Constraints on the pMSSM from searches for squarks and gluinos by ATLAS

We study the impact of the jets and missing transverse momentum SUSY anal- yses of the ATLAS experiment on the phenomenological MSSM (pMSSM). We investigate sets of SUSY models with a flat and logarithmic prior in the SUSY mass scale and a mass range up to 1 and 3 TeV, respectively. These models were found previously in the study ’Supersymmetry without Prejudice’. Removing models with long-lived SUSY particles, we show that 99 % of 20000 randomly generated pMSSM model points with a flat prior and 85 % for a logarithmic prior are excluded by the ATLAS results. For models with squarks and gluinos below 600 GeV all models of the pMSSM grid are excluded. We identify SUSY spectra where the current ATLAS search strategy is less sensitive and propose extensions to the inclusive jets search channel.


Introduction
Supersymmetry [1][2][3][4][5][6][7][8][9][10][11][12][13][14] is one of the conceivable extensions of the Standard Model (SM). It could provide a natural candidate for cold dark matter [15,16] and stabilize the electroweak scale by reducing the fine tuning of higher order corrections to the Higgs mass [14,[17][18][19][20][21] . Supersymmetry (SUSY) proposes superpartners for the existing particles. Squarks and gluinos, superpartners of the quarks and the gluon are heavy coloured particles, which can decay to jets and the Lightest Supersymmetric Particle (LSP), i.e. the neutralino. The neutralino is only weakly interacting and stable since we assume the conservation of Rparity. The LSP escapes detection which results in missing transverse momentum in the detector. Channels with jets and missing transverse momentum have a large discovery potential at the LHC [22], since the coupling strength of the strong force would cause an abundance of squarks and gluinos if these particles are not too heavy.
In the present study we investigate the reach of the ATLAS search with jets and missing transverse energy in the phenomenological MSSM (pMSSM) [23] . A primary objective of our study is to identify possible parameter regions of pMSSM scenarios where the ATLAS analysis is insensitive. This has not been studied before. There are other similar searches from CMS and ATLAS which look into the same signature (see for example [24][25][26]). The reach of the CMS searches in a pMSSM model has been studied recently in ref. [27].
The ATLAS collaboration has analyzed their data to search for squarks and gluinos in events with 2-4 jets and missing transverse momentum corresponding to an integrated luminosity L int of 35 pb −1 in ref. [28] and 1.04 fb −1 in ref. [29]. No excess above the SM background expectation was observed in the analyzed data. Although these searches are designed to be quite independent of SUSY model assumptions, mass limits are presented JHEP05(2012)150 only for a constrained Minimal Supersymmetry Standard Model (cMSSM) model and for simplified models with only squarks, gluinos and the lightest neutralino.
In the pMSSM the more than 120 free parameters of the MSSM are reduced to 19 by demanding CP-conservation, minimal flavor violation and degenerate mass spectra for the 1st and 2nd generations of sfermions. In addition it is required that the LSP is the neutralinoχ 0 1 . The 19 remaining parameters are 10 sfermion masses, 1 3 gaugino masses M 1,2,3 , the ratio of the Higgs vacuum expectation values tan β, the Higgsino mixing parameter µ, the pseudoscalar Higgs boson mass m A and 3 A-terms A b,t,τ . This work is based on "Supersymmetry Without Prejudice" [30]. The model points presented in [30] are used for our purpose. Each model point was constructed by a quasi-random sampling of the pMSSM parameters space. The points were required to be consistent with the experimental constraints prior to the LHC [30].

