Searches for direct pair production of third generation squarks with the ATLAS detector

Naturalness arguments for weak-scale supersymmetry favour supersymmetric partners of the third generation quarks with masses not too far from those of their Standard Model counterparts. Top or bottom squarks with masses less than or around one TeV can also give rise to direct pair production rates at the Large Hadron Collider (LHC) that can be observed in the data sample recorded by the ATLAS detector. This document presents recent ATLAS results from searches for direct top and bottom squark pair production considering both R-parity conserving and R-parity violating scenarios, using the data collected during the LHC Run 2 at a centre-of-mass energy of √ s = 13 TeV.


Introduction
Supersymmetry (SUSY) [1] is one of the most attractive extensions of the Standard Model (SM) of particle physics. It can resolve the gauge hierarchy problem [2][3][4][5] by introducing supersymmetric partners of the known bosons and fermions and extending the Higgs boson sector to 5 Higgs bosons, whose superpartners mix together with the electroweak gauginos to the neutralinos and charginos.
Since the supersymmetric Langrangian contains terms which can violate the baryon and lepton number which allows for rapid proton decay, often R-parity conservation (RPC) is introduced which results in the lightest supersymmetric particle (LSP) being stable and thus, in case the LSP is the lightest neutralino, to an ideal dark matter candidate [6,7]. If R-parity is violated, this for example can nicely explain the baryon-lepton-asymmetry or the masses of neutrinos [8][9][10].
Naturalness arguments favour the third-generation squarks to be the lightest colored supersymmetric particles [11,12], i.e. their masses should be in the TeV range and thus, directly accessible at the Large Hadron Collider (LHC) at CERN. This document summarizes the ATLAS [13] search program for third-generation squarks performed during LHC Run 2 at a centre-of-mass energy of √ s = 13 TeV. The datasets used by the analyses mentioned in this document comprise an integrated luminosity of 36.1 fb −1 and 36.7 fb −1 from 2015 and 2016 depending on the data quality requirements.
a) pure bino LSP b) wino NLSP c) higgsino LSP d) bino/higgsino mix a) pure bino LSP b) wino NLSP c) higgsino LSP d) bino/higgsino mix a) pure bino LSP b) wino NLSP c) higgsino LSP d) bino/higgsino mix a) pure bino LSP b) wino NLSP c) higgsino LSP d) bino/higgsino mix sparticle masses Figure 1: Illustration of the sparticle mass spectrum for various LSP scenarios: a) Pure bino LSP, b) wino next-to-lightest supersymmetric particle (NLSP), c) higgsino LSP, and d) bino/higgsino mix. Thet 1 andb 1 decay into different electroweakino states in the scenarios: the bino state (red lines), the wino states (blue lines), or the higgsino states (green lines), with possibly the subsequent decays into the LSP [14].˜t  Figure 2: Illustration of the preferred top squark decay modes in the plane of thet 1 andχ 0 1 mass, where the latter is assumed to be the lightest supersymmetric particle. Top squark decays to supersymmetric particles other than the LSP are not displayed [14].

Final states with no leptons
If the top quark from thet 1 → t +χ  Figure 3a shows the masses of the leading and subleading reclustered radius R = η 2 + φ 2 = 1.2 jets for a simulatedt 1 → t +χ 0 1 scenario. The peaks around m t and m W allow for a good discrimination against all SM backgrounds not containing 2 top quarks (TT), 1 top quark and 1 W boson (TW) or at least 1 top quark (T0) [15]. Another very useful variable is the transverse mass between the b-quark jet closest to E miss T and E miss T itself, which is called m b,min T (cf. Figure 3b). For top quark pair production (tt), it has a kinematic endpoint at m t , which allows for a good tt suppression.     Compressed scenarios (mt 1 − mχ0 1 ∼ m t ) suffer from low E miss T which results in final states looking similar to tt. In case of an energetic jet from initial state radiation (ISR), the whole system gets boosted which results in a significant amount of E miss T . In order to increase the sensitivity in those regions, the so-called recursive jigsaw algorithm [16] is applied. The algorithm maximizes the amount of backto-back transverse momenta (p T ) of all possible hemispheres created by splitting the event by a plane into 2 pieces (cf. Figure 4a). Ideally, after having applied the algorithm, one hemisphere contains the decay products of the top squarks, including the E miss T , whereas the other one includes the ISR jet and thus, is called ISR system. The ratio of the E miss T and the p T of the ISR system is called R ISR and is shown in Figure 4b.
In none of the signal regions any excess above the SM expectation was found, exclusion limits were set combining all 0-lepton signal regions. Figure 5a shows the 95% confidence level exclusion limits. The exclusion shape along the mass diagonal is obtained by the recursive jigsaw algorithm.
Decays of the lighter bottom squarkb 1 are kinematically very similar tot 1 decays which allows to also interpret the 0-lepton selection with few adaptions in scenarios where theb 1 decays viab 1 → t+χ

