SModelS: a tool for interpreting simplifiedmodel results from the LHC and its application to supersymmetry
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Abstract
We present a general procedure to decompose Beyond the Standard Model (BSM) collider signatures presenting a \(\mathbb {Z}_2\) symmetry into Simplified Model Spectrum (SMS) topologies. Our method provides a way to cast BSM predictions for the LHC in a model independent framework, which can be directly confronted with the relevant experimental constraints. Our concrete implementation currently focusses on supersymmetry searches with missing energy, for which a large variety of SMS results from ATLAS and CMS are available. As showcase examples we apply our procedure to two scans of the minimal supersymmetric standard model. We discuss how the SMS limits constrain various particle masses and which regions of parameter space remain unchallenged by the current SMS interpretations of the LHC results.
Keywords
Monte Carlo Minimal Supersymmetric Standard Model Production Cross Section Mass Vector Branch Ratio1 Introduction
Searches at the ATLAS and CMS experiments at the LHC show no signs of physics beyond the Standard Model (BSM). After the first phase of LHC operation at centreofmass energies of 7–8 TeV in 2010–2012, the limits for the masses of supersymmetric particles, in particular of 1st/2nd generation squarks and gluinos, have been pushed well into the TeV range [1, 2]. Likewise, precision measurements in the flavor sector, in particular in \(B\)physics, are well consistent with Standard Model (SM) expectations [3, 4] and show no sign, or need, of new physics. At the same time the recent discovery [5, 6] of a Higgslike particle with mass around 125 GeV makes the question of stability of the electroweak scale—the infamous gauge hierarchy problem—even more imminent. Indeed, supersymmetry (SUSY) is arguably the bestmotivated theory to solve the gauge hierarchy problem and to explain a light SMlike Higgs boson. So, the Higgs has very likely been discovered—but where is supersymmetry?
Looking closely [7, 8, 9, 10, 11, 12] one soon realizes that many of the current limits on SUSY particles are based on severe model assumptions, which impose particular relations between particle masses, decay branching ratios, etc. The prime example is the interpretation of the search results within the Constrained Minimal Supersymmetric Standard Model (CMSSM). The interpretation of the search results within a much more general realization of the MSSM is perfectly feasible, see [7, 8, 13], but computationally very demanding and certainly not suitable for a “quick” survey.
An approach which has therefore been adopted systematically by the ATLAS and CMS collaborations, is to interpret the results within socalled Simplified Model Spectra [14, 15]. Simplified Model Spectra, or SMS for short, are effectiveLagrangian descriptions involving just a small number of new particles. They were designed as a useful tool for the characterization of new physics, see e.g. [16, 17]. A large variety of results on searches in many different channels are available from both ATLAS and CMS, providing general cross section limits for SMS topologies. However, using these results to constrain complex SUSY (or general BSM) scenarios is not straightforward.
In this paper, we present a method to decompose the signal of an arbitrary SUSY spectrum into simplified model topologies and test it against all the existing LHC bounds in the SMS context. The computer package doing all this is dubbed SModelS [18]. (A similar approach was in fact proposed some time ago in [19].) As we will show, this decomposition allows a vast survey of SUSY models, and enormously simplifies the task of identifying the regions of parameter space which are still allowed by the current searches. Our method also allows us to discuss the current coverage of the simplified models considered so far by the ATLAS and CMS searches. We can, for instance, identify possible regions of parameter space which are not tested by any of the simplified models assumed by the current searches. Two scans of the MSSM with parameters defined at the weak scale, one with 7 and one with 9 free parameters, are used as showcase examples to demonstrate the use of our method. Our results show that the SMS interpretation of the LHC results indeed provide important constraints on SUSY scenarios. At the same time, however, large regions of interesting parameter space with SUSY particles below 1 TeV remain unchallenged by the current SMS results.
It is important to note that, while our method was originally developed with SUSY searches in mind, and the application presented here focusses on the MSSM, our approach is perfectly general and easily extendible to any BSM model to which the experimental SMS results apply.
The rest of this paper is organized as follows. In Sect. 2 we briefly describe the general procedure for the decomposition and the use of the experimental results. A more detailed description is given in Sect. 3; readers who are not interested in technicalities may skip this section altogether. Section 4 discusses the validation of the SModelS framework. In Sect. 5 we then apply SModelS in two scans of the MSSM and discuss how the SMS limits constrain various particle masses, and which regions of parameter space remain untested. Conclusions and an outlook are given in Sect. 6.
2 General procedure
Currently most ATLAS and CMS experimental analyses consider specific simplified models to present their constraints on new physics. The number of signal events expected in a given signal region is then obtained using the signal efficiency times acceptance for the specific model assumed. In general, the signal efficiency is model dependent and must be calculated for each specific model considered. Nonetheless, most current experimental analyses aim for model independent constraints and consider sufficiently inclusive signal regions. The guiding principle behind the procedure discussed here is the assumption that the signal efficiencies for most experimental searches for new physics depend mostly on the event kinematics and are just marginally affected by the specific details of the BSM model. This allows us to map the full model’s signals to its SMSequivalent topologies and use the latter to constrain the full model.
Clearly, this assumption, which from now on we call SMS assumption, is not always valid. For instance, it is expected to be violated for searches which strongly rely on shape distributions. The signal efficiencies can moreover depend on spin correlations, or on properties of offshell states in production channels (schannel or tchannel production) or in decays. A quantitative discussion of the sensitivity of signal efficiencies to various model properties is analysis dependent and a complicated matter, being out of the scope of the current work. Dedicated studies will be presented in future publications. Generally, it is the responsibility of the user to apply SModelS only to models and experimental results for which the SMS assumption is approximately valid. (Note that it is possible to use only a subset of experimental results in the database.) Let us now outline the general SModelS procedure.