Event generation, fast simulation and analysis
We study the reach of the ATLAS search by emulating the ATLAS analysis chain. First we generate events from LHC collisions for each pMSSM SUSY model with a Monte Carlo generator for SUSY processes. These events are then simulated by a fast detector simulation and the acceptance and efficiency is determined by applying the most important ATLAS analysis cuts on the simulated events. Finally these numbers are used to calculate the expected number of signal events for each signal region and analysis. These numbers are compared to the model-independent 95% C.L. limits provided by ATLAS. PYTHIA 6.4 [31] is used for the event simulation of proton-proton collisions at a 7 TeV centre-of-mass energy. All squark and gluino production processes are enabled as they are of most importance for the inclusive jets search channel. For every model point 10000 events are generated which we found to be enough even for the models with the smallest selection efficiencies. To get as close as possible to the ATLAS analysis we use DELPHES 1.9 [32] as a fast detector simulation with the default ATLAS detector card, modified by setting the jet cone radius to 0.4. The PYTHIA output is read in by DELPHES in HepMC format, which is produced by HepMC 2.04.02 [33]. The object reconstruction is done by DELPHES, which uses the same anti-k T jet algorithm [34] as ATLAS. Also included in the reconstruction are isolation criteria for electrons and muons. We do not emulate pile-up events.
Reconstructed events are analyzed with the same event selections as used by te ATLAS analysis with 35 pb −1 (shown in table 1) and also with the event selections used in the 1.04 fb −1 analysis (see table 2). In these tables ∆φ(jet i , E miss T ) min is the minimum of the azimuthal angles between the jets and the 2-vector of the missing transverse momentum E miss T . The invariant mass m eff is calculated as the scalar sum of E miss T and the magnitudes of the p T of the leading jets required in the selection (i.e. 2 jets for the 2-jet selection in region A), except for signal region E, where m eff is the sum of E miss T and all reconstructed jets with p T > 40 GeV.

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Signal region: for all regions >100 leading jet p T [GeV] for all regions >120 >500 >500 >1000 f=E miss T /m eff >0.3 >0.25 >0.25 95% C.L. limit on σ [pb] 1.3 1.1 0.11 Table 1. Requirements for the signal regions A,C and D for the ATLAS analysis with an integrated luminosity of 35 pb −1 . In addition the number of reconstructed leptons has to be zero; also shown are the 95% C.L. upper limits on the cross section for new physics processes σ.
For both analyses there are several signal regions differing mainly by the number of required jets. For all signal regions E miss T has to be larger than 100 GeV for L int = 35 pb −1 (130 GeV for L int = 1.04 fb −1 ). The selection for the leading jet p T is identical for all signal regions, it has to be larger than 120 GeV(130 GeV ). The analysis for L int = 35 pb −1 includes signal regions for two and three jets, this is expanded to four and five jet signal regions in the L int = 1.04 fb −1 analysis. The required jets have to exceed a p T of at least 40 GeV. The specifications for m eff and E miss T /m eff vary for each signal region, in general the threshold for m eff is higher for the L int = 1.04 fb −1 analysis. In addition to these cuts a veto on electrons and muons with p T > 20 GeV was required.
After this selection the event counts are scaled to the luminosities considered in the analyses, i.e. 35 pb −1 and 1.04 fb −1 , respectively. The NLO cross section used for this is calculated by LHC-Faser light [35,36] from PROSPINO2.1 [37,38] cross section grids.
The limits on the effective cross sections given by the ATLAS analyses are used to calculate a limit on the number of signal events passing the cuts, also given in table 1 and 2. No attempt was made to include theoretical uncertainties. In the studied SUSY mass range these uncertainties are small compared to the differences of the ATLAS and DELPHES setups and would not change drastically any conclusion of this work.
In order to compare our setup to ATLAS we determined the relative efficiency difference for each SUSY point studied by ATLAS in the m 0 -m 1/2 plane for the cMSSM grid with tan β = 10, A 0 = 0 and µ > 0. Here A * E is the acceptance times efficiency of the ATLAS and DELPHES analysis setups. Figure 1 shows ∆C C for the cMSSM. Numerical examples for the ATLAS and DELPHES efficiencies are shown in table 3. The efficiency of our setup is found to be in agreement with the ATLAS efficiency [39] on the level of 10 − 30% for the 2-and 3-jet signal regions A − B and SUSY masses around the present ATLAS limits. These limits are ranging for m 1/2 from 200 − 500 GeV and go up to intermediate m 0 of 1000 GeV.

