Experimental Status of Supersymmetry after the LHC Run-I

Experimental Status of Supersymmetry after the LHC Run-I

Christian Autermann auterman@cern.ch I. Phys. Inst. B, RWTH Aachen University, Germany
Abstract

The ATLAS and CMS experiments at the Large Hadron Collider (LHC) at CERN have searched for signals of new physics, in particular for supersymmetry. The data collected until 2012 at center-of-mass energies of  and  TeV and integrated luminosities of  fb and  fb, respectively, agree with the expectation from standard model processes. Constraints on supersymmetry have been calculated and interpreted in different models. Limits on supersymmetry particle masses at the TeV scale have been derived and interpreted generally in the context of simplified model spectra. The constrained minimal supersymmetric standard model is disfavored by the experimental results. Natural supersymmetry scenarios with low supersymmetry particle masses remain possible in multiple regions, for example in those with compressed spectra, that are difficult to access experimentally. The upgraded LHC operating at  TeV is gaining sensitivity to the remaining unexplored SUSY parameter space.

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http://dx.doi.org/10.1016/j.ppnp.2016.06.001
0146-6410/© 2016 Elsevier B.V. All rights reserved.
Published in Progress in Particle and Nuclear Physics 90 (2016) 125-155.
Contents

1 Introduction

A major motivation for the largest experiment ever built, the Large Hadron Collider (LHC) at CERN, is the search for new physics beyond the standard model. In particular after the standard model (SM) Higgs boson has been discovered Aad:2012tfa (); Chatrchyan:2012xdj (), the experiments focus on searches for new physics which is expected to explain some of the open questions of the standard model, like the so-called gauge hierarchy problem or the nature of the dark matter in the universe. While the standard model is a remarkably successful theory, it has multiple free parameters with values constrained only by experimental observations. A grand unified theory (GUT) could reduce the number of free parameters by virtue of a larger symmetry.

In this article the experimental results of searches for supersymmetry (SUSY) at the LHC with the ATLAS and the CMS experiments are discussed. Supersymmetry is one of the most popular theories for physics beyond the standard model, and can solve some of the open questions. The implications for the excluded SUSY mass-ranges and the still allowed SUSY phase space regions are reviewed. The experimental methods are summarized, focusing on the published results with the dataset collected until 2012 at a center-of-mass energy of  TeV, corresponding to an integrated luminosity of about  fb per experiment. During the writing of this article the first results using data recorded at  TeV become available.

Supersymmetry Ramond (); Ramond:1971kx (); Golfand (); Volkov (); Wess:1974tw (); Freedman:1976xh (); Deser:1976eh (); Ferrara:1976fu (); Fayet (); Kane () is a space-time symmetry developed since the 1970s, relating fermions and bosons. SUSY multiplets contain particles differing in spin by , but having otherwise the same properties, as for example the Yukawa coupling to the Higgs field. The masses of the superpartners differ, because SUSY is a broken symmetry. The minimal supersymmetric standard model (MSSM) PrimerMartin (); Feng:2009te () contains chiral supermultiplets, e.g. a spin- fermion and two scalar bosons. The fermion has two spin helicity states, therefore two real scalar bosons have the same number of degrees of freedom. Other vector supermultiplets contain spin- vector bosons and spin- fermions, both having two helicity states. In extended supersymmetry models the supermultiplets are enlarged. These extended theories are not considered in the following interpretations of the experimental results.

1.1 The particle content of supersymmetry

The MSSM is minimal with respect to the field content by which the standard model is extended. The particle content in the MSSM more than doubles the number of SM particles. No known particle of the standard model can be the superpartner of another SM particle, and in contrast to the standard model two electroweak Higgs doublets are necessary to keep the theory free of anomalies and to generate the masses of up-type and down-type fermions. In the standard model the masses are generated by Yukawa couplings to the Higgs field and , but complex-conjugate fields are not allowed in the superpotential. Therefore, at least two Higgs doublets and are required in supersymmetric theories, that have together eight degrees of freedom. When the and bosons have acquired mass, the remaining five degrees of freedom generate the spin- Higgs bosons , , , and .

The Higgs bosons and all other particles of the standard model get supersymmetric partner “sparticles”. The sparticle names refer to the SM partner with prefix “s” for bosonic superpartners and suffix “ino” for fermionic superpartners. The supersymmetric particle content is summarized in Tab. 1.

Gauge eigenstates Spin Mass eigenstates
bino, wino, higgsinos neutralinos
wino, higgsinos charginos
gluinos no mixing
selectron, smuon, stau sleptons
sneutrinos sleptons or sneutrinos
sup, scharm, stop squarks
sdown, sstrange, sbottom
Table 1: Supersymmetric partner particles content in the minimal supersymmetric standard model

The superpartner gauge eigenstates of each line can mix, i.e. the mass eigenstates are linear combinations of the gauge eigenstates. The neutral gauginos , i.e. the SUSY partners of the standard model U(1) and the neutral SU(2) gauge bosons respectively, and the neutral higgsinos mix to form four neutralinos , where the mass increases with respect to the lower index. Similarly, the charginos are mixings of the charged gauge eigenstates and the charged higgsinos. The gluinos do not mix, and for the sleptons and quarks the mixing of the first and second generation sparticles is usually assumed to be small. The so-called left- and right-handed third generation squarks, e.g. where the name refers to the chirality of the standard model spin- partner, mix to form two mass-eigenstates and , and similarly for the sbottom and the stau .

If supersymmetry is imposed as a local symmetry then gravity is naturally included. This constitutes another theoretical motivation for SUSY. In this case, the MSSM can contain the spin- graviton and its supersymmetric partner the spin- gravitino . The graviton is massless and the gravitational coupling is suppressed by the Planck mass.

1.2 The hierarchy problem and the SUSY particle mass scale

Supersymmetry solves the hierarchy problem associated with the higher order corrections to the Higgs mass-squared parameter . The spin- Higgs boson receives quadratically divergent higher-order quantum corrections , due to loops of every particle that couples to the Higgs field, e.g. for a scalar with mass

(1)

The cutoff scale can be as large as the Planck scale , where gravitational effects are no longer negligible. The large difference to the electroweak scale is referred to as the hierarchy problem Barbieri198863 (). This problem does not arise in supersymmetric theories, because supersymmetry is introduced as a new symmetry between bosons and fermions. The quadratically divergent corrections to the Higgs mass of any supersymmetric multiplet cancel Witten1981513 (); Dimopoulos1981150 ().

Supersymmetry is broken at low energy scales, allowing the masses of the supersymmetric partners to avoid current experimental observations. Soft SUSY breaking mass terms maintain the approximate cancelation of the Higgs mass correction terms. Various supersymmetric models are known where supersymmetry is broken spontaneously. The models used to interpret the experimental results extend the minimal supersymmetric standard model by gravity-mediated breaking terms, referred to as minimal supergravity models (mSUGRA) or as constrained-MSSM (cMSSM) PhysRevLett.49.970 (); Barbieri (); Hall (); NILLES19841 (). In a second type of models the supersymmetry is broken by gauge-mediated breaking terms (GMSB) GGMa (); GGMd2 (); GGMd3 (); GGMd4 (); GGMd5 (); GGMd1 (); GGMd (). Anomaly-mediated supersymmetry breaking Randall:1998uk (); Giudice:1998xp () is another breaking scenario, which will not be considered in the following.

