Phenomenological MSSM interpretation of the CMS 2011 5/fb results (SUS-12-030)

Further information

This analysis is documented in SUS-12-030.

Abstract

We interpret within the phenomenological MSSM (pMSSM) results obtained by CMS using a pp data set collected in 2011 at 7~TeV, corresponding to an integrated luminosity of 5 / fb. The pMSSM is a 19-parameter realization of the MSSM defined at the SUSY scale, that captures most of the features of the general R-parity conserving weak-scale MSSM. A global Bayesian analysis is performed that yields posterior probability densities of model parameters, masses and observables. We provide conclusions that are more generic, and therefore more robust, than those derived in more constrained setups, including simplified models and models that impose particular SUSY breaking schemes, such as the CMSSM. We also study implications for the MSSM Higgs sector, as well as for dark matter searches. Furthermore, we discuss which scenarios currently escape detection despite a high production cross section. Our study thus gives a coherent global picture of how the current CMS searches constrain supersymmetry in general.

Analysis Summary

We have investigated the impact of a subset of the 7 TeV CMS SUSY searches on a potentially accessible sub-space of the pMSSM, a 19-dimensional proxy of the MSSM defined at the SUSY scale. By construction, the pMSSM explicitly avoids GUT scale assumptions. What may or may not happen at the GUT scale is an interesting theoretical question that is not our focus.

A 19-dimensional sub-space of the pMSSM has been sampled using an MCMC method and a posterior density --- subsequently used as the prior in the interpretation of the CMS results --- that is proportional to a likelihood function, constructed from a variety of pre-CMS results, times a flat ``ur-prior", that is, a prior that starts the chain of inference. Because the ur-prior is chosen to be flat, the sampled points also constitute a discrete approximation to the pre-CMS likelihood to which, in principle, likelihood methods could be applied. However, we have pursued a Bayesian approach. The sub-space has been chosen to cover sparticle masses up to about 3 TeV. The seven analyses implemented span a variety of final states, which, in principle, permit a broad exploration of the pMSSM and by association the MSSM.

Approved Tables and Plots ( click on plot to get larger version )

N.B.:

• For histograms depicting a probability density, no labels on the y axes are printed, since the labels are a function of the binning of the x axes.
• BCR = Bayesian Credibility Region

Section 3: Analysis

Figure	Caption
	Table 1: The measurements that are the basis of our pMSSM prior ppreCMS(θ). All measurements except the measurement of mh at the LHC were used to sample points from the pMSSM parameter space via Markov Chain Monte Carlo (MCMC). The mh likelihood was imposed as a weight on the sampled points. See the PAS for the references.
	Table 2:: List of implemented CMS analyses, which are used for building the CMS likelihood L(DCMS | θ). The references are: 42,43,44,45,46,47,48