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Signal region: for all regions >130 leading jet p T GeV for all regions >130   Table 3. Accepted signal fraction (E * A) for the ATLAS and DELPHES setup and shown for the analysis with L int = 1.04 fb −1 .
At m 1/2 < 200 GeV larger deviations occur. Here both the statistical uncertainty of the ATLAS and DELPHES efficiencies are larger and the selection efficiencies are tiny. The largest deviations occur if in addition m 0 is large. The signal regions are not intended for SUSY signals at m 1/2 < 200 GeV and large m 0 and do therefore not contribute to the search for such SUSY signals. Note that the ATLAS analysis selects always the signal region with the largest exclusion potential for each SUSY model.
For the 4 and more jet channels C-E we observe quite good agreement for 100 GeV < m 1/2 < 400 GeV, for m 1/2 < 100 GeV the same problem as for signal regions A and B occurs. At m 0 > 1000 GeV and m 1/2 > 400 GeV there is slightly worse agreement. Here our DELPHES setup underestimates the efficiency by up to 50−70%. The increased differences JHEP05(2012)150 at larger jet multiplicities are probably caused by the slightly different jet reconstruction. DELPHES assumes a perfect clustering algorithm and does not apply corrections for jet energy underestimation as ATLAS does.
In view of the mostly smaller efficiencies of DELPHES compared to ATLAS, our study can be regarded as conservative.
In addition we compared the limit curve in the m 0 -m 1/2 plane of the cMSSM model as set by ATLAS [39] with the the limit curve produced with our DELPHES setup.

pMSSM random points
The pMSSM points are taken from "Supersymmetry Without Prejudice" [30] (related work [40,41]). All details can be found in these references.
The Monte Carlo method evolved with the availability of computer generated pseudo random samples. The method was already reviewed in 1949 by Metropolis and Ulam [42].
Any probabilistic sampling on a set of parameters does depend on the boundaries on the parameters as well as the underlying probability density functions, which are assigned to each parameter. The outcome of the sampling does depend on the choice of these probability density functions, here called "priors". The correct choice of the prior is connected to the a priori information available, e.g. in a perfect situation one would know that underlying probability density function of a parameter has a Gaussian shape. However the information about the behaviour of the parameter is often only known partially or might be even totally unknown. Then assumptions have to be made. If this is the case any result obtained by such a sampling is dependent on these assumptions, i.e. on the choice of the prior(s).
If there is no or not much information available on a parameter the first choice/guess is usually a flat prior, that is the parameter is equally distributed in the allowed range. Each element has the same probability to be chosen in the sampling. If the prior shape is unknown it is common to present results in light of several different choices of priors to show the impact of these.
In this study parameters are sampled using a flat and a logarithmic prior. The a priori information is here only used to constrain the parameter ranges , but not the underlying probability distributions. Thus any result presented in this paper can only be interpreted in the context of the underlying prior and the allowed ranges of the parameters. Please note that we do not intend to study "best fit parameters", but are interested in investigating a broad range of various parameter sets with viable SUSY spectra.
19 free parameters were randomly sampled, one set with a flat prior with masses up to 1 TeV and another one with a logarithmic prior and masses up to 3 TeV, each parameter was varied in the range given in table 4. Where flat prior means that the value for each