The mass scale of the SUSY particles is generally undetermined by the theory, but can be constrained by the following considerations. The higher-order corrections to the Higgs mass depend on the particle masses but only logarithmically on the cutoff scale and thus matter only if the differences in mass of the members of a supermultiplet become too large. This is in particular relevant for the third quark generation supermultiplet of the top with the large top-quark Yukawa couplings at first-loop order, and for gluinos at second-loop order. Heavy third generation squarks and gluinos have large contributions to . The non-observation of the Higgs boson near the electroweak scale at LEP was referred to as little hierarchy problem Barbieri:2000gf (), as a large Higgs mass requires large radiative corrections and thus large stop masses between  GeV and  TeV Papucci:2011wy () in the MSSM. The supersymmetry naturalness requirement is illustrated Papucci:2011wy () by the tree-level relation in the MSSM

(2)

with the -boson mass , where the -term is directly linked to the higgsino masses, and to the gluino and stop masses as discussed above. A natural supersymmetry spectrum without fine-tuning requires light stop, gluino, and higgsino masses. A natural supersymmetry scenario should be accessible at the LHC and motivates in particular searches for low-mass superpartners of the top-quark.

1.3 Supersymmetry models and simplified scenarios

Another motivation for supersymmetry is, that it can deliver a candidate particle for the dark matter, if the -parity FARRAR1978575 () is conserved. The baryon number and lepton number that are conserved in the SM become in supersymmetry the quantum number -parity, which is defined as where is the spin quantum number. equals for standard model and for SUSY particles. -parity violating (RPV) trilinear and bilinear terms exists in the superpotential Rparity ():

(3)

where and are the lepton and quark SU(2) doublet superfields, , , the singlet superfields, and are the family indices. The gauge indices are not shown. The coupling strengths are given by the Yukawa constants , , and . The bilinear term allows the mixing of the lepton and Higgs superfields. RPV implies lepton- or baryon number violation and sufficiently large couplings allow the decay of the lightest supersymmetric particle, the LSP. If -parity is conserved because all RPV couplings vanish or at least are sufficiently small, then supersymmetric particles are only produced in pairs, and the LSP is stable. If the RPV-couplings are so small or zero, that the LSP-lifetime is large compared to the age of the universe, then the LSP is a particle candidate for dark matter. The dark matter candidate has to be a massive, only weakly interacting particle, like the lightest neutralino . In the following, RPV couplings are assumed to be zero.

The minimal supergravity model or the cMSSM is a MSSM scenario with gravity-mediated SUSY breaking determined by five parameters , , , , and the sign of . The universal scalar mass determines the mass of the scalar sparticles, i.e. the squarks and the sleptons masses at the GUT scale  GeV. The common mass of the gauginos and higgsinos at is . is the universal trilinear coupling defined at and is the ratio of the vacuum expectation values of the two Higgs doublets. The absolute value of the higgsino mass parameter is determined by the electroweak symmetry breaking, leaving only the sign of as discrete free cMSSM parameter. , , and the sign of have generally only a small influence on the experimentally observables and are choosen such, that the predicted Higgs mass is consistent with the measurement of approximately  GeV. The and parameters determine the masses and branching ratios of the supersymmetric particles. The relation of the supersymmetric particles masses are therefore constrained by effectively only two degrees of freedom. On one hand this allows for concise comparisons of experimental results in the and parameter plane, on the other hand many different mass spectra and branching ratios viable in other SUSY models are not examined. Past  TeV searches for supersymmetry often used the cMSSM for interpretation of the experimental results. Recently, less constrained models like the phenomenological minimal supersymmetric standard model (pMSSM) Djouadi:1998di (); CMS-PAS-SUS-2015-10 (); ATLAS-SUS-2014-08 () gained attention. The pMSSM is more difficult to scrutinize and the results are harder to display, because of the much larger number of free parameters. The theoretical viable phase space of the cMSSM is challenged Fittino-2015 (); Buchmueller:2013rsa () by recent experimental results discussed in the following.

Models of gauge mediated supersymmetry breaking can guarantee flavor universality for the MSSM sfermion masses avoiding the so-called SUSY flavor-problem Dimopoulos:1995ju (). The lightest supersymmetric particle is here the gravitino . The is produced in decays of the next-to-lightest SUSY particle (NLSP), which in the studied GMSB scenarios is assumed to be the neutralino , together with a standard model boson . Prompt decays of the NLSP into the are assumed in all GMSB scenarios discussed in the following. Non-prompt decays would lead to displaced vertices or heavy stable charged particles, depending on the nature of the NLSP. The coupling to the gravitino is significantly weaker compared to other particles and inverse proportional to its mass. The gravitino mass is negligible in the studied scenarios, typically significantly smaller than  GeV. Depending on their mass, gravitinos are dark matter candidate particles Steffen:2006hw (); MOROI1993289 (). The direct decay occurs only if the chargino and neutralino masses are almost mass-degenerate and the decay is suppressed. The GMSB final state topology depends strongly on the nature of the NLSP and therefore on the neutralino mixing. The SUSY model of general gauge mediation (GGM) GGMe (); GGMf (); Ruderman:2011vv (); Kats:2011qh (); Kats:2012ym () is used in the following to interpret the experimental results of GMSB inspired searches.

In order to characterize the wide range of possible signal scenarios in terms of masses of supersymmetric particles, production channels, and decay modes, i.e. in terms of directly experimentally accessible parameters, so-called simplified model spectra (SMS) ArkaniHamed:2007fw (); Alwall:2008ag (); Alves:2011wf () have been developed. The current experimental results at  TeV are commonly interpreted using these simplified scenarios SMS_ATLAS (); SMS_CMS (). The SMS are effective-Lagrangian descriptions of single processes involving just a small number of new particles, to which the analyses have direct sensitivity. These simplified models feature a clear final state topology: All supersymmetry particles which do not directly enter the production and decay chain are effectively decoupled and at high mass scales, in sharp contrast to full models of supersymmetry, that have characteristic complex compositions of processes and final states. The relation of the relevant SUSY masses for the studied process can be chosen freely, which overcomes limitations of full models with few free parameters, like the constrained-MSSM. While the decomposition of a supersymmetry model scenario into different SMS is easily possible, interpreting a combination of different SMS results in any SUSY model is more difficult SModelS (). For example, analyses strongly dependent on data-driven background estimation methods can be subject to signal contamination in the control regions, which is usually irrelevant for an individual simplified model scenarios of a single process, but can significantly lower the sensitivity to full model scenarios of many supersymmetry processes.

No excess in the data recorded by ATLAS or CMS incompatible with statistical fluctuations is observed. The derived limits obtained by searches for supersymmetry are summarized in this article with the help of simplified models. Exclusion contours derived by different analyses and sometimes by different model assumptions are compared in the summary figures, if the free parameters of the studied models are compatible. The shown analyses and results illustrate the general sensitivity to the most relevant SUSY parameter space. More information and interpretations are available in the quoted references. Physics beyond the standard model scenarios other than supersymmetry are discussed for example in Golling:2016thc ().

Organization of this article

The article is organized as follows: The LHC experiments ATLAS and CMS and different experimental aspects relevant for searches for supersymmetry are introduced in section 2. The spectrum of the various searches for supersymmetry are discussed, from very inclusive to very specific search strategies. In section 3 inclusive search strategies in the all-hadronic final state and with leptons are discussed, together with elementary standard procedures to model the SM background using the data. The results are discussed with respect to the simplified pair production of gluinos and light-flavour squarks and in the constrained MSSM. In section 4 gluino-mediated third generation squark production is discussed, while the direct production of third generation squarks is covered in section 5. Electroweak production of supersymmetric particles is presented in section 6, and gauge-mediated supersymmetry breaking scenarios are presented in section 7. Resonances and signals with kinematic edges are discussed in section 8.1, before the experimental status of the searches for supersymmetry is summarized in the conclusion in section 9.