Section 4.1: Results: Impact of the CMS searches

Figure	Caption
	Figure 1: Marginalized 1D posterior probability distributions for gluino mass. The line histograms in the three plots show posterior densities after including the three of the seven implemented CMS analyses: HT + HTmiss, HT + ETmiss + b-jets and EWKino. Within each analysis, different search regions are combined if they are exclusive, or shown separately otherwise. Solid curves show the posterior densities obtained from likelihoods calculated using the central values of estimated signal counts s, whereas the dashed and dotted lines show the posterior densities obtained from likelihoods calculated using s - 0.5s and s + 0.5s respectively.
	Figure 2: Marginalized 1D posterior probability distributions for the sup mass, stop1 mass and sbottom1 mass. The filled blue histograms in each plot show the posterior densities after preCMS measurements. In each row, the line histograms in the three plots show posterior densities after including the three of the seven implemented CMS analyses: HT + HTmiss, HT + ETmiss + b-jets and EWKino. Within each analysis, different search regions are combined if they are exclusive, or shown separately otherwise. Solid curves show the posterior densities obtained from likelihoods calculated using the central values of estimated signal counts s, whereas the dashed and dotted lines show the posterior densities obtained from likelihoods calculated using s - 0.5s and s + 0.5s respectively.
	Figure 3: Marginalized 1D posterior probability distributions for χ10 mass, χ20 mass and χ1± mass. The filled blue histograms in each plot show the posterior densities after preCMS measurements. In each row, the line histograms in the three plots show posterior densities after including the three of the seven implemented CMS analyses: HT + HTmiss, HT + ETmiss + b-jets and EWKino. Within each analysis, different search regions are combined if they are exclusive, or shown separately otherwise. Solid curves show the posterior densities obtained from likelihoods calculated using the central values of estimated signal counts s, whereas the dashed and dotted lines show the posterior densities obtained from likelihoods calculated using s - 0.5s and s + 0.5s respectively.
	Figure 4: Marginalized 2D posterior probability distributions for χ10 mass versus gluino mass and χ10 mass versus supR mass. In each row, the 1st plot shows the preCMS posterior density. The 2nd and 3rd plots show the posterior densities after applying the HT + HTmiss, HT + ETmiss + b-jets BT results respectively. The grey and black contours enclose the 68% and 95% Bayesian credible regions respectively.
	Figure 5: Marginalized 2D posterior probability distributions for χ1± mass versus χ20 mass and χ1± mass versus χ0+ mass. In each row, the 1st plot shows the preCMS posterior density. The 2nd plot shows the posterior densities after applying the EWKino combined results. The grey and black contours enclose the 68% and 95% Bayesian credible regions respectively.
	Figure 6: Marginalized 1D posterior probability distributions for the total sparticle production cross section. The filled blue histograms in each plot show the posterior densities after preCMS measurements. The line histograms in the three plots show posterior densities after including the three of the seven implemented CMS analyses: HT + HTmiss, HT + ETmiss + b-jets and EWKino. Within an analysis, different search regions are combined if they are exclusive, or shown separately otherwise. Solid curves show the posterior densities obtained from likelihoods calculated using the central values of estimated signal counts s, whereas the dashed and dotted lines show the posterior densities obtained from likelihoods calculated using s − 0.5s and s + 0.5s respectively.
	Figure 7: Marginalized 2D posterior probability distributions for gluino mass versus log total sparticle production cross section and supR mass versus log total sparticle production cross section. In each row, the 1st plot shows the preCMS posterior density. The 2nd and 3rd plots show posterior densities after applying the HT + HTmiss combined and HT + ETmiss + b-jets 2BT results respectively. The grey and black contours enclose the 68% and 95% Bayesian credible regions respectively.

Section 4.2: Results: Current sensitivity to the pMSSM

Figure	Caption
	Figure 8: Marginalized 1D posterior distributions for the best significance Zbest weighted according to preCMS likelihood without and with a lower limit on the production crosssection of σ > 10 fb. As expected, the lower bound on the cross section pushes the distribution towards pMSSM points that would be decisively excluded by the CMS analyses.
	Figure 9: Marginalized 1D posterior distributions for the best significance Zbest weighted according to preCMS likelihood without and with a lower limit on the production crosssection of σ > 10 fb. As expected, the lower bound on the cross section pushes the distribution towards pMSSM points that would be decisively excluded by the CMS analyses.

Appendix A: Chargino–neutralino mass degeneracy in pMSSM

Figure	Caption
	Figure 10: LSP mass versus M1, M2 and μ for the prior p(θ) obtained by a random scan of the pMSSM parameter space. Distributions are shown for all parameter configurations (1st column), for |M1| smallest (2nd column), for |M2| smallest (3rd column) and for |μ| smallest (4th column).
	Figure 11: χ1± - χ10 mass difference versus M2 and μ for the prior p(θ) obtained by a random scan of the pMSSM parameter space. Distributions are shown for all parameter configurations (1st column), for |M1| smallest (2nd column), for |M2| smallest (3rd column) and for |μ| smallest (4th column).

Appendix B: PreCMS distributions of pMSSM parameters and masses

Figure 12 : Marginalized 1D posterior densities for various pMSSM model parameters based on the ``preCMS'' measurements of Table 1 and various constraints on prompt charginos (prmt), the mass, mh, of the light neutral Higgs boson, h0, and LSP relic density Ω(χ10) h2 (UL0.136: Ω(χ10)h2 < 0.136, WMAP: Ω(χ01)h2=0.1123±0.0035obs± 0.01123theory). The yellow histograms show the sampled distributions with a flat prior. The last plot shows that large values of Xt = (At - μ / tan β)/MSUSY are required in order that mh lie in the 123 - 128 GeV range.