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Parameter Flat prior set Log prior set mf 100 GeV -1 TeV 100 GeV -3 TeV |M 1,2 , µ| 50 GeV -1 TeV 10 GeV -3 TeV M 3 100 GeV -1 TeV 100 GeV -3 TeV |A b,t,τ | 0 -1 TeV 10 GeV -3 TeV tanβ 1 -50 1 -60 m A 43.5 GeV -1 TeV 43.5 GeV -3TeV Table 4. Parameter range for flat and log prior model sets parameter was chosen under the assumption of a uniform distribution in its parameter range. In the same way the logarithmic prior assumes a logarithmic distribution in each parameter range. The objective of choosing two different priors is to detect any bias introduced by how one chooses the parameter space points. The parameters are: 10 sfermion masses mf ; 3 gaugino masses M 1,2,3 ; the ratio of the Higgs vacuum expectation values tan β; the Higgsino mixing parameter µ; the pseudoscalar Higgs boson mass m A and 3 A-terms A b,t,τ , the A-terms for the first and second generations can be neglected due to the small Yukawa couplings.
It was assumed that the neutralino is the LSP and that the first two squark generations are degenerate. For the flat prior 10 7 model points are generated, for the logarithmic prior two sets of 10 6 model points. The values of the SM parameters which are used as input for the generation are given in [30]. Afterwards several experimental and theoretical constraints are applied on the generated points. Thus the number of model points which can be analyzed in the end is greatly reduced. The implemented constraints are the following (all can be found in more detail in [30]): • already during generation the sparticle spectrum is demanded to be tachyon free and to not lead to color or charge breaking minima; also the electroweak symmetry breaking has to be consistent and the Higgs potential has to be bounded from below; • the neutralino as Weak Interacting Massive Particle (WIMP) is assumed to be a conventional thermal relic, so that the LSP is the lightest neutralino; • precision electroweak constraints by the use of the 95% CL allowed experimental range for ∆ρ: −0.0007 ≤ ∆ρ ≤ 0.0026 [43]; • the branching ratios for two rare decays B b→sγ (combined experimental result by HFAG [44] and current theoretical predictions [45,46]) and B Bs→µµ (combined limit by CDF and D0 [47]); • the difference of the measured anomalous magnetic moment of the muon (g − 2) µ to the prediction of the SM is allowed to be: • constraints from heavy flavor measurements: B B→τ ν (combined experimental result by HFAG [44] and theoretical analyses [48,49]); meson-antimeson constraints on the squark mass spectra and similar constraints on the slepton spectra;

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• the WMAP measurement [50] of the relic density by the use of an upper limit on the LSP contribution: Ωh 2 | LSP ≤ 0.1210 • cross section limits from direct detection dark matter searches by XENON10 [51], CDMS [52], CRESST I [53] and DAMA [54] • constraints from LEP and LEPII data [55], here especially that there cannot be any new charged sparticles or Higgs boson below the M Z /2 mass and also no new stable particles with masses below 100 GeV, also the lower limit for light squark masses when the gluino is heavier than the squarks by ALEPH [56] • and finally constraints from Tevatron data, where the limits for squark and gluino masses [57,58] are generalized to model independent constraints, also applied are the limits on tanβ by both CDF and D0 [59] and the lower limits for heavy stable charged particles, here the stronger limit by D0 [60] was applied.
In addition to [30] we have required that the mass splitting between the chargino and the lightest neutralino is ∆m > 0.05 GeV with ∆m = m Chargino − mχ 0 , to avoid mishandling by PYTHIA. Small mass splittings make charginos stable and PYTHIA yields error messages in the hadronization routines and drops these events. The problem is avoided by a decay of the chargino before the hadronization routine, i.e. by a sufficiently large mass splitting between the chargino and the neutralino. About 1% of the remaining model points could not be generated with PYTHIA due to other compressed mass spectra, i.e. due to very small mass differences between SUSY particles. Here mostly the mass difference of the sbottom or stop to the neutralino was small. These compressed mass spectra lead to long lived squarks which can not be handled by PYTHIA nor by the detector simulation and causes PYTHIA to stop. These model points are dropped. The following studies are therefore not valid if the SUSY model leads to long-lived particles in the spectrum besides the lightest neutralino.