2 Experimental methods

The analysis strategies differ in the way the standard model background estimation is approached and in the choice of the kinematic variables used to enrich the signal-to-background ratio for the statistical interpretation. In the following the experiments are introduced and then different experimental methods are discussed. Data-driven background estimation techniques will be summarized, which are necessary for the precise estimation of the standard model background.

2.1 The ATLAS and CMS experiments at the LHC

ATLAS ATLAS () and CMS CMS () are multipurpose experiments located at the proton-proton collider LHC. The LHC delivered collision data at a center-of-mass energy of up to  TeV, corresponding to about  fb of integrated luminosity for each of the experiments. ATLAS and CMS have comparable sensitivity and discovery potential, though the detector designs differ in detail.

The ATLAS detector includes a silicon pixel detector, a silicon microstrip detector, and a straw-tube tracker that can also provide transition radiation measurements for electron identification. The inner tracking detectors are enclosed in a superconducting solenoid producing a magnetic field of  T, that allows for precise tracking up to pseudo-rapidities . A high-granularity liquid-argon (LAr) sampling calorimeter with lead absorber is used as electromagnetic calorimeter, hadronic showers are measured by an iron/scintillator tile calorimeter and by a LAr calorimeter in the end-caps. The very large muon spectrometer in the magnetic field, provided by three air-core toroidal magnets, consists of a set of fast trigger chambers and high resolution muon chambers for the precise measurement of muon momenta, making use of the large leverage arm, due to the size of the ATLAS detector.

CMS in contrast is a rather “compact” detector but much heavier compared to ATLAS, because of the iron return yoke for the magnetic field, which is produced by a single solenoid magnet. The CMS muon system consisting of high resolution muon drift chambers and fast responsive resistive plate chambers used for triggering is integrated in the iron yoke. The superconducting solenoid magnet delivers a magnetic field of  T enclosing the calorimeter and the tracking system, consisting out of a large silicon strip and the innermost silicon pixel detector. The inner part of the calorimeter system is a lead-tungstate crystal electromagnetic calorimeter, the outer part is a brass-scintillator sampling calorimeter. The inferior energy resolution of the stand-alone CMS hadronic calorimeter for hadronic jets compared to ATLAS is compensated by a particle-flow-algorithm CMS-PAS-PFT-09-001 (), which aims at the best possible use of all detector components, in order to reconstruct the momenta of all identified particles.

2.2 Kinematic variables for signal selection and background rejection

The classic kinematic variable to search for signals of supersymmetry is the missing transverse energy, defined as the absolute value of the momentum imbalance of all reconstructed objects in the event:

(4)

The offers a good separation power between signal and background events, as in supersymmetry the lightest stable particles, e.g. the or the , can carry away a large amount of energy. The energy of the only electroweakly interacting LSP cannot be detected, resulting in missing transverse energy which is typically larger than the produced in standard model background processes. An excess of events in the high energy tail of a kinematic variable like is a signal expected for supersymmetry, in particular for models that contain a dark matter candidate particle.

Though is a very signal sensitive variable, i.e. the variable is able to separate signal and standard model backgrounds with good power, other kinematic variables have been studied and used in analyses in addition to, or instead of . The precise prediction of the standard model background in the high energy tail of the search variable is of crucial importance for a good signal sensitivity of the search. This is particularly difficult for , because the variable is directly affected by all other objects in the event, as illustrated by Eq. (4). is sensitive to multiple effects like detector noise, multiple -interactions (pile-up), energy depositions not clustered in jets, and the energy resolution of all reconstructed objects most relevantly of jets. The , , Razor, and variables introduced in the following are less sensitive to these effects, but maintain signal sensitivity and signal to background discrimination power, by exploiting different properties of the signal or the standard model background.

The variable is defined as the scalar sum of the transverse momentum of all jets or leptons in the event and :

(5)

In the all-hadronic state is equivalent to the variable used in other experiments, defined as . is the scalar sum of hadronic energy clustered in jets exceeding a transverse momentum threshold, typically of the order of  GeV. The is correlated with the overall mass scale of the hard scattering. The / ratio is useful to remove events, where the is largely due to poorly measured jets.

The kinematic variable aims at the mass reconstruction of pair-produced particles that each decay into visible and one invisible particle. The is defined mt2_lester (); mt2_barr () analogously to the transverse mass , which is used for example for -mass measurements in events at hadron colliders:

(6)

The corresponds in events to the not reconstructed transverse energy of the neutrino. Searches for supersymmetry with the variable assume, that the signal events are due to the pair-production of two SUSY particles of the same mass (e.g. ) and each undergo cascade decays into at least one or more jets and the LSP (e.g. a neutralino ), as shown in Fig. 1. The visible objects, such as jets, are clustered into two pseudo-jets using hemisphere algorithms hemisphere (). is defined as the larger of the two transverse masses and , where the transverse mass is calculated analog to Eq. (6), where the pseudo-jet replaces the lepton and the corresponding transverse momentum of replaces .

(7)

The momenta of the invisible particles and are inaccessible, only the sum of is constrained by . The ambiguity is resolved by minimizing over all possible momenta of the undetected particles that fulfill the constraint.

The variable alphat_randall () aims at the best possible suppression of QCD multijet events, that are characterized by non-genuine . The in the QCD multijet background events is created by jet-resolution effects or non-prompt neutrino production in the hadronization, but not by undetectable particles created in the hard interaction. In a dijet event the dimensionless variable is defined as

(8)

where is the transverse energy of the less energetic jet and is the transverse mass of the dijet system defined analog to Eq. (6), where the transverse momentum vectors of both jets replace the lepton and the neutrino i.e. the . In contrast to the missing transverse energy, is less sensitive to jet energy mismeasurements and therefore to beam conditions and the detector performance. In events with genuine as expected for the SUSY signal the variable has a long tail with values larger than . For QCD dijet events is constrained to values ; the two jets in a perfectly measured event are balanced in and thus and . Any jet energy mismeasurement reduces , while the jet direction in the transverse plane is not and is only minimally affected, leading to for QCD dijet events. Multijet events are combined into a pseudo-dijet system using hemisphere algorithms.

The “Razor” Razor () variables and are motivated by the pair production of two heavy particles such as squarks or gluinos, each decaying to an undetected particle and jets. Multiple jets in each event are combined by hemisphere algorithms into two pseudo-jets. The razor variables are defined as:

(9)
(10)
(11)

quantifies the transverse momentum imbalance of the event, while is proportional to the mass-scale of the produced particles in the event. The shape of the standard model backgrounds can be estimated in data sideband regions of and the dimensionless variable , where the potential signal contribution is negligible. The name “Razor” refers to the modeling of the SM background, which efficiently enables the separation of signal and the standard model background, and might also be inspired by the first set of  TeV SUSY searches at CMS nicknamed “reference analyses”, abbreviated e.g. Ra1.

2.3 Background estimation techniques using data events

The key to searches for supersymmetry is the precise understanding of the various standard model background contributions, especially in the high energy tail of distributions like and at high jet multiplicities. An excess over the standard model expectation in the observed data would indicate a signal of “New Physics”, such as supersymmetry.