the diagram topology: number of vertices and SM final state particles in each vertex;

the masses (mass vector) of the \(\mathbb {Z}\)odd BSM particles appearing in the diagram;

the diagram weight (\(\sigma \times \mathcal {B}\)).
The next and more involved step is to confront the theoretical predictions obtained from the decomposition with the experimental constraints. For that it is necessary to map the signal topologies produced in the decomposition to the SMS topologies constrained by data. For some experimental analyses this is a trivial matter, since they provide an upper limit for a single topology cross section as a function of the relevant BSM mass vector. Examples are constraints on squark pair production, with \(\tilde{q}\rightarrow q+\tilde{\chi }^0_1\), which give an upper limit on \(\sigma \times \mathcal {B}\) as a function of \((m_{\tilde{q}},m_{\tilde{\chi }^0_1})\), or gluino pair production, with \(\tilde{g}\rightarrow t\bar{t}+\tilde{\chi }^0_1\), which limit \(\sigma \times \mathcal {B}\) as a function of \((m_{\tilde{g}},m_{\tilde{\chi }^0_1})\). However it is often the case that the experimental analysis does not constrain a single topology but rather a sum of several topologies, assuming a specific relative contribution from each of them. As an example, consider the slepton pair production limits, where the interpretation constrains the sum over final state lepton flavors (\(e\)’s and \(\mu \)’s) under the assumption that each flavor contributes 50 % to the signal and that selectrons and smuons are mass degenerate, \((m_{\tilde{e}},m_{\tilde{\chi }^0_1}) = (m_{\tilde{\mu }},m_{\tilde{\chi }^0_1})\). In order to apply this experimental constraint to the signal topologies obtained from the decomposition, it is necessary to combine all topologies with a single lepton being emitted in each branch and which have the same mass vector. Moreover, in order for the experimental constraint to be valid, it is necessary to verify the analysis conditions: topologies with \(e\)’s and \(\mu \)’s contribute equally to the final theoretical prediction (\(\sigma \times \mathcal {B}\)). A more involved example are the constraints from trilepton+MET searches: here the SMS results for \(\tilde{\chi }^\pm _1\tilde{\chi }^0_2\) production with decays through sleptons assume the intermediate slepton being a selectron, smuon or stau (including or not including sneutrinos) so that the limits on \(\sigma \times \mathcal {B}\) only apply for specific flavordemocratic, tauenriched, taudominated, etc., cases. Such constraints need to be carefully taken into account when mapping the signal topologies obtained from the decomposition to the experimental results. A detailed description of how the analyses assumptions and constraints are described in a model independent language is presented in Sect. 3.2. The procedure for matching the decomposition results to the analysis constraints is discussed in detail in Sect. 3.3.
Finally when all signal topologies are combined according to the assumptions of each experimental result, the resulting theoretical predictions for the cross sections of the combined topologies can be directly compared to the experimental upper limits. Thus it can be decided whether a particular parameter point (a particular BSM spectrum) is excluded or not by the available SMS results.
3 Detailed description
In this section, we discuss the technical details of the main building blocks of SModelS: the decomposition procedure, the analysis database, and the matching of theoretical and experimental results.
3.1 Decomposition procedure
As explained in the previous section, under the SMS assumption, all the complexity of the BSM model can be replaced by the knowledge of the signal topologies and their weights, together with the relevant BSM masses.^{4} The topologies can then be classified according to the number of vertices in each branch and the SM states appearing in each vertex. In order to properly classify the signal topologies, we introduce a formal labeling scheme, which is (i) model independent, (ii) general enough to describe any topology, (iii) sufficiently concise and (iv) allows us to easily combine topologies according to the assumptions and conditions in the experimental analyses.
Given a BSM model—described by its spectrum, branching ratios and production cross sections—we need to obtain all the possible signal topologies and compute their weights (\({\sigma \times \mathcal {B}} \)). The procedure of computing these corresponds to the decomposition of the full model in terms of simplified model topologies. There are two ways to actually perform the SMS decomposition. The first requires the generation of partonlevel Monte Carlo (MC) events, followed by the mapping of each event into the corresponding SMS topology. The second method is purely based on the SLHA [20] spectrum file and decay table, supplemented by theoretically computed cross sections. Below we describe both approaches in more detail.
Monte Carlo based decomposition
The decomposition based on parton level MC events is the most general one, since it can decompose any type of BSM model, as long as it is possible to simulate MC events for it. In this case an event file in the LHE format is used as input and each event is mapped to a simplified model topology. The mapping is obviously not onetoone, since more than one event can generate the same exact SMS topology. Then the sum of MC weights for all events contributing to the same topology directly gives \({\sigma \times \mathcal {B}} \) for the corresponding topology. The disadvantage of this method is the introduction of MC uncertainties in the decomposition result; this can however be easily solved by increasing the MC statistics. We also note that the recent advances on NLO MC generators will allow to produce decomposition results at NLO even in the MC based decomposition.
SLHAbased decomposition
In the SUSY case, there are a number of public codes for the computation of the mass spectrum and decay branching ratios with output in the SLHA [20] format. The production cross sections can then be computed at leading order (LO) through a Monte Carlo generator, or at nexttoleading order (NLO) with Prospino [21]. For gluinos and squarks, cross sections at nexttoleading log (NLL) precision can be computed using NLLFast [22]. These cross sections can be included in the SLHA file [23], which then holds all the required information for the SMS decomposition.