Models from a linear prior in the SUSY mass scale
For each SUSY model signal events were generated. Each event was analyzed after a detector simulation with DELPHES and the number of signal events was determined for each SUSY model and each of the 8 studied signal regions. In the following we call "excluded models" SUSY models which produced a larger number of signal events than excluded by the ATLAS model-independent limits in at least one of the signal regions studied. The model-independent limits are listed in table 1 and table 2. Only the SUSY models which yield less signal events in all regions are not excluded by these ATLAS searches. These models are called "not excluded models".   Table 5. Important properties of some not excluded pMSSM models out of 20000with flat prior. Shown are the mass of the lightest squark in the 1. and 2. generation mq; the gluino mass, mg; the mass of the lightest neutralino mχ 0 ; the NLO cross section σ NLO ; the average values of E miss T , m eff , the average number of jets N Jets and the average number of leptons N Lep ; 1 st p jet T and 2 nd p jet T are the average of the leading and second highest jet p T and ∆φ is the average of the ∆φ(jet i , E miss T ) min variable.  scale, models not excluded as black triangles. We show that 99% of the points are excluded with the current ATLAS analyses in the jets and missing transverse momentum channels. All studied points with a mass of the squarks and the mass of the gluino < 600 GeV are JHEP05(2012)150 excluded. This means that there is not much room anymore in the pMSSM for having both light squarks of the first generations and at the same time a light gluino.
Remarkably, also points with small mass splittings between the squarks or gluino and the neutralino are excluded in this mass range. The reason is quite simple. It is very unlikely that a "random" sampling yields cases where the mass splittings of all squarks and the gluino to the neutralino are small. If one of the squarks or only the gluino is a bit heavier than the neutralino such processes yield detectable rates in the ATLAS signal regions. Note that in these models the left and right handed squarks can have quite different masses.
In table 5 a subset of the not excluded model points are presented together with some of their properties. A complete list of all not excluded model points can be found in appendix A.
We found some features why model points are not excluded. We determined average values for some properties for each SUSY model point, neglecting the fact that these values are coming from different SUSY decay chains. The investigated properties of the JHEP05(2012)150 non-excluded SUSY models are shown in table 5. The following features have been found to be significant.

Low cross section.
A large fraction of model points at high squark and gluino masses cannot be excluded because the cross section is simply too low to be observed for the integrated luminosity. Figure 4 shows the fraction of not-excluded points as a function of the total SUSY squark and gluino cross section. Below 0.1 pb less than 50% of the SUSY models can be excluded with the analysis setup. These are mainly points with a large average effective mass value. At large cross sections of greater 5 pb all studied pMSSM models can be excluded by the ATLAS analyses.
Lepton and multi-jet events (long decay chains). Around 25% of the not excluded model points have a large average number of leptons. In addition we find that these SUSY models do often have a large average number of jets. It is trivial to note that, because of the lepton veto, there is not much sensitivity to these models with the inclusive jets analysis. These points can most likely be excluded with the single or multi-lepton analyses. These searches do have signal regions investigating events with up to 4 jets [61,62]. Some SUSY models with long decay chains would yield lepton(s) together with multiple jets.
Compressed spectra together with high squark and gluino masses. Figure 5 shows the excluded and non-excluded SUSY models from the grid with the flat prior as a function of M SUSY and the mass difference of M SUSY and the mass of the lightest neutralino. In this note, the SUSY mass scale M SUSY is defined as the minimal mass of all first and second generation squarks and the gluino. The figure shows the interesting feature that the non-excluded points are mostly located at small mass differences (relative to M SUSY ) and high M SUSY .
Small mass differences between the colored particles and the neutralino yield events with small transverse momentum jets. Figure 6 shows the average effective mass (calculated with the leading 3 jets) as a function of M SUSY . More than half of the not-excluded SUSY models at high M SUSY have an effective mass that is significantly below the value found for the excluded SUSY models. We conclude that the cut on the effective mass is too harsh for these models. For those compressed models the effective mass is differently correlated with the SUSY mass scale.
A lower cut on the effective mass, however, would cause a significant increase in the number of background events. We therefore studied additional features of these nonexcluded models. A comprehensive study yields as the most significant feature a large average value of missing transverse momentum. Figure 7 shows the ratio f of the missing transverse momentum over the effective mass as a function of the effective mass. The notexcluded models at m eff < 600 GeV do have average f -values above 0.3−0.35. It is interesting to note that for higher m eff values smaller cuts on f seem to be appropriate. Increasing the cuts on f for the high m eff regions seems not to yield to an improved performance.
In addition these points do show a typical average jet multiplicity as can be seen in figure 8, also at m eff < 600 GeV. The non-excluded points have jet multiplicities between 2 − 7.      Table 6. Important properties of some not excluded pMSSM models out of 1000 with logarithmic prior. Shown are the mass of the lightest squark in the 1. and 2. generation mq; the gluino mass, mg; the mass of the lightest neutralino mχ 0 ; the NLO cross section σ NLO ; the average values of E miss T , m eff , the average number of jets N Jets and the average number of leptons N Lep ; 1 st p jet T and 2 nd p jet T are the average of the leading and second highest jet p T and ∆φ is the average of the ∆φ(jet i , E miss T ) min variable.