The tails of signal-sensitive distributions like are hard to simulate by Monte Carlo methods for the known standard model backgrounds and therefore carry large or even unknown uncertainties. Rare or unknown detector and reconstruction effects must be modeled sufficiently correct, like detector responses and noise, efficiencies and resolutions. The common way to avoid or at least reduce the influence of these effects and the corresponding systematic uncertainties, is to make use of the data itself. Data sideband regions, similarly affected by detector and reconstruction effects but depleted of signal can, appropriately weighted, be used instead of simulated samples, such that the systematic effects cancel out. Depending on the variable separating the signal and control regions, the weights for the control events can also be derived from the data: This is usually possible if the variable is uncorrelated to the kinematics of the event, as for example to a certain extent the particle identification criteria like lepton isolation or the -tag probability. If a variable correlated with the kinematics is used to separate the regions, like the jet multiplicity or the hadronic activity in the event, MC simulations are usually required to derive the normalization of the control events. Depending on the details of the reweighting and the available MC statistics, this is comparable to using Monte Carlo simulation for the modeling of a background in the signal region, that was “tuned” by reweighting or validating it in a data sideband region. Exemplary data-driven background estimation methods for the all-hadronic final state are discussed in the following in more detail.

The “rebalance + smear” method to estimate the QCD multijet background

The QCD multijet background in the all-hadronic final state is particularly difficult to model with Monte Carlo simulations because of the large production cross section and the multiple but very rare effects that lead to in the reconstructed events. Even though multijet events have no intrinsic , jet energy mismeasurements and misreconstructions summarized as jet energy resolution can lead to a sizable missing transverse energy tail. Typically, high-statistics data sideband regions are employed to model the QCD multijet background. These sidebands can be obtained by loosening a selection such as the requirement, a lepton identification, or for example a b-tagging qualifier. Alternatively, jet-resolution measurements derived from +jets and dijets events can be used to create a high-statistics generated “Pseudo-Monte Carlo” QCD sample in a data-driven fashion: In a first step data events are selected similar to the signal selection criteria, except for the -cut. The reconstructed jets in every event are then varied in energy according to the jet-resolution probability density function (PDF), such that the in each event vanishes. In a second step, the jets are smeared again according to random numbers drawn from the jet resolution PDFs. Each seed event is used of the order of times with different random numbers to minimize the statistical uncertainty of the sample. Signal contamination as well as contamination from other standard model backgrounds with genuine to the sample of proxy events is negligible because of the large QCD cross section and because the first rebalancing step transforms the contaminating events into QCD-like events. This “rebalance + smear”-method predicts the QCD multijet and other fully hadronic standard model backgrounds without genuine with a good precision.

The “lost-lepton” and the “embedding” methods to estimate the top and backgrounds

An important background to the hadronic final state can arise from standard model backgrounds with single leptons, i.e. electrons or muons including or from leptonic tau decays. The background composition is dominated by +jets and events, where the lepton is not identified and the event therefore passes the signal selection including the lepton-veto cut. This happens if the lepton is close to a jet or not-isolated, not properly reconstructed, or out of the geometrical acceptance region. These “lost-lepton” backgrounds are modeled using a data-control sample with exactly one isolated muon. The control sample can be enlarged using isolated electrons in addition to reduce statistical uncertainties at the price of larger systematics. To limit possible signal contamination to the control sample that could lead to an over-prediction, the control events are required to have small , typically less than  GeV consistent with from SM +jets or backgrounds. The control events are weighted according to the lepton (in-)efficiencies and kinematic acceptance factors, which can be obtained from the MC simulation and validated in data on the peak with a “tag & probe” method. The tag & probe method utilizes that events can be selected in the data with high purity (“tag”), without applying a specific selection, for which the efficiency should be calculated, on one of the leptons (the “probe”). The relative precision of the “lost-lepton” background estimation is of the order of and up to in large jet multiplicity signal regions.

If the background contains a hadronically decaying tau lepton the event also has a large probability to pass the lepton veto. The same data control sample with one isolated muon is used for the prediction of hadronically decaying taus from SM processes like +jets and . The “embedding method” corrects the control events for the muon efficiencies and replaces the muon in each event by a simulated jet, whose value is randomly sampled from an response PDF. For each seed event the tau-jet response function is sampled of the order of one hundred times. , , and the jet multiplicity are recalculated for all events.

For supersymmetry searches in the final state with one isolated lepton the lost-lepton and hadronic-tau backgrounds are equally relevant, but here the events originate from the dilepton standard model processes dominated by , , and diboson production. Accordingly, a dilepton data control sample can be used to model the background.

The “” estimation method

An irreducible background for search analyses in the all-hadronic final state originates from +jets. Three different data control regions can be used to estimate the background: events offer a straightforward possibility with small systematics. However, since the branching ratio of the to neutrinos is roughly three times larger than to electrons and muons, the prediction suffers from large statistical uncertainties especially in the high energy tails of the search variables, where the signal is expected. Better statistical precision is expected from events, which can be used as an alternative control sample. But in this case a clean selection without contamination is more challenging, because the background from other standard model processes or possible signal events is larger than for dileptons in the narrow invariant mass window around the mass. Commonly used is therefore a +jets control sample exploiting the similarity to +jets, which is given at high boson transverse momenta. The total uncertainties are dominated by the theoretical uncertainties on the +jets/+jets cross section ratio. The uncertainties can be constraint using data. The relative prediction precision is of the order of at low and at high jet multiplicities.

2.4 Limit calculation

Upper limits on the amount of signal events, that could be present in the observed data under the assumption that the data are statistically distributed according to the standard model background-only expectation, are derived using the CLs method Junk (); Read (). The CLs method, often called modified frequentist approach, is designed to avoid the exclusion of possible signals, to which the analysis is not really sensitive to. A statistical under-fluctuation in the data compared to the background-only expectation could lead to an exclusion of zero or even a negative amount of signal events at a certain confidence level. To avoid this unwanted behavior, the is defined as

(12)

The is the probability to observe a test statistic value at least as signal-like as the one observed under the signal+background test hypothesis for a certain signal expectation . is analogously the probability to observe under the background-only null-hypothesis . For the test statistics typically a likelihood-ratio is chosen, which allows for the most efficient separation of both hypotheses NeymanPearson (). Ignoring systematic uncertainties, the test statistic can be defined as the ratio of two Poisson probability functions

(13)

where the measurement can be the observed data or the outcome of a pseudo-experiment. The test statistics of multiple exclusive signal search regions can be combined to a single function, as likelihoods are multiplicative. Different ways to incorporate systematic uncertainty nuisance parameters are used by the discussed analyses. The standard limit calculation procedure procedure is defined by the ATLAS and CMS Higgs boson search combination CMS-NOTE-2011-005 ().

A signal of at least events is excluded at a confidence level (CL) of , if the . The resulting limits and exclusion contours presented in the following have been derived at  CL. The expected limit is defined by the quantile of calculated limits, where the observed data event yield is replaced repeatedly by random pseudo-data event yields distributed according to the background-only expectation.

For a single-channel counting experiment the limit is generally independent of any signal hypothesis and can be translated into a cross section limit using the signal acceptance and the data luminosity, i.e. a limit with respect to a signal cross section expectation for a specific point of a given supersymmetry model, defined by a set of model parameters. Multi-channel counting experiments implicitly depend on the relative signal acceptance in the different search bins and depend therefore on the signal model. Exclusion contours in a plane of the supersymmetry model parameters are derived, by comparing the calculated limits to the signal expectations per point. In this article, only limits with respect to the supersymmetric particle masses in specific models or signal scenarios are discussed. The cross section limits are not shown, but can be found in the quoted references.