Figure 13 : Marginalized 1D posterior densities for various sparticle masses based on the ``preCMS'' measurements of Table 1 and various constraints on prompt charginos (prmt), the mass, mh, of the light neutral Higgs boson, h0, and LSP relic density Ω(χ10) h2 (UL0.136: Ω(χ10)h2 < 0.136, WMAP: Ω(χ01)h2=0.1123±0.0035obs± 0.01123theory). The yellow histograms show the sampled distributions with a flat prior.

Appendix C: Results of the CMS analyses

	Table 3: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the hadronic HT + HTmiss search CMS-SUS-12-011 .
	Table 4: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the hadronic Jets + ETmiss + b-jets search CMS-SUS-12-003.
	Table 5: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the hadronic HT + ETmiss + τs search CMS-SUS-12-004 .
	Table 6: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the hadronic monojet + ETmiss search CMS-EXO-11-059.
	Table 7: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the same sign di-lepton search CMS-SUS-11-010.
	Table 8: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the opposite sign di-lepton search CMS-SUS-11-011.
	Table 9: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the 3-lepton channel of the search for electroweak (EWK) production of charginos and neutralinos CMS-SUS-12-006.
	Table 10: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the same-sign di-lepton channel of the search for electroweak (EWK) production of charginos and neutralinos CMS-SUS-12-006.
	Table 11: Signal search regions, observed event counts Nl and SM background estimates Bl ± δ Bl for the channel with two leptons and two jets of the search for electroweak (EWK) production of charginos and neutralinos CMS-SUS-12-006.

Appendix D: Designing disjoint analyses

Figure 14: Marginalized 1D posterior probability distributions for gluino mass and supR mass. The filled blue histograms in each plot show the posterior densities after preCMS measurements. The line histograms show posterior densities after including the HT + HTmiss analysis. The green histograms show the distributions for the 14 exclusive HT + HTmiss search regions given in Table 3, whereas the red line shows the distribution after combining the 14 regions.

Appendix E: Consequences for the Higgs boson

	Figure 15: Marginalized 2D posterior densities for Xt vs. m(stop1). The left plot shows the preCMS posterior density. The right plot includes in addition the requirement |Zbest| < 2 computed after incorporating the full set of CMS analyses.
	Figure 16: Marginalized 1D posterior probability distributions for Rgg(γγ), Rgg(ZZ) and Rgg(bb) (upper row) and for RVBF(γγ), RVBF(ZZ) and RVBF(bb) (lower row). The filled blue histograms in each plot show the posterior densities after preCMS measurements. The line histograms show the normalized distributions of points that have best significance |Zbest| < 2, i.e., points that are not excluded. Solid curves show the distributions obtained from likelihoods (and significances) calculated using the central values of estimated signal counts s, whereas the dashed and dotted lines show the distributions obtained from likelihoods (and significances) calculated using s - 0.5s and s + 0.5s respectively.
	Figure 17: Marginalized 2D posterior probability distributions for Rgg(ZZ) vs. Rgg(γγ), RVBF(ZZ) vs. RVBF(γγ), Rgg(γγ) vs. Rgg(bb) and RVBF(γγ) vs. RVBF(bb). For each variable pair, the 1st plot shows the preCMS posterior density, and the 2nd plot shows the normalized distributions of points that have best significance |Zbest| < 2, i.e., points that are not excluded. The grey and black contours enclose the 68% and 95% Bayesian credible regions respectively.
	Figure 18: Marginalized 2D posterior probability distributions for mH - mA vs. mA. The 1st plot shows the preCMS posterior density, and the 2nd plot shows the normalized distributions of points that have best significance |Zbest| < 2, i.e., points that are not excluded. The grey and black contours enclose the 68% and 95% Bayesian credible regions respectively.
	Figure 19: Marginalized 2D posterior probability distributions for tanb vs. mA with 123 GeV < mh < 128 GeV required. The 1st plot shows the preCMS posterior density, and the 2nd plot shows the normalized distributions of points that have best significance |Zbest| < 2, i.e., points that are not excluded. The grey and black contours enclose the 68% and 95% Bayesian credible regions respectively.
	Figure 20: Marginalized 1D posterior probability distributions for br(A -> SUSY), br(H -> SUSY) and br(H+ -> SUSY), where SUSY represents the sum over all sparticle pair states. The filled blue histograms in each plot show the posterior densities after preCMS measurements. The line histograms show the normalized distributions of points that have best significance |Zbest| < 2, i.e., points that are not excluded. Solid curves show the distributions obtained from likelihoods (and significances) calculated using the central values of estimated signal counts s, whereas the dashed and dotted lines show the distributions obtained from likelihoods (and significances) calculated using s - 0.5s and s + 0.5s respectively.