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In conclusion we propose that ATLAS adds to future analyses signal regions with f > 0.3 − 0.35 and a reduced effective mass cut of m eff > 500 GeV for high and low jet multiplicities. A similar conclusion has been found for lower jet multiplicities in an independent study dedicated to compressed spectra [63]. Some of the non-excluded points found in our study could be used as benchmark sets to further optimise the cut values with a detailed ATLAS simulation including background events. Figure 9 shows the result of our analysis of 1000 points made with the logarithmic prior up to 3 TeV in the mass scale of SUSY. Excluded points are shown as green points, not excluded ones as black triangles. Due to possible larger masses of the squarks and gluinos more points survive at higher masses. In total we find that 85% of the model points are excluded.

Models from a logarithmic prior in the SUSY mass scale
In table 6 a subset of the not excluded model points are presented together with some of their investigated properties. A complete list of all not excluded model points can be found in appendix A.
Lepton and multi-jet events Again around one quarter of the not excluded model points have an average lepton number exceeding one. These points cannot be excluded JHEP05(2012)150 Figure 10. The total NLO squarks and gluino production cross section as a function of the minimal mass of the first and second generation squarks and the gluino m SUSY for excluded model points (green dots) and not excluded models (black triangles). For some high mass model points the cross section is significantly enhanced by sbottom and stop production processes.
because of the lepton veto. As observed for the flat prior grid these model points do also lead to multi-jet events.
Low M SUSY combined with low cross section A new feature is found in the logarithmic grid. Some SUSY models with gluino masses above 1000 GeV and squark masses between 300 − 600 GeV are not excluded. Figure 10 shows the total cross section for squark and gluino production processes as a function of the SUSY mass scale M SUSY . All notexcluded SUSY models with M SUSY < 600 GeV are close to the minimal SUSY cross section at a given value of M SUSY . The cross section is minimal since here only thed R ands R or theũ R andc R are light. All other squarks and the gluino have much larger mass values.
These SUSY scenarios might also be missed in future searches, if the cuts on mass scale related variables (as m eff ) are raised further. Limits on squark masses derived at a minimum SUSY cross section might be helpful.
Compressed spectra In contrast to the flat-prior model points compressed mass spectra do not seem to be an important issue for the log-prior grid as far as we could infer from only 1000 model points.

Summary
We show that the "Search for squarks and gluinos using final states with jets and missing transverse momentum" of the ATLAS experiment excludes up to 99% of the model points of the randomly generated pMSSM grid of "Supersymmetry without Prejudice" assuming a flat prior for a SUSY mass scale below 1 TeV. For the model points assuming a logarithmic prior up to 85% are excluded.
Besides the models with a high average number of leptons, the most frequent reasons for the model points not to be excluded are a too low cross section below the discovery potential, a too low mass splitting between the lightest coloured sparticle and the neutralino JHEP05(2012)150 resulting in a low effective mass m eff . We propose to add selections with an increased missing transverse momentum cut and a decreased m eff cut, both with low and high jet multiplicities. In addition we find that the search is quite insensitive if only one type right handed squarks is light, i.e. if the SUSY cross section is smaller than usually assumed. These scenarios might also profit from low mass signal regions with minimal statistical and systematic uncertainties.

Acknowledgments
We wish to thank Tom Rizzo, Carola Berger, James Gainer and JoAnne Hewett for providing the pMSSM model files. We thank Tom Rizzo for helpful comments.
We also thank Ben O'Leary for providing the cross section calculating program.  Table 8: Important properties of all not excluded pMSSM models with log prior. Masses and energies are given in GeV, the cross section is given in pb, except masses and cross sections all values are average values. A cross section of 0 indicates a value smaller than 0.001 pb.

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Open Access. This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.