Final states with one lepton
The analysis searching for direct top squark production with one isolated lepton in the final state covers scenarios with 2-, 3-and 4-bodyt 1 decays [14]. For the 2-body decay, besides a high E miss T , also one hadronically decaying top quark is required. Additional cuts on variables which try to reconstruct the leptonic decay, such as the transverse mass between the lepton and the E miss T and the asymmetric stransverse mass help to reject the SM backgrounds which are mainly tt production. While in case of 2-body decay scenarios, a cut&count analysis is used, for the 3-and 4-body decays, kinematic shapes are needed, since the same final-state objects have significanctly lower momenta which are typically still above the reconstruction thresholds. The asymmetric stransverse mass am T2 shown in Figure 6a) is a powerful discriminant for separating dileptonic tt (where both W bosons decay leptonically) from signal since it has an kinematic endpoint at m t . For the 4-body decay scenario, a shape-fit in am T2 is applied whereas for the 3-body decay scenario, a shape-fit of the lepton p T divided by the E miss T distribution is applied (cf. Figure 6b). (a) am T2 in the 4-body decay scenario signal region bWN as described in [14].  The full event selection in the corresponding signal region is applied, except for the requirement that is imposed on the variable being plotted. The predicted SM backgrounds are scaled with the normalisation factors obtained from the corresponding control regions. The hashed area around the total SM prediction includes statistical and experimental uncertainties. The last bin contains overflows. Benchmark signal models are overlaid for comparison. The bottom panels show the difference between data (n obs ) and the predicted SM background (n exp ) divided by the total uncertainty (σ tot ) [14].
As for the 0-lepton final state, the recursive jigsaw algorithm is used for the the compressed region, but the ISR variables are additionally put into a boosted decision tree [19] in order to increase the sensitivity since the 1-lepton final state has an additional neutrino which contributes to the E miss T .

Final states with two leptons
A final state with two leptons has the smallest branching fraction compared to the 0-lepton or 1-lepton final states, but the leptonic top quark decay allows for the best coverage of the 3-and 4-body decay scenarios [20]. For the 4-body decay scenario, where objects with low momenta are expected, an E miss T trigger is used assuming the presence of an ISR jet. For this region, the ratio between the E miss T and the p T of the 2-lepton system (R 2 , cf. Figure 7a) is used as discriminating variable. For the 3-body decay scenario, there are dedicated signal regions for mt 1 − mχ0 1 being either close to m t or m W . Here, so-called super-razor variables are used, similar to the recursive jigsaw variables in the 0-lepton and 1-lepton final states. Figure 7b shows the ratio between the sum of transverse momenta of the visible particles including the E miss T and the energy of the razor frame R p T , similar to R ISR mentioned before.      shown assume that R-parity is conserved, only one-step-decays occur and the LSP is bino-like.

pMSSM-inspired models
It is also possible to interpret results in the phenomenological Minimal Supersymmetric SM (pMSSM) [22,23]. In case there is a wino-like next-to-lightest supersymmetric particle (NLSP) in addition, for example aχ ± 1 or aχ 0 2 , they are usually motivated to have masses twice as much as theχ 0 1 by models with gauge unification at the GUT scale (cf. Figure 1b). Theχ 0 2 can either decay into a Higgs or a Z boson and aχ 0 1 [14]. Figure 9a shows the derived exclusion limit interpreting the results from the 1-lepton final state in the pMSSM. The same selections can also be interpreted forb 1 pair production which is sketched as the dashed and dotted grey lines. In case the LSP is a mixed state of bino and Higgsino which is often referred to as the well-tempered neutralino (cf. Figure 1d), the typical mass splitting between the bino and higgsino states is around 20 -50 GeV. Figure 9b shows the exclusion contours derived from the 1-lepton final state for a rather left-handedt 1 .
There are more two-step top squark decays targeted by the ATLAS experiment, e.g. the decaỹ t 1 → t +χ 0 2 where theχ 0 2 then further decays into aχ 0 1 and a Higgs or a Z boson. Here, mt 1 < 900 GeV can be excluded almost independently of mχ0 2 [24]. The same analysis can also be interpreted in the scenario where the heaviert 2 is produced and then decays intot 1 and a Higgs or a Z boson. A mt 2 < 800 GeV is excluded for the decay via a Z boson, while a mt 2 < 900 GeV is excluded for the decay via a Higgs boson assuming a lightχ 0 1 [24].     1 for the directt 1 /b 1 pair production [14].

R-parity violating scenarios
In searches for directt 1 production, only the R-parity violating λ or λ terms of the superpotential are considered. For a non-zero λ , the lepton number is violated, thus thet 1 , which is now the LSP, can decay into a bottom quark and a lepton. Searching for this decay, two oppositely charged leptons and two jets where at least one of them is arising from a b-quark are required [25]. For pairing the leptons ( ) and jets (b) correctly, the mass asymmetry m is used. Figure 10a shows that the m asym b allows for a good background suppression. No excess above SM expectation was found and exclusion limits dependent on the branching ratio of thet 1 into b-quark and lepton flavour were set (cf Figure 10b). Depending on the branching ratio, mt 1 < 1.5 TeV can be excluded at 95% CL.
In case of a non-zero λ , the baryon number can be violated and thet 1 decays into 2 jets which results in a 4-jet final state. The dominant background in this analysis comes from large multi-jet background arising from various other processes of strong interaction described by the QCD. It is estimated by a data-driven (DD) ABCD-method as defined in [26] using the mass asymmetry and the angle between the dijet system and the beamline. With this data-driven estimation, the multi-jet background is in good agreement with the experimental data as shown in Figure 11a. In case of a λ 323 coupling, thet 1 decays into bs-quark-pairs and thus, one can require 2 b-tagged jets which significantly improves the multi-jet rejection (cf. Figure 11b). For the inclusive λ scenarios, a mt 1 < 410 GeV is excluded while for the λ 323 scenarios, a mt 1 < 610 GeV is excluded at 95% CL.

Summary
ATLAS has performed a vast program of searches for direct third generation squark production based on the 2015 and 2016 dataset at √ s = 13 TeV. No excess over SM expectation was found, which lead to a significant improvement of the exclusion limits. The covered models are ranging from simplified