3 Inclusive searches for strong production of gluinos and first or second generation squarks

Generally, inclusive searches for supersymmetry have the largest sensitivity in the studied supersymmetric models and with respect to the wide range of supersymmetric particle masses and cross sections Beenakker:1996ch (); Kramer:2012bx (). However, more specialized searches extend the reach significantly in relevant corners of the phase space, as will be discussed in the following sections. Inclusive searches make few model assumptions, typically only missing transverse energy or a similar correlated quantity is required in the selected events.

The requirement, or any other similar kinematic property exploiting the non-observation of two LSPs with high energy, implicitly constrains the analysis sensitivity to R-parity conserving models with a stable and electrically neutral, thus only weakly interacting lightest supersymmetric particle. However, also -parity violating SUSY scenarios can be probed, that lead either through neutrinos from non-zero or couplings to in the final state, or lead to because the RPV couplings are sufficiently small so that the LSP decays unobserved outside the detector. Squarks and gluinos are generally produced at higher energy scales compared to standard model processes because of the larger particle masses due to the existing limits Feng:2009te (). This typically leads to either long decay chains with many SM particles as for example for production as shown in Fig. 1(a) or to few high energy particles and therefore also large as for production as shown in Fig. 1(b). Because of the large hadronic branching ratio, the final state of strongly-produced supersymmetry events consists generally of many jets leading to good sensitivities for searches in the all-hadronic final state, which comes at the price of a more difficult to estimate standard model background.

(a)
(b)
Figure 1: Effective Feynman diagrams for the simplified pair production of gluinos (a) and first- or second generation squarks (b).

3.1 All-hadronic final state

ATLAS ATLAS-SUS-2013-02 (); ATLAS-SUS-2013-04 () as well as CMS CMS-SUS-2013-12 () have searched for SUSY in the fully hadronic final state with the classical variable, no leptons, and at least two jets.

The search CMS-SUS-2013-12 () at CMS relies on the “rebalance + smear”-method to predict the QCD multijet background in the tails. A precision of depending on the signal region can be achieved. The method has been validated in QCD enriched data control regions as well as on Monte Carlo simulation. The backgrounds from and +jets, where at least one lepton fails identification are estimated using the “lost lepton” method. The method is validated with Monte Carlo simulation and the precision of the prediction is typically , depending on the jet multiplicity. The “embedding method” is used to estimate the contribution from hadronically decaying taus. For the irreducible process +jets events are used to model the background. The , , and the jet multiplicity variables are used to define exclusive signal regions, in order to optimize the sensitivity to the different regions of the signal parameter space for gluino or squark pair or associated production. High jet multiplicity bins are for example more sensitive to production, while processes produce a smaller particle multiplicity, but more . The individual counting experiments per signal region are combined into one test statistic. The characteristic feature of the analysis is the careful estimation of all standard model backgrounds, using only data-driven methods that are validated in data control regions as well as with Monte Carlo simulation.

The and jets ATLAS analysis ATLAS-SUS-2013-02 () follows a slightly different strategy compared to the previously discussed search, where the statistically exclusive signal regions were combined in a final likelihood fit. Here, the signal regions are defined inclusively, i.e. containing at least 2,3,4,5, or 6 jets and are further divided into inclusive loose, medium, tight, or -candidate selections according to the variables ,, , and /. Each region is optimized to target a specific scenario depending on the production scenario and the particles masses m(), m(). The standard model backgrounds for each signal region are estimated from data sideband regions scaled by transfer factors estimated from Monte Carlo simulation except for the QCD multijet background. The QCD background contribution to the signal regions is small, but the total uncertainties on the prediction are still relevant. The QCD control region is obtained by inverting the cut, which depends on the signal region, and the requirement on or /. The transfer factors are determined by a data-driven technique applying a jet energy resolution function to estimate the impact of a jet mismeasurement. The systematic uncertainties of the QCD background prediction are dominated by the uncertainties on the estimated transfer factors and are smaller than for all signal regions. The total uncertainty of the combined background estimation is between and . The results from the signal regions are combined, by using the result from the signal region with the most stringent expected sensitivity to set a limit on a given signal parameter point.

The ATLAS search using 7-10 jets ATLAS-SUS-2013-04 () and up to two -tags aims at longer supersymmetry decay chains and complements the inclusive analysis with jets ATLAS-SUS-2013-02 (). The analysis targets gluino mediated squark production and has also good sensitivity to gluino mediated stop production as discussed in the section 4 and to gluino mediated chargino or neutralino production as discussed in the following section 3.2, that all lead to many jets in the final state. The sensitivity of the analysis is enhanced by the sum of masses of large radius jets in the event. These large radius jets are clustered by an anti- algorithm with a distance parameter from the four-momenta of anti- jets with  GeV. The jet multiplicity, the -tagged jet multiplicity, , as well as the variables are used to define  partially overlapping signal regions. For the QCD multijet background estimation the observation that the resolution is proportional to independently of the jet multiplicity is exploited: The shape is extracted from data sidebands in the jet multiplicity, for each bin of -tag multiplicity as the shape depends on the number of -tags in the event. Soft unclustered energy in the event distorts the proportionality and leads to the largest systematic uncertainty on the QCD background estimation.

SUSY searches relying on the kinematic variables , , and the Razor variable and have been pursued. The general advantage of these analyses is the reduced dependency on pileup, unclustered energy, and other detector effects that influence the in an event. Especially QCD multijet background events can acquire through these effects and are difficult to estimate. The alternative kinematic variables therefore offer a better handle to reduce or to estimate QCD multijet events. Disadvantages arise from the more complicated definition and used assumptions compared to the variable which is clearly defined for all signals and standard model backgrounds.

The variable explored at ATLAS and CMS CMS-SUS-2013-19 (); ATLAS-SUS-2014-07 () allows to control the QCD multijet contribution, which is small at large values of . The amount of QCD background is further reduced by requiring , where is the minimal azimuthal angle between the and any of the four leading jets in , again exploiting the origin of from jet energy mismeasurements. The surviving QCD background is estimated from the control region, scaled according to a transfer factor depending on . Two analysis strategies are pursued for the all-hadronic final state at CMS CMS-SUS-2013-19 (): An inclusive search for supersymmetry spans the signal region by the variable, the jet and the -tagged jet multiplicity, and by . The second approach makes use of and the invariant dijet mass of -tagged jets aiming at the reconstruction of a light Higgs boson produced in supersymmetry cascade decays.

The search for supersymmetry CMS-SUS-2012-28 () uses a different kinematic variable to identify possible signal events and to efficiently suppress the QCD multijet background. QCD events do not have genuine , so that the measured is mostly due to jet resolution effects, resulting in for QCD multijet. Detector effects do not significantly influence in an event, so that the QCD background can be efficiently removed by a selection requirement. The signal region is further categorized by the , the jet multiplicity, and the -tagged jet multiplicity to maximize the analysis sensitivity to wide range of possible signals of supersymmetry like , , and production and in particular also those with third generation squarks, that lead to -jets. The analysis determines the sum of the remaining standard model background from QCD multijet, , , and processes by a binned simultaneous likelihood fit to event yields in the signal regions and in jets, jets, and jets control regions. Data collected in the first half of the  TeV data taking period corresponding to an integrated luminosity of  fb was used.