In the SLHAbased decomposition the cross sections for pair production of BSM states and the corresponding branching ratios are used to generate all possible signal topologies. The only theoretical uncertainties in this case come from the crosssection uncertainty, hence being much smaller than the uncertainties in the MCbased method, which depends on the MC statistics. In order to avoid dealing with a large number of irrelevant signal topologies, only the ones with \({\sigma \times \mathcal {B}} \) above a minimal cut value are kept. For the results presented below we take this cut value to be \(0.03\) fb.^{5}
Compression of topologies
3.2 Analysis database
3.2.1 Anatomy of an SMS result
The interpretation of the BSM search results in the context of simplified models has become the defacto standard for the experimental collaborations. The ATLAS and CMS collaborations typically produce two types of SMS results: for each simplified model, values for the product of the experimental acceptance and efficiency (\(A \times \epsilon \)) are determined to translate a number of signal events after cuts into a signal cross section. From this information, a 95 % confidence level upper limit (UL) on the product of the cross section and branching fraction (\(\sigma \times \mathcal {B}\)) is derived as a function of the BSM masses appearing in the SMS. Finally, assuming a theoretical “reference” cross section for each mass combination, an exclusion curve in the plane of two masses is produced.
Metadata describing the SMS result from CMS in Fig. 7 (left plot)
sqrts: 8.00 
lumi: 19.50 
url: https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsSUS13006 
constraint: TChiChipmSlepStau > [[[‘L’],[‘L’]],[[‘nu’],[‘ta’]]] 
fuzzycondition: TChiChipmSlepStau > 
Cgtr([[[‘mu’],[‘mu’]],[[‘nu’],[‘ta’]]] , [[[‘e’],[‘e’]],[[‘nu’],[‘ta’]]]) 
Cgtr([[[‘e’],[‘e’]],[[‘nu’],[‘ta’]]] , [[[‘ta’],[‘ta’]],[[‘nu’],[‘ta’]]]) 
category: TChiChipmSlepStau > eweakino 
axes: TChiChipmSlepStau: M1 M0 005  M1 M0 050  M1 M0 095 
Finally, the entry ‘axes’ describes the available slices of the \((m_{\tilde{\chi }_1^{\pm }},\, m_{\tilde{L}},\,m_{\tilde{\chi }_1^0})\) parameter space, which in this example corresponds to \(m_{\tilde{l}}= 0.5m_{\tilde{\chi }^{\pm }_1} + 0.5m_{\tilde{\chi }_1^0}\), \(m_{\tilde{l}}= 0.95m_{\tilde{\chi }^{\pm }_1} + 0.05m_{\tilde{\chi }_1^0}\) and \(m_{\tilde{l}}= 0.05m_{\tilde{\chi }^{\pm }_1} + 0.95m_{\tilde{\chi }_1^0}\). This information is used to interpolate between the values in the experimental results. Since different experimental analyses adopt distinct slicing methods of the parameter space, we use a general interpolation procedure which works for any slicing choice. It is based on a tesselation of the mass vector space and a linear interpolation on each simplex.
Metadata describing the SMS result from ATLAS in Fig. 7 (right plot)
sqrts: 8.00 
lumi: 20.30 
url: https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLASCONF2013049/ 
constraint: TSlepSlep > [[[‘e+’]],[[‘e’]]]+[[[‘mu+’]],[[‘mu’]]] 
fuzzycondition: TSlepSlep > Cgtr([[[‘mu+’]],[[‘mu’]]],[[[‘e+’]],[[‘e’]]]) 
category: TSlepSlep > directslep 
axes: TSlepSlep: M1 M0 
3.2.2 List of analyses in database
The analyses that are currently implemented in the database are:
Gluino and squark searches

ATLAS: SUSY201304 [26], ATLASCONF2012105 [27], ATLASCONF2013007 [28], ATLASCONF2013047 [29], ATLASCONF2013061 [30], ATLASCONF2013062 [31], ATLASCONF2013089 [32]

CMS: SUS11022 [33], SUS11024 [34], SUS12005 [35], SUS12011 [36], SUS12024 [37], SUS12026 [38], SUS12028 [39], SUS13002 [40], SUS13004 [41], SUS13007 [42], SUS13008 [43], SUS13012 [44], SUS13013 [45]
Direct slepton searches

ATLAS: ATLASCONF2012166 [54], ATLASCONF2013001 [55], ATLASCONF2013007 [28], ATLASCONF2013024 [56], ATLASCONF2013025 [57], ATLASCONF2013037 [58], ATLASCONF2013047 [29], ATLASCONF2013048 [59], ATLASCONF2013053 [60], ATLASCONF2013062 [31], ATLASCONF2013065 [61], SUSY201305 [62]

CMS: SUS11022 [33], SUS12028 [39], SUS13002 [40], SUS13004 [41], SUS13008 [43], SUS13011 [63], SUS13013 [45]
3.3 Matching theoretical and experimental results
Once a BSM spectrum is decomposed according to the procedure described in Sect. 3.1, all the relevant information for confronting the model with the experimental results is encapsulated in the SMS topologies plus their mass vectors and weights. Any specific model dependent information can be dropped at this point. As discussed in Sect. 3.2, it is however often the case that the experimental result constrains a sum of topologies instead of a single one. Before a direct comparison with the experimental constraints, it is necessary to combine single SMS topologies (which means adding their weights) according to the experimental analysis’ assumptions (described in the metadata of the analysis). Furthermore, it is always implicitly assumed that all summed topologies have a common BSM mass vector (for the slepton pair production example this means \((m_{\tilde{e}},m_{\tilde{\chi }_{1}^{0}}) = (m_{\tilde{\mu }},m_{\tilde{\chi }_{1}^{0}})\)). Therefore, when combining signal topologies according to the analysis constraints, we must ensure that they have similar mass vectors.
