smeared step-function likelihoods at 95% CL for generic limits implemented in another work, as in this paper.

The Power of Genetic Algorithms: what remains of the pMSSM? (2018) · 0.95 · paraphrased: the licence does not allow quoting

By the same authors

Referred the reader to this paper for a detailed description of the likelihood function.

Dark Matter Searches: The Nightmare Scenario (2011) (same authors) · 0.82 · paraphrased: the licence does not allow quoting
Included the uncertainty in the likelihood following this paper's procedure for the treatment of upper bounds.

Bayesian Implications of Current LHC Supersymmetry and Dark Matter Detection Searches for the Constrained MSSM (2012) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Following this paper's procedure, implemented positive measurements through a Gaussian likelihood and upper or lower limits through an error function smeared with theory and, when available, experimental error.

The Constrained NMSSM with a 126 GeV Higgs boson: A global analysis (2012) (same authors) · 1.00 · paraphrased: the licence does not allow quoting
Following this paper's procedure, implemented positive measurements through a Gaussian likelihood with experimental and theoretical uncertainties added in quadrature.

Two ultimate tests of constrained supersymmetry (2013) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

Uses its data or values 1 paper

Based its updated bounds upon the sparticle spectrum bounds collected in this paper.

Natural Priors, CMSSM Fits and LHC Weather Forecasts (2007) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

73 arXiv papers cite this in 127 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 · 49 sentences without a confident label

Uses its method or tool 28 papers

We use our updated and modified version of the [ref] computer program to perform four scans of the CMSSM:

Bayesian Implications of Current LHC and XENON100 Search Limits for the Constrained MSSM · The statistical framework · 0.98
To this end, we follow the strategy outlined in Refs. [ref] .

Constrained MSSM favoring new territories: The impact of new LHC limits and a 125 GeV Higgs boson · The framework · 1.00
We refer the reader to [ref] for a detailed description of the likelihood function.

Dark Matter Searches: The Nightmare Scenario · Cosmological and collider constraints · 0.82

Uses its data or values 1 paper

Bounds upon the sparticle spectrum have been updated and are based upon the bounds collected in Ref. [ref] .

Natural Priors, CMSSM Fits and LHC Weather Forecasts · The Likelihood · 0.95

Compares with it 8 papers

The sparticle mass distributions for priors that are flat in $tanβ$ were displayed in Refs. [ref] and show a spread up to much higher values of the masses.

Natural Priors, CMSSM Fits and LHC Weather Forecasts · CMSSM Fits With the New Priors · 0.88
[ref] However, the precise value of this upper bound turns out to be irrelevant, as the region of very large $tanβ$ is strongly suppressed (see the discussion after eq.

MSSM Forecast for the LHC · High-energy vs Low-energy regions and the EW breaking · 0.97
Despite our updated constraints and additional observables, the flat $tanβ$ posterior looks indistinguishable to the eye to previous determinations [ref] , where the connection between a preference for the focus point and good direct detection prospects were pointed out.

Panglossian Prospects for Detecting Neutralino Dark Matter in Light of Natural Priors · Direct Detection · 0.99

Cites it as background 25 papers

In [ref] , Bayesian statements were made about the posterior probability density of the CMSSM, after indirect data had been taken into account.

Natural Priors, CMSSM Fits and LHC Weather Forecasts · Introduction · 0.90
More recently, many studies have been performed to extract the preferred values for the CMSSM parameters using low-energy precision data, bounds from astrophysical observables and flavour related observables [ref] .

Prediction for the Lightest Higgs Boson Mass in the CMSSM using Indirect Experimental Constraints · Introduction · 0.85
Recently, Bayesian parameter estimation techniques using the Markov Chain Monte Carlo (MCMC) sampling have been applied to the study of mSUGRA, performing a multi–dimensional Bayesian fit to indirect constraints [ref] .

Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results · Introduction · 0.93

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.

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