Searches for new physics relying on the shape of the “Razor” Razor () variables and have been carried out at the ATLAS ATLAS_7TEV_Razor (); ATLAS-SUS-2013-20 () and the CMS experiments CMS-SUS-2013-04 (); CMS-PAS-SUS-2014-11 (). The final state with at least one -tagged jet and with and without leptons has been analyzed at CMS using the full  TeV data set as reported in CMS-SUS-2013-04 (). The ATLAS inclusive search with at least one lepton ATLAS-SUS-2013-20 (), using also the Razor variables is discussed below in the following section 3.2.

Figure 2: Exclusion contours at  CL for the inclusive searches for strong production of supersymmetry signal events of ATLAS and CMS. Gluino pair production is shown in (a), where the gluino decay through off-shell squarks as . Squark pair production asssuming eight mass degenerate light flavor squarks is shown in (b), where the squarks decay as . The analysis labels refer to Table 2.

The inclusive searches for supersymmetry in the all-hadronic final state are interpreted in the simplified models of squark- or gluino-pair production as shown in Fig.1. For the on-shell squark-pair production case eight mass-degenerated light squarks , , , are assumed, that each decay into a quark and the neutralino LSP. The squark mass and the neutralino mass are varied for each point of the generated signal Monte Carlo simulation scan. In the case of the gluino-pair production scenario all squark masses are assumed to be decoupled at high energy scales. Each gluino undergoes an effective three-body decay into two quarks and the neutralino LSP. Again, two parameters define all experimental observables; the gluino mass and the neutralino mass. All hadronic inclusive searches follow different search and background estimation strategies with different strengths, setting the strongest limits in the and the light-flavor scenarios. The and jets analysis as well as the and analyses are expected to perform better for squark-pair production, where lower jet multiplicities but more energetic jets are produced, leading to an optimal performance of the hemisphere algorithms, compared to the jets and the analyses, that perform best for gluino-pair production with many jets in the final state. In the cMSSM this corresponds to low values of the universal scalar mass , where squark-pair production is dominant because m()m() and high values of where m()m() leading to dominant production. The resulting limits in the cMSSM are compared in the following section 3.2 to the sensitivity of the inclusive leptonic searches.

The results of the all-hadronic searches for supersymmetry ATLAS-SUS-2013-02 (); ATLAS-SUS-2013-04 (); CMS-SUS-2013-12 (); CMS-SUS-2013-19 (); CMS-SUS-2012-28 () are translated into cross section limits in the and light-flavor pair-production. Model-dependent exclusion contours, as shown in Fig. 2 for the simplified pair-production are derived, by comparing the cross section limits to the signal cross section prediction in the corresponding model. For the simplified model of gluino-pair production with gluinos masses up to  TeV and neutralino masses up to  GeV are probed. Similarly, for the simplified model of squark-pair production with squark masses up to  GeV and neutralino masses up to  GeV are probed. The squark mass limits are weaker compared to the gluino mass limits. In the diagonal region of Fig. 2, where the gluino or squark masses become almost mass-degenerate with the neutralino LSP mass, only little hadronic energy in the form of soft hadronic jets is created in the gluino or squark decays. The analyses acceptance drops, depending on the details of jet energy and multiplicity requirements. Uncertainties from initial state radiation and parton density functions for standard model background and signal Monte Carlo simulations are relevant in this region of phase space.

3.2 Inclusive searches with leptons

The additional requirement of leptons in the final state restricts the analyses to signal scenarios with longer decay chains, where leptons are created through sleptons , or through vector boson , decays, as shown in Fig. 3. Also third generation squark production discussed in the following section can lead to lepton final states through top-quark decays. Direct electroweak slepton production offers usually no competitive sensitivity on slepton or gaugino masses compared to the indirect production through gluino- or squark decays, if the gluino or a squark mass is sufficiently small, or the slepton masses are not too light Beenakker:1996ch (); Kramer:2012bx (). If the signal contains leptons, additional sensitivity compared to the inclusive all-hadronic analyses can be gained by the explicit selection of leptons. The branching fraction of neutralinos and charginos to leptons is usually smaller than to jets, but this is also true for the standard model background and a lepton in the final state simplifies the background estimation, because more possibilities for kinematically identical data sideband regions for the modeling of a background or for validation are offered.

(a)
(b)
Figure 3: Effective Feynman diagrams for gluino mediated production of gauginos leading to quarks and , bosons in the final state (a) and gluino decays through gauginos and sleptons leading to leptons and/or neutrinos in the final state (b).

Combining all-hadronic analyses and searches with leptons in the final state from the same experiment is, unfortunately, often difficult if the analyses were not designed with a combination in mind from the beginning. The reason for this is the non-trivial correlation of systematic uncertainties and most importantly the partially overlapping signal and control regions. Nevertheless, several ATLAS and CMS analyses have combined search channels and have been reinterpreted in several models of new physics beyond the standard model, e.g. ATLAS-SUS-2014-06 (); CMS-SUS-2013-04 ().

A search for supersymmetry with at least one isolated electron or muon, jets, and  ATLAS-SUS-2013-20 () has been carried out by the ATLAS experiment on a dataset of  fb. Different signal regions with optimal sensitivity to different signal scenarios have been defined: At least one low or one high lepton selection, or , offer complementary sensitivity to low and large mass splittings. Dilepton selections, , , or , cover different signal production modes and cascade decay chains. Various further criteria are applied individually in the signal regions, optimized for the different signal models. For example, small jet multiplicities are required for squark pair-production, large multiplicities for gluino production (Fig. 1). For gluino pair production dileptons are expected through decays via sleptons and sneutrinos or via intermediate gaugino decays as shown in Fig. 3. The dominant background originates from production. In the dilepton channels the SM is suppressed by applying a veto on -tagged jets. The transverse mass , defined in Eq. (6) is used in all single-lepton regions to reject the sub-dominant background from . Similarly, the invariant dilepton mass is used to reject in dilepton regions, where no on-shell -bosons are expected in the signal. The signal regions are defined orthogonal, except for the specifically designed inclusive single-lepton and low- dilepton regions. The binned variables , , , and the Razor variable , defined in Eq. (9), are used to exploit the expected signal shape in order to optimize model-dependent limits. The dominant standard model backgrounds from , +jets, and +jets are modeled by Monte Carlo simulation, which are normalized for the numerous signal regions in kinematically similar control regions, obtained e.g. by inverting the -tag requirement, the , or the selection. The normalization factors are constrained by a simultaneous fit based on the profile likelihood method to all control regions per signal region and are checked in multiple validation regions. Another non-negligible background to signal-regions with leptons originates from QCD-multijet and +jets events, where the lepton requirement is fulfilled by non-prompt leptons or misidentified jets. This “fake-lepton” background can be estimated from the data, by measuring the lepton fake-rate in events with loosely identified leptons and applying it to an appropriately weighted data control sample with the same requirements than the signal selection, except for the lepton identification. Since the fake-rate is usually orders of magnitude smaller than the lepton identification efficiency, the data-driven background estimation has small uncertainties of statistical origin due to the much larger control sample. The total uncertainties of the estimation is dominated by the sytematical uncertainty of and on the quality of the kinematic similarity of the signal and the loose-lepton control region.