Since different analysis have different sensitivities to the mass vector, we do not use the simple mass distance in GeV in order to verify if two vectors are similar or not. Instead we consider the sensitivity of the analysis in question to the difference between the two vectors. In order to quantify this sensitivity we use the analysis upper limit for each individual mass vector. If both upper limits differ by less than a maximal amount (20 %), we render the mass vectors as similar with respect to this particular analysis. However, if the upper limits differ by more than 20 %, we consider the two vectors as distinct. Moreover, in order to avoid cases where two upper limits are coincidentally equal, but they correspond to completely different mass configurations, we also require the mass values not differ by more than 100 %.
Once again we illustrate this procedure using the slepton pair production constraint as an example. In the MSSM we usually have \(m_{\tilde{e}_L} {=}\,\, m_{\tilde{\mu }_L}\) and \(m_{\tilde{e}_R} {=}\,\, m_{\tilde{\mu }_R}\), but \(m_{\tilde{e}_L} \ne m_{\tilde{e}_R}\). The experimental constraint on slepton pair production requires to combine the topologies \([[[e^+]],[[e^]]]\) and \([[[\mu ^+]],[[\mu ^]]]\) with \((m_{\tilde{e}},m_{\tilde{\chi }_{1}^{0}}) \simeq (m_{\tilde{\mu }},m_{\tilde{\chi }_{1}^{0}})\). Since \(\tilde{e}_{L,R}^+\tilde{e}_{L,R}^\) and \(\tilde{\mu }_{L,R}^+\tilde{\mu }_{L,R}^\) contribute to \([[[e^+]],[[e^]]]+[[[\mu ^+]],[[\mu ^]]]\), we must first group the sleptons (\(\tilde{e}_{L}\), \(\tilde{e}_{R}\), \(\tilde{\mu }_{L}\), \(\tilde{\mu }_{R}\)) with similar masses before we can combine the topologies. In order to identify the similar mass vectors we first obtain, for the given analysis, the upper limit for each vector (\((m_{\tilde{e}_L},m_{\tilde{\chi }_{1}^{0}})\), \((m_{\tilde{\mu }_R},m_{\tilde{\chi }_{1}^{0}})\),...) and cluster together the masses with similar upper limit values. If the analysis is sensitive to the lefthanded/righthanded slepton mass splitting, the upper limits will differ significantly and the grouped masses will correspond to (\(\tilde{e}_L\), \(\tilde{\mu }_L\)) and (\(\tilde{e}_R\), \(\tilde{\mu }_R\)). On the other hand, if the mass spliting is small and the analysis is not sensitive to it, all upper limits will be similar and all the sleptons will be grouped together.
After the topologies with similar mass vectors have been identified, we can combine them (add their \({\sigma \times \mathcal {B}} \)) according to the experimental constraint (\(\sigma ([[[e^+]],[[e^]]])+\sigma ([[[\mu ^+]],[[\mu ^]]])\) for the example above). However, as mentioned in Sect. 3.2, for most constraints involving a sum of single topologies, the experimental assumptions include conditions on each topology contributing to the sum, such as \(\sigma ([[[e^+]],[[e^]]]) \simeq \sigma ([[[\mu ^+]],[[\mu ^]]])\) for the slepton analysis. These conditions need to be taken into account when interpreting the experimental results, since each topology may have a different signal efficiency. Therefore we must also verify that these conditions are satisfied, otherwise the experimental upper limit can not be applied. Finally, if the experimental assumptions are satisfied, the resulting theoretical predictions (\(\sigma \times \mathcal {B}\)) obtained after combining the topologies can be directly compared to the corresponding experimental upper limit.
In Fig. 1 we summarize the main steps required to confront the BSM model predictions with the experimental constraints: the SMS decomposition, the combination of SMS topologies with identical or similar masses into the topology sums assumed by the analyses and finally the comparison with the experimental upper limits obtained from the database of LHC results described in Sect. 3.2.