Appendix F: Consequences for dark matter observables

Figure 21: Marginalized 1D posterior probability distributions for the neutralino relic density Ω(χ10) h2. The filled blue histogram in the plot shows the posterior density after preCMS measurements. The line histograms show the posterior densities for the non-excluded |Zbest|<2 points. The solid curve shows the posterior density obtained from likelihoods calculated using the central values of estimated signal counts s, whereas the dashed and dotted lines show the posterior density obtained from likelihoods calculated using s - 0.5s and s + 0.5s respectively.

Figure 22: Marginalized 2D posterior probability distributions for neutralino relic density Ω (χ10) h2 (top row), spin-independent direct DM detection cross section ξσSI (middle row), and spin-dependent direct DM detection cross section ξσSD (bottom row) versus LSP mass. The rescaling factor ξ=Ω(χ10) h2/0.1123. For each variable pair, the 1st plot shows the preCMS posterior density, and the 2nd plot shows the normalized distributions of points that have best significance |Zbest| < 2, i.e., points that are not excluded. The grey and black contours enclose the 68% and 95% Bayesian credible regions respectively.

Appendix G: Exploring the unexplored

	Figure 23: Number of unexplored pMSSM points, as a function of the production cross section.
	Table 12: Overall fractions of production mechanisms in the unexplored high-σ points. Eg. in 40.4% of all unexplored high-σ pMSSM points, weakino (``nn'') production amounts to more than 90% of all events.
	Figure 24: Production mechanisms for unexplored high-σ pMSSM points, ``point-for-point'' -- the x-axis simply sorts the 2198 points. Weakino and squark-squark productions dominate.
	Figure 25: A few simplified models for squark-squark production: top row, from left to right: T2, T2bb, TNS. Bottom row, from left to right: T4C1, T4N2, T6C1C1.
	Figure 26: The most important simplified models for the electroweak case: top row, from left to right: TChiC1N1, TChiN2C1, TChiC1C1. Bottom row, from left to right: TChiN2N1, TChiwz.
	Figure 27:Lengths of the SUSY decay chains, counting from the SUSY mother particle to the LSP, for both legs, given as a percentage, for the high-σ electroweak sample (left), and leading SMS topologies for the case of weakino production (right). Chargino-- LSP (TChiC1N1) production dominates, followed by the production of a chargino and a heavy neutralino (TChiN2C1) and the production of two charginos (TChiC1C1). The plus sign in TChiC1N1+ indicates the production of a chargino and the LSP with a non-trivial decay of the chargino. All numbers have been weighted with the production cross sections times branching ratios. See figure 26 for the SMS topology names.
	Figure 28: Chargino / heavy neutralino mass versus LSP mass.
	Figure 29: Lengths of the SUSY decay chains (left) and occurrences of SMS topologies for the squark production cases (right). Direct decays {q}→ q χ0 and {b}→ b χ0 dominate. All numbers have been weighted with the production cross sections times branching ratios. See Figure 25 for the SMS topology names.
	Figure 30: Mass of lightest squark versus LSP mass.
	Figure 31: Cross check between pMSSM results and SMS results, for SUS-12-011. The histograms show the distributions of |Z| values, which are calculated through implementing the full analysis chain on each point. Points with Z > 2 are excluded whereas points with |Z| < 2 are unexplored (note that points with Z > 2 would point to discovery, however we do not have any such points in our list, therefore our set of points with |Z| > 2 fully consist of excluded points with Z < -2). The red histogram shows the |Z| distribution for points that are excluded by the SMSs, and the black curve shows the Z distribution for the points that are missed, or unexplored by the SMSs. The red histogram almost always has |Z|>2, which means that the points excluded by the SMSs are also excluded by the full analysis. The black histogram almost always has |Z|<2, which means that the points unexplored by the SMSs are also unexplored by the full analysis. A small part of the black histogram lies beyond |Z|>2, corresponding to points missed by the SMS results but excluded by the direct analysis.