A slightly different approach is used by the like-sign (LS) dilepton analysis CMS-SUS-2013-13 () at the CMS experiment. Like-sign lepton final states are very rare in the standard model, but occur naturally in supersymmetry since, for example, the two decays chains of pair produced gluinos are not correlated. The dominant SM background therefore arises from misidentified “fake leptons”, which are estimated from the data with loose lepton identification criteria. Rare standard model processes yielding like-sign dileptons like diboson production, , and , where the denotes a vector boson or , are estimated from Monte Carlo simulation. Four variables, that are able to discriminate signal against standard model backgrounds, are used to define several exclusive signal regions: , the scalar sum of hadronic transverse energy clustered in jets , the jet multiplicity, and the -tagged jet multiplicity. For each variable two sets of regions are defined; one loose selection with depleted signal contribution in order to validate the SM background description, and one with tighter requirements where exclusive signal bins are defined. The analysis is carried out with two different thresholds for the two leptons of either  GeV each, or with thresholds of  GeV for both leptons. The low- selection increases the sensitivity to SUSY models with off-shell -bosons. The threshold in this case is increased from  GeV to  GeV to ensure the full efficiency of the trigger. The high- selection is partially overlapping but has complementary sensitivity to scenarios with on-shell bosons. In addition to the results interpreted in the signal scenarios discussed in this section, the analysis uses the higher -tag multiplicity regions and a low signal region to set limits on third generation squark production and -parity violation models, respectively.

Figure 4: Exclusion contours at  CL of the inclusive searches with leptons for strong production of supersymmetry signal events at ATLAS and CMS. Result for production is shown in (a), for different gluino decay topologies. The results for production is shown in (b), where either light-flavor squarks or single or squarks are assumed to be pair produced. The different squark decay modes assumed by the analyses are specified in the legend. The analyses use different analyses strategies as discussed in the text. The analysis labels refer to Table 2.
Figure 5: Exclusion contours at  CL in the constrained MSSM/mSUGRA with , , and , such that the Higgs mass is approximately  GeV in the studied parameter space. The CMS analysis used a cMSSM scan with . The analysis labels refer to Table 2.

The results of the different inclusive searches with leptons in the final state are shown in Fig. 4 for the simplified gluino-pair and for squark-pair production. The analyses assume a variety of different production and decay topologies, that make direct comparisons of the different analyses sensitivities problematic. Interpretations in the same signal model are not available. The shown exclusion contours give however a good overview of the experimental sensitivity for a variety of scenarios. Typically long decay chains are studied, compared to the previously discussed results displayed in Fig. 2.

For production shown in Fig. 4, the gluino effectively decays into two quarks and the lighter chargino , the decays further into the LSP as identified in the figure legend. The chargino mass is fixed in between the gluino or squark mass and the neutralino with equal mass difference, unless otherwise specified in the figure legend. In the signal scenarios, where intermediate sleptons or sneutrinos are produced in the final state, the gluinos or squarks decay with equal probability via either the lightest chargino or the next-to-lightest neutralino . These subsequently decay via left-handed sleptons (or sneutrinos) into a lepton (or neutrino) and the lightest neutralino . The masses of the intermediate charginos/neutralinos are set to be equal, while the slepton and sneutrino masses (all three lepton flavors are mass degenerate in this model) are fixed to lie in the middle of m(/) and m().

For production shown in Fig. 4, different production and different decay topologies are assumed by the shown analyses. The inclusive search with at least one lepton ATLAS-SUS-2013-20 () assumes pair production of first- or second-generation squarks that decay either through sleptons or SM -bosons. The Razor analysis CMS-SUS-2013-04 () with one -tagged jet and combined no-lepton and one-lepton final state is targeted at stop-pair production, where the stop decays into a SM top-quark and the . More analyses specialized for this decay are discussed in Sec. 5. The results of the like-sign dilepton search CMS-SUS-2013-13 () are interpreted with respect to bottom squark pair production, where the sbottom decays via charginos as . Two scenarios for chargino masses and are shown.

The free parameters of the simplified model are the gluino (squark) mass and the neutralino mass, which span the plot plane. Depending on the model of supersymmetry, gluino masses up to  TeV, squark masses up to  GeV, and neutralino masses up to  GeV can be excluded.

Exclusion contours for the cMSSM for , and in the plane of the universal scalar mass and the common mass of the gauginos and higgsinos are derived, as shown in Fig. 5. Models like the cMSSM are helpful to compare different analysis search results on equal footings. However, only few analyses have produced exclusion contours in the cMSSM, because of the limitations of the model that significantly reduce the possible relations between supersymmetric masses or branching fractions. The cMSSM exclusion contours of the inclusive analyses discussed above, where available, are shown in Fig. 5. All light-flavour squark masses below  TeV and gluino masses below  TeV masses can be excluded at  CL. The exclusion contours reach  GeV at small values of , and  GeV at large values of .

The and jets analysis ATLAS-SUS-2013-02 () targeted at low jet multiplicities is most sensitive at low where squark masses are light and production is largest. At large values of , where squarks are heavy and gluino mediated production leads to long decay chains, the inclusive search with leptons ATLAS-SUS-2013-20 () sets the best exclusion.

The Fittino and Mastercode collaborations Fittino-2015 (); Buchmueller:2013rsa () have investigated the remaining allowed parameter space with a global fit, in order to identify the set of cMSSM parameters best compatible with standard model precision measurements, astrophysics, and direct LHC searches. The precision observables include for example the anomalous magnetic moment of the muon, direct dark matter detection bounds, the dark matter relic density, and the Higgs boson mass. The global minimum was found at small values of just outside the direct search limits from the LHC experiments with respect to . The fit -value, i.e. the consistency with the model is smaller than . In this sense, the cMSSM can be excluded by the LHC searches at a confidence level of at least  Fittino-2015 (); Buchmueller:2013rsa ().

4 Inclusive searches for gluino mediated production of third generation squarks

As discussed before, the mass difference to the standard model partners of the third generation multiplets with large Yukawa couplings should not be too large MassDiff (), in order to minimize necessary fine-tuning. The lighter mass-eigenstate is typically the lightest squark. Since the belongs to the same weak isospin doublet as the bottom squark , and is therefore controlled by the same supersymmetry-breaking mass parameter, a light can also imply light . In simplified models of third generation squark production (or the ) is typically assumed to be the only accessible squark, all other squarks are assumed to be decoupled at high energy scales. Direct strong pair production of third generation quarks is possible and will be discussed in the following section. Here, the gluino mediated production, favored by naturalness arguments, i.e. Eq. (2), shall be discussed, which is similar to the inclusive searches for gluino and light-flavor squark production discussed previously. In general, an increased signal sensitivity to stop or sbottom masses can be achieved by the usage of -tagging or top-tagging information. The relevant gluino-mediated stop-quark production channels are shown in Fig. 6. Assuming sufficiently heavy gluinos, top-squark decays can lead to final states with up to four real top-quarks and two neutralino LSPs in the final state, e.g. , depending on m() and m().

4.1 Searches in the all-hadronic final state

(a)
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Figure 6: Effective Feynman diagrams for the simplified gluino mediated top production and the effective decay through an off-shell stop (a) and gluino mediated stop production and the successive decay (b) relevant if the stop and the neutralino LSP are almost mass degenerate.

Analyses CMS-SUS-2012-28 (); CMS-SUS-2013-19 () based on the kinematic variables and introduced in Eq. (7) and Eq. (8) were carried out at CMS. The variables provide powerful discrimination against the QCD multijet background. The -tag multiplicity as well as the total number of jets are used to define exclusive signal regions, maximizing the analysis sensitivity to different signal scenarios like gluino- or squark pair production, and in particular also to direct and gluino mediated production of third generation quarks. In addition to and light-flavor production discussed in the last section, the analyses results are interpreted for gluino-pair production, where the gluino decays to two top-quarks and the neutralino LSP, as shown in Fig. 6(a).