4 Validation
A simple and robust way to validate the SModelS procedure described in Sect. 3 consists in applying it to a simplified model. In this case, the experimental assumptions are exactly satisfied by the full (simplified) model and we should be able to reproduce the exclusion curve given by the experimental collaboration. For instance, to validate the ATLASCONF2013035 \(\tilde{\chi }^\pm _1\tilde{\chi }^0_2 \rightarrow WZ\tilde{\chi }_1^0\tilde{\chi }_1^0\) analysis, we assume the full model only consists of a pair of massdegenerate \(\tilde{\chi }^\pm _1\) and \(\tilde{\chi }^0_2\) (both pure Winos) and the neutralino LSP (pure Bino), \(\tilde{\chi }^0_1\), with \(\mathcal{B}(\tilde{\chi }^\pm _1\rightarrow W^{(*)}\tilde{\chi }_1^0) = \mathcal{B}(\tilde{\chi }^0_2\rightarrow Z^{(*)}\tilde{\chi }_1^0) = 1\). All the other particles in the spectrum are taken to be in the multiTeV scale and decoupled. Scanning over \(m_{\tilde{\chi }^\pm _1}\) and \(m_{\tilde{\chi }_1^0}\) and verifying which points are excluded by the ATLASCONF2013035 analysis, we then expect to reproduce the official exclusion curve obtained by the experimental collaboration.^{7}
5 Application to the MSSM
5.1 Parameter scans

the gaugino mass parameters \(M_1\), \(M_2\) and \(M_3\), assuming the approximate GUT relation \(M_1:M_2:M_3=1:2:6\);

the higgsino mass parameter \(\mu \), the pseudoscalar mass \(m_A\) and \(\tan \beta =v_2/v_1\);

a common mass parameter \(M_{\tilde{q}}\equiv M_{\tilde{Q}_{1,2}}=M_{\tilde{U}_{1,2}}=M_{\tilde{D}_{1,2}}\) for the first two generations of left and righthanded squarks;

mass parameters and trilinear couplings for stops and sbottoms: \(M_{\tilde{Q}_3}\), \(M_{\tilde{U}_3}\), \(M_{\tilde{D}_3}\), \(A_t\), \(A_b\)

for left and right sleptons, we take common mass parameters \(M_{\tilde{L}}\), \(M_{\tilde{R}}\) for all three generations, supplemented by the trilinear couplings for staus, \(A_\tau \);
Scan ranges and values for fixed parameters used in this study; dimensionful quantities are in TeV units. \(R\equiv \max (M_{\tilde{Q}_3},M_{\tilde{U}_3})\). The parameters are scanned over randomly assuming a flat distribution
\(M_2\)  \(\mu \)  \(\tan \beta \)  \(M_{\tilde{L}}\)  \(M_{\tilde{E}}\)  \(M_{\tilde{q}}\)  \(M_{\tilde{Q}_3}\)  \(M_{\tilde{U}_3}\)  \(M_{\tilde{D}_3}\)  \(A_t\)  \(A_b\)  \(A_\tau \)  

ScanI  0.1–1  0.1–1  3–60  0.1–1  0.1–1  5  2  2  2  \(\pm 6\)  \( 0 \)  \(\pm 1\) 
ScanII  0.1–1  0.1–1  3–60  5  5  0.1–5  0–2  0–2  0–2  \([1,3R]\)  \(\pm 1\)  \( 0 \) 
Constraints used to define the valid parameter space before applying the SMS limits
Observable  Experimental result  Theory uncert.  Constraint imposed 

\(\mathcal {B}(b \rightarrow s\gamma )\)  \((3.43 \pm 0.21 \pm 0.07)\times 10^{4}\) [3]  \(0.23 \times 10^{4}\) [70]  \([2.79,\,4.07] \times 10^{4}\) 
\(\mathcal {B}\) \((B_s \rightarrow \mu ^+ \mu ^)\)  \((2.9\pm 0.7) \times 10^{9}\) [71]  10 %  \([1.4,\,4.4] \times 10^{9}\) 
\(\Delta a_\mu \)  \((26.1 \pm 8.0)\times 10^{10}\) [72]  \(\sim 8\times 10^{10}\)  \({<}5\times 10^{9}\) 
\(\Delta \Gamma (Z\rightarrow \mathrm{inv})\)  –  \({<}3\) GeV  
\(m_h\)  \(125.5\pm 0.2\,^{+0.5}_{0.6}\) GeV (ATLAS) [73]  \(125.5\pm 3\) GeV  
\(125.7\pm 0.3\pm 0.3\) GeV (CMS) [76]  
Sparticle masses  LEP  – 
5.2 Results from ScanI (EWino and slepton focus)
The purpose of ScanI is to test the sensitivity to EWino and slepton searches. Moreover, as we assume a GUT relation between the gaugino masses, it will also be susceptible to limits from threebody gluino decays. To begin with, we show in Fig. 9 scatter plots of the scan points in the \(m_{\tilde{\chi }^\pm _1}\) versus \(m_{\tilde{\chi }^0_1}\), \(M_2\) versus \(\mu \), \(m_{\tilde{\mu }_1}\) versus \(m_{\tilde{\chi }^0_1}\) and \(m_{\tilde{g}}\) versus \(m_{\tilde{\chi }^0_1}\) planes. The red points, which form the top layer, are excluded by at least one analysis, while the blue points are not excluded by any single SMS limit. The grey points do not have any experimental limits either because their topologies do not match any of the existing experimental results or because their masses fall outside the ranges considered by the experimental searches. These points are labeled ‘not tested’ and mostly appear when both the chargino and gluino masses fall outside the grids of the experimental results.
Some comments are in order regarding the differences between the areas covered by the red points and the naive expectations from the official exclusion curves. One issue concerns the gaugino–higgsino mixing. As seen in Fig. 9a, excluded points are concentrated along the \(m_{\tilde{\chi }_{1}^{\pm }} \sim 2m_{\tilde{\chi }_{1}^{0}}\) (or \(m_{\tilde{g}} \sim 7m_{\tilde{\chi }_{1}^{0}}\)) line, which corresponds to model points with a pure wino chargino (\(\tilde{\chi }_1^{\pm } \simeq \tilde{W}^{\pm }\)). Once \(\tilde{\chi }_{2}^{0}\) and \(\tilde{\chi }_{1}^{\pm }\) acquire a higgsino component, the constraints become significantly weaker. Notice that this happens even for points with large \(m_{\tilde{\chi }_{1}^{\pm }}m_{\tilde{\chi }_{1}^{0}}\) mass splittings, far from the pure higgsino region. This is explicitly visible in Fig. 9b, which shows the projection onto the \(M_2\)–\(\mu \) plane. As we can see, almost all excluded points lie in the wino chargino region (\(\mu > M_2\)).
