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

We study the impact of the jets and missing transverse momentum SUSY analyses 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 87% 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] is one of the conceivable extensions of the Standard Model (SM). It could provide a natural candidate for cold dark matter and stabilise the electroweak scale by reducing the fine tuning of higher order corrections to the Higgs mass. 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 R-parity. 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 [2], since the coupling strength of the strong force would cause an abundance of squarks and gluinos if these particles are not too heavy. The ATLAS collaboration has analysed 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. [3] and 1.04 fb −1 in Ref. [4]. No excess above the SM background expectation was observed in the analysed data. Although these searches are designed to be quite independent of SUSY model assumptions, mass limits are presented only for a constrained Minimal Supersymmetry Standard Model (cMSSM) model and for simplified models with only squarks, gluinos and the lightest neutralino.
We will study the exclusion range of the ATLAS search for phenomenological MSSM (pMSSM) [5] scenarios, which have a more diverse spectrum of characteristics than the cMSSM. We identify some of the regions in the pMSSM parameter space where the current search strategy is insensitive.
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 neutralinõ χ 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" [6]. The model points presented in [6] 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 [6].

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 [7] 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 largest cross sections. To get as close as possible to the ATLAS analysis we use DELPHES 1.9 [8] 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 [9]. The object reconstruction is done by DELPHES, which uses the same anti-k T jet algorithm [10] as ATLAS. Also included in the reconstruction are isolation criteria for electrons and muons. We do not emulate pile-up events. Reconstructed events are analysed with the same event selections as used by the 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. 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 [11,12] from PROSPINO2.1 [13,14] 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.  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 .  Table 3. The efficiency of our setup is found to be in agreement with the ATLAS efficiency[15] 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. 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 signal region C − E and for the 4 and more jet channels we observe better agreement at low m 1/2 and slightly worse agreement at m 0 > 1000 GeV and m 1/2 > 400 GeV. Here our DELPHES setup underestimates the efficiency by up to 50−70%. The increased differences at larger jet multiplicities might be caused by the cummulative effects of the the ATLAS and DELPHES jet response. In view of the mostly smaller efficiencies of DELPHES compared to ATLAS, our study can be regarded as conservative.

pMSSM random points
The pMSSM points are taken from "Supersymmetry Without Prejudice" [6] (related work [16,17]). All details can be found in these references. 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. 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. Several experimental and theoretical constraints [18] are applied on the generated points, i.e. the current dark matter density and constraints from LEP and Tevatron data.
Additionally 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 analysed 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".      gluino M gluino . The SUSY points which are excluded by ATLAS are shown as green points, 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 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 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 3 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 [19,20]. 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 4 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 5 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 non-excluded models. A comprehensive study yields as the most significant feature a large average value of missing transverse momentum. Figure 6 shows the ratio f of the missing transverse momentum over the effective mass as a function of the effective mass. The not-excluded 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  7, also at m eff < 600 GeV. The non-excluded points have jet multiplicities between 2 − 7. 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 [21]. 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 8 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 87% of the model points are excluded. Again around one quarter of the not excluded model points have an average lepton number exceeding one. These points cannot be excluded because of the lepton veto.

Models from a logarithmic prior in the SUSY mass scale
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 9 shows the total cross section for squark and gluino production processes as a function of the SUSY mass scale M SUSY . All not-excluded 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. Figure 9. 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.
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. 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 87% 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 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.