The search analysis CMS-SUS-2012-24 () uses the shape of the conventional and variables to search for supersymmetry. By dividing and into four bins each and in addition to the -tag multiplicity bins, 176 mutually exclusive signal regions are defined, in order to target gluino-mediated top- or bottom-squark production. The dominant standard model backgrounds originate from QCD multijet production, from “lost leptons” of +jets and +jets processes and from . The shapes of these backgrounds are obtained from data-sidebands: For the QCD background, control events are selected with low , lost-lepton proxy event samples require exactly one electron or one muon with a small transverse mass  GeV as defined by Eq. (6) to limit possible signal contamination, and for the to invisible background and events are selected. The shape of these three backgrounds is fitted to the three-dimensional signal region in , , and the number of -tags, except for the background, where only and are fitted to solve the low-statistics problem of the control events. In the limit of a massless lightest supersymmetric particle, gluinos with masses below  GeV are excluded for gluino mediated stop production.

4.2 Top squark searches with leptons in the final state

Extending the examined final states to include leptons can increase the sensitivity to gluino mediated stop production , because up to four leptons from the -bosons from the top-quark decays can be produced. The disadvantage of the small branching ratio can be compensated by a better handle on the separation and the description of the remaining standard model backgrounds.

The search for gluino-mediated top-squark production in  fb reported by CMS CMS-SUS-2013-07 () is based on events with a single isolated lepton (electron or muon) and at least six high- jets, at least two of which are identified as -jets. Two scenarios with on- or off-shell top squarks are considered. In both scenarios the stop decays into a top quark and the neutralino LSP . The final state contains four standard model top quarks and , which means that four jets originating from -quarks and can be -tagged. The probability that in at least one of the four -bosons decays one charged lepton or is created is , well motivating the single lepton requirement. The SM background is dominated by processes, where large stems from the leptonic decay of a heavily boosted -boson and -tag multiplicities larger than two can originate from gluon splitting or mistagged jets. Contributions from +jets and other rare diboson processes are suppressed by the high jet multiplicity requirement. Three complementary analysis strategies with respect to the chosen kinematic variables and data-sets are pursued: The first two methods rely on the evaluation of the distribution in bins of the amount of hadronic energy in the event . The shape of the remaining SM backgrounds is estimated in two independent ways. The missing transverse momentum template method (MT) determines a parametrized description of the distribution by fits to control regions at low-. The lepton spectrum method (LS) exploits the correlation of the direction of the lepton momentum and the originating from a neutrino from the same decay in the standard model background. Another independent method is based on the azimuthal angle between the reconstructed -direction and the lepton to separate a signal-depleted background dominated region at small . The variable is comparable to with respect to the separation power of signal and standard model and background, but has superior resolution in this analysis. The signal region is binned in , which includes also signal events with low but high lepton momenta. The three different data-driven analysis strategies MT, LS, and increase the robustness of the search, while avoiding uncertainties due to potential mismodelling of SM simulation. Upper limits are set for gluino pair production with , where each of the two top squarks decays into a top quark and the lightest supersymmetric particle, as shown in Fig. 7 in the gluino - neutralino LSP mass plane and in the gluino - stop mass plane.

Figure 7: Exclusion contours at  CL for the inclusive searches for strong gluino pair-production and the subsequent decay of both gluinos in the gluino - neutralino mass plane (a) and the m() - m() plane (b). The analysis labels refer to Table 2.

Two isolated leptons ( or ) with the same electric charge (like-sign, LS), or at least three isolated leptons are required in the search for strongly produced supersymmetric particles ATLAS-SUS-2013-09 () at the ATLAS experiment. In addition to requiring multiple energetic jets, also the -tag multiplicity is taken into account to increase the sensitivity in particular to gluino mediated stop production. The analysis strategy and the SM background composition is comparable to its CMS counterpart CMS-SUS-2013-13 () discussed in the previous section.

The final state with and without at least one high lepton or was analyzed simultaneously by the ATLAS analysis ATLAS-SUS-2013-18 (), combining the limits from different signal regions, based on their expected sensitivity. The analysis was designed specifically for gluino mediated production of third generation squarks and requires at least three -tagged jets. The standard model backgrounds are divided into reducible backgrounds, where at least one -tagged jet is mistagged, and irreducible backgrounds dominated by production with genuine -jets. The reducible backgrounds are modeled using data-sidebands weighted according to the -misidentification rate. The rate was measured using MC simulation and validated in enriched data control regions. The irreducible background is described by Monte Carlo simulation, where the dominant contribution from is normalized in a control region with two isolated leptons and relaxed requirements. The sensitivity to different signal scenarios is optimized by binning the -lepton signal region with respect to , , , , and . The -lepton signal region is binned in and the transverse mass . Due to the simultaneous analysis of the - and -lepton final states and the combination of multiple signal regions very compatible sensitivities to gluino mediated  generation squarks production are obtained.

ATLAS searches for gluinos and first- and second-generation squarks in final states containing jets and missing transverse momentum, with or without leptons or -jets are summarized in Ref. ATLAS-SUS-2014-06 (). The combination is further extended by a new search for squarks and gluinos in inclusive final states with , high- jets, with and without leptons and -tags, thus improving the sensitivity to a wide range of supersymmetry models and in particular to gluino-mediated third generation squark production. The resulting limits on gluino mediated stop production are shown in Fig. 7 for the discussed analyses. In the case of decays via virtual top squarks and for light LSPs, gluino masses below  TeV are excluded. Viable scenarios remain possible with light and masses below approximately and  TeV, respectively, in particular if the mass difference between the gluino and the neutralino LSP is similar to or smaller than the standard model top mass.

5 Direct production of top squarks

Naturalness arguments prefer light top squark masses , as previously discussed, leading to a production cross-section StopXsec () interesting for direct searches in this topology. The produced top squarks decay into the neutralino and further standard model particles, depending on the mass difference between stop and neutralino . Scenarios where the is the lightest supersymmetric particle eliminate the possibility of a supersymmetric candidate particle to explain the dark matter problem of the universe. These scenarios are not considered here, because astrophysical observations place stringent constrains on strongly and/or electromagnetically interacting LSPs PhysRevLett.42.1117 (), or require sufficiently large -parity violating couplings to explain the non-observation of exotic atoms or nuclei Rparity ().

In the following, pair production of the lightest stop quark is considered, where the details of the decay topology depend on as demonstrated by Fig. 8. The four different decay regimes will be discussed with respect to the most sensitive analyses. The relevant Feynman diagrams are shown in Fig. 9 and the results of the ATLAS and CMS experiments are summarized in Fig. 10. Pair production of sbottom quarks is not discussed here, as the scenarios and the analyses are very comparable to the pair production of light-flavor quarks, except for the -jets, that can be tagged. Results for can be found in the quoted references.

Figure 8: Top squark decay topologies depending on the mass difference between the lightest stop and the neutralino LSP.
(a)  four-body decay
(b)
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(d)
Figure 9: Effective Feynman diagrams for direct stop production and the following stop decay to the neutralino LSP and a stop four-body decay (a), a stop three body decay into the neutralino, a -quark and an on-shell -boson (b), an on-shell top (c), or through trough a chargino followed by a three-body decay of the (d).

5.1 Stop-decay to soft decay products and