In Fig. 9c we show the same results, but now in the \(\tilde{\mu }_1\)–\(\tilde{\chi }^0_1\) mass plane, where we see that for \(m_{\tilde{\chi }_1^0} \lesssim 125\) GeV there are excluded points for any slepton mass, due to constraints on light charginos (decaying to \(WZ\)) and gluinos. Once the LSP becomes heavier, the constraints for \(\tilde{\chi }_{1}^{\pm }\tilde{\chi }_{2}^{0}\) decaying through sleptons become relevant and exclude the region \(m_{\tilde{\mu }_1} \lesssim 2m_{\tilde{\chi }_1^0}\) up to \(m_{\tilde{\chi }_1^0} \sim 250\) GeV (\(m_{\tilde{\chi }_1^{\pm }} \sim 500\) GeV). Finally, in Fig. 9d, the gluino versus neutralino mass plane, we see once again that the points are concentrated along the bino LSP line (\(m_{\tilde{g}} \sim 7m_{\tilde{\chi }_{1}^{0}}\)).
It is also interesting in this respect to look at a more detailed breakdown of how different analyses constrain the parameter space. In Fig. 10 we show the most constraining topology for each excluded point in the chargino–neutralino and slepton–neutralino mass planes.^{9} We also split the constraints by ATLAS (left panel) and CMS (right panel) results. The first interesting point to notice is that the constraints coming from gluino decay topologies (mostly from \(\tilde{g}\tilde{g}\) production with \(\tilde{g}\rightarrow b\bar{b}\tilde{\chi }^0_1\)) are stronger then those from EW production only at low chargino masses (\(m_{\tilde{\chi }^\pm _1} \lesssim 250\) GeV), while the high mass region is constrained by either slepton pair production or \(\tilde{\chi }_{1}^{\pm }\tilde{\chi }_{2}^{0}\) production followed by decay through onshell sleptons. Both ATLAS and CMS results show a similar behavior.^{10} The main differences come from the ATLAS offshell WZ analysis, which can extend the constraints to a significant part of the mixedchargino region (at low chargino masses), and from the ATLAS \(\tilde{l} \tilde{l}\) search, which obtained stronger constraints than the equivalent CMS analysis. On the other hand, the 2012 CMS EWino analysis [52] saw an underfluctuation in the BG, which resulted in stronger constraints for some regions of parameter space than the ATLAS results.^{11}
Finally, the constraints from direct slepton production can also be suppressed when \(m_{\tilde{l}_R} \ll m_{\tilde{l}_L}\), since righthanded sleptons have smaller production cross sections. Hence we conclude that the parameter space excluded by the current SMS results can be drastically reduced when compared to the naive expectations from the official exclusion curves. For the slepton and EWino signal topologies this reduction is mostly due to the suppression of production cross sections and/or small sensitivity to some signal topologies (such as neutralino decays to Higgs). On the other hand, the constraints on gluino production can be potentially enhanced if new analyses include SMS results for the most relevant gluino topology: \(\tilde{g} \rightarrow \tilde{\chi }_1^\pm + tb \rightarrow \tilde{\chi }_1^0 + W^{\pm } + tb\).
Last but not least note that we do not combine limits from distinct SMS topologies, which corresponds to a conservative estimate of the excluded region. In particular our results tend to underestimate the exclusion obtained from gluino production: as explained above the light gluino scenarios marked as “allowed” in our plots typically show a rather complicated mix of gluino threebody decays into \(\tilde{\chi }^0_{1,\ldots ,4}+q\bar{q}\) and \(\tilde{\chi }^\pm _{1,2}+q\bar{q}'\), and of loopinduces decays into \(\tilde{\chi }^0_{1,\ldots 4}+g\), such that the SMS limits may be evaded despite a production cross section of the order of 1 pb. At least part of these points are effectively excluded by the generic multijet and/or multijet plus leptons searches.^{13} A way to improve this situation may be the use of efficiency maps, as discussed at the recent LPCC workshop [77].
5.3 Results from ScanII (gluino and squark focus)
Let us now turn to the case that squarks of the 1st/2nd and also of the 3rd generation are allowed to be light. Here, we assume decoupled sleptons. The EWino spectrum still is constrained by the assumption of gauginomass unification and \(\mu \) is allowed to vary within 0.1–1 TeV. The full range of parameters is listed in Table 3. In Fig. 14 we show again the excluded points (in red) on top of the SMSallowed points (in blue), but now in the \(m_{\tilde{\chi }^0_1}\) versus \(m_{\tilde{g}}\), \(m_{\tilde{\chi }^0_1}\) versus \(m_{\tilde{q}}\), \(m_{\tilde{\chi }^0_1}\) versus \(m_{\tilde{t}_1}\), and \(m_{\tilde{\chi }^0_1}\) versus \(m_{\tilde{b}_1}\) planes. Since the first two generations of squarks are degenerate, the average squark mass is given by \(m_{\tilde{q}}\equiv (m_{\tilde{u}_L}+m_{\tilde{u}_R}+m_{\tilde{d}_L}+m_{\tilde{d}_R})/4\).
From Fig. 14a we once again notice that the exclusion region is mostly concentrated in the bino LSP region (\(\mu > M_1\)), despite the potential presence of points with light squarks. Nonetheless the excluded region in the \(m_{\tilde{\chi }_1^0}\) versus \(m_{\tilde{g}}\) plane is considerably larger than in ScanI and it extends well beyond the gluino 3body decays exclusion curves. This is expected since the presence of light squarks allows points to be excluded even for very heavy gluino masses. This is explicitly visible in Fig. 14b, where we see that excluded points with heavy gluinos (\(m_{\tilde{g}} > 1.8\) TeV or \(m_{\tilde{\chi }_1^0} > 250\) GeV) correspond to light squark masses, \(m_{\tilde{q}} < 1\) TeV. It is also interesting to note that the excluded points in the squark versus neutralino mass plane extend well beyond the exclusion curves for squark production and direct decay to the LSP, even for heavy gluino masses. The reason is that even a 2–3 TeV gluino is not yet decoupled but gives a tchannel contribution to squarkpair production. Finally, in Fig. 14c, d, the excluded points are projected onto the LSP–stop and LSP–sbottom mass planes. While the density of excluded points seems to depend weakly on the stop mass, it is concentrated in the light sbottom region, agreeing well with the expectation of the exclusion curves, except for light LSP masses, where constraints from gluino and EWino topologies become relevant.
In Fig. 15c, d we show the same points, but in the squark versus neutralino mass plane. The points excluded by squarks topologies (\(\tilde{q} \tilde{q} \rightarrow qq \tilde{\chi }_1^0 \tilde{\chi }_1^0\)) extend up to \(m_{\tilde{q}} \sim 1.4\) TeV, well beyond the naive expectations from the exclusion curves. As mentioned, this is due to the tchannel gluino contribution to the squark production cross section, which enhances \(\sigma (\tilde{q} \tilde{q})\) with respect to the fully decoupled gluino case. Since the exclusion curves assume decoupled gluinos, the squark cross sections are significantly reduced, resulting in a smaller reach. As the gluino mass increases (for a fixed squark mass), the squark cross section slowly decreases as well as the corresponding reach in squark mass. This is explicitly seen in the plots of squark versus gluino mass in Fig. 15.
The same enhancement is not present for the 3rd generation squarks since the tchannel gluino contribution is strongly suppressed by the negligible bottom and top PDFs. This is also shown by the plots in Fig. 15, where we see that the reach from sbottom and stop topologies are independent of the gluino mass up to \(m_{\tilde{g}} \approx 1.5\)–1.7 TeV. For even higher gluino masses, points with a bino LSP have \(m_{\tilde{\chi }_1^0} > 250\) GeV and are beyond the reach of the sbottom/stop SMS constraints, as shown by the exclusion curves in Fig. 14c, d. The few points above \(m_{\tilde{g}} \sim 1.5\)–1.7 TeV excluded by the sbottom and stop signal topologies have a light higgsino LSP.
6 Conclusions
We presented a new tool, SModelS, to decompose the LHC signatures expected from BSM spectra presenting a \(\mathbb {Z}_2\) symmetry into SMS topologies and test the predicted cross sections (\(\sigma \times \mathcal {B}\)) for each topology against the existing 95 % CL upper limits from ATLAS and CMS. The program consists of three parts, the decomposition procedure, which can be MonteCarlo based or SLHA based, the database of ATLAS and CMS SMS results, and the interface to match model predictions onto the experimental results. Our concrete implementation currently focusses on SUSY searches with missing energy, for which a large variety of SMS results from ATLAS and CMS are available. SModelS can be used “out of the box” for the MSSM and its extensions, like the nexttoMSSM. The approach is however perfectly general and easily extendible to any BSM model to which the experimental SMS results apply. (Of course, the SMS assumption is subject to several caveats, as explained at the beginning of Sect. 2 and in footnotes 3 and 4.)
As a proof of principle, we applied our procedure in two scans of the weakscale MSSM and discussed which parameter regions are excluded by the SMS limits and which scenarios remain untested. As we showed, SModelS can be useful for several purposes. First of all it is a convenient tool for relatively fast surveys of complex parameter spaces in order to devise the regions that are definitely excluded by data. Second, it can be used to find relevant topologies for which no SMS results exists—this may be helpful for the experimental collaborations for designing new SMS interpretations. An example that we already identified is “mixed” topologies with \(tb\) final states, which can arise e.g. from \(\tilde{g} \rightarrow tb\tilde{\chi }_1^\pm \) or from \(\tilde{t}_1\) pair production with one stop decaying into \(t\tilde{\chi }_1^0\) and the other one into \(b\tilde{\chi }_1^\pm \). Third, one may use the decomposition procedure of SModelS independent of the results database in order to identify the most important signal topologies in regions of parameter space. Finally, in the case of a positive BSM signal, the SModelS framework may be helpful for characterizing which new physics scenarios may explain the observations.
While SModelS is already a powerful and useful tool for phenomenological studies, there is of course still much room for improvement. For instance, as we have shown, scenarios with complicated decay patterns—as typical for e.g. light gluinos and heavy squarks—are not well constrained with the current framework, which is based on testing the \(\sigma \times \mathcal {B}\) upper limits topologybytopology without the possibility of combining results. Here the use of efficiency maps, once available in a systematic fashion, would allow for significant improvements. This is clearly a development which we will follow. We also foresee to extend SModelS to multiple branches, including subbranches originating from the main cascade decay chains. This is relevant, e.g., for heavy Higgses (or other nonSM “Reven” particles as present in models with extra dimensions) appearing in the decay chains. We also conceive the inclusion of resonant production of new particles, as well as violation of the \(\mathbb {Z}_2\) symmetry; in the context of SUSY this means extension to Rparity violation. Regarding the statistical treatment, for identifying the most sensitive analysis (in order not to alter the effective CL), it would be of great help if the experimental collaborations systematically provided also the expected \(\sigma \times \mathcal {B}\) upper limits in addition to the observed ones.
Last but not least note that the mapping from the full model signal to a sum over simplified model signal topologies is clearly not an exact procedure. It assumes that, for most experimental searches, the BSM model can be approximated by a sum over effective simplified models. The validity of this approximation, in particular (i) regarding the question how the type of production channel or the nature of the offshell states mediating the decays affects the signal efficiencies, and (ii) regarding the question of using SMS limits derived in the SUSY context for nonSUSY models, will be a subject of future work.
The publication of the SModelS code with a dedicated online manual is in preparation [18].
Note added
Shortly before submission of this paper another program package, CheckMATE [78], became available for confronting BSM scenarios with LHC Data. CheckMATE determines whether a model is excluded or not at 95 % C.L. by comparing to many recent experimental analyses, based on fast simulation. It thus represents an interesting alternative to the SMS approach followed by SModelS.
Moreover, while the SModelS paper was being refereed, another program based on SMS results, Fastlim [79], was published. Fastlim employs efficiency maps and currently takes into account 11 ATLAS analyses, which are mainly focused on stop and sbottom searches. Restricting the SModelS database to the 11 ATLAS analyses implemented in Fastlim, we have verified that for ScanII about \(70~\%\) of the points excluded by SModelS are also excluded by Fastlim and viceversa. Interestingly, from all the points excluded by SModelS, \(\approx \)30 % are not excluded by Fastlim; a part of these points features a light LSP with mass of 45–65 GeV—this region does not seem to be covered by Fastlim. The reverse is also true: from all the points excluded by Fastlim, \(\approx \)30 % are not excluded by SModelS. A detailed comparison of the two approaches is on the way. We recall, however, that SModelS includes in total more than 50 analyses from both ATLAS and CMS, which allows to exclude an additional 54 % of points in ScanII.
Footnotes
 1.
By full model we mean, for instance, a specific MSSM parameter point.
 2.
Throughout this work we ignore BSM particles which are \(\mathbb {Z}_2\) even, such as heavy Higgs bosons in the MSSM. The light MSSM Higgs \(h\) is treated as a SM particle.
 3.
One has to keep in mind, however, that the color factor of the initially produced BSM particles influences the QCD activity in the final state and may thus significantly affect the signal efficiency. This is not a worry in the following as we did not come across any example where constraints from a experimental result assuming QCD production are used to exclude an EW produced topology, or viceversa, but one might encounter such cases in principle.
 4.
As discussed in Sect. 2, the SMS assumption may be violated for specific analyses given a particular model. For instance, if the signal efficiency for a specific analysis is too sensitive to the shape of the signal distributions and these are strongly affected by the type of production channel (schannel or tchannel) or by the nature of the offshell states mediating the decays, the reduction of a full model to its SMS topologies no longer encapsulates all the necessary information. We leave it to the user to evaluate which analyses may be applied for the input model considered.
 5.
Note that since experimental results often constrain sums of topologies, individual signal topologies with small \({\sigma \times \mathcal {B}} \) may still be relevant for the final theoretical prediction. This is why we take such a small value for the minimal cross section cut.
 6.
The actual function used is \(Cgtr(x,y) = \left( xy  (xy)\right) /\left( 2(x+y)\right) \).
 7.
Since we compute the EW gauginos and sleptons cross sections at LO, while the experimental collaborations assume NLO cross sections, we multiply the LO cross sections by a constant Kfactor (1.2) to more accurately reproduce the official curve.
 8.
In ScanII it is much more efficient to find points which pass all constraints, in particular the \(\mathcal {B}(b \rightarrow s\gamma )\) constraint, if \(A_t>0\) than for \(A_t<0\). Since the physical observables we are interested in (i.e. the coverage of masses and decay branching ratios) are largely insensitive to the sign of \(A_t\), we choose to consider only positive \(A_t\). Concretely we limit the scan to \(A_t>1\) TeV as for lower \(A_t\) we obtain too low \(m_h\).
 9.
By most constraining we here mean the topology that gives the largest ratio of predicted \({\sigma \times \mathcal {B}} \) over the 95 % UL \({\sigma \times \mathcal {B}} \).
 10.
In the righthand side (CMS) plots of Fig. 10, the pink points excluded by gluino topologies are shown as the bottom layer and are hence partly covered by the yellow points excluded by EWino topologies, but they do extend up to \(m_{\tilde{\chi }^\pm _1}\lesssim 250\) GeV.
 11.
In principle one should of course use only the constraints from the most sensitive analysis, in order not to alter the effective CL. Ideally, this should be based on the expected limits. Since the expected limits are however not provided by the experimental collaborations systematically for all results, for the time being we choose to use all constraints in a democratic manner. We hope that situation will improve as SMS results become more widely used (see, e.g., the recent LPCC workshop [77]).
 12.
 13.
We thank Lukas Vanelderen and Matthias Schroeder for explicit checks against the CMS RA2 results.
Notes
Acknowledgments
We thank D. Liko for help in using the Vienna Tier2 Grid, and the reactor physics group of LPSC Grenoble for the use of part of their computer resources. This work was supported in part by the PEPSPTI project “LHCitools”, by the ANR project DMAstroLHC and by FAPESP. U.L. and D.P.S. are grateful for financial support by the FEMtech initiative of the BMVIT of Austria. A.L. gratefully acknowledges the hospitality of LPSC Grenoble.
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