Search for bottom-squark pair production in pp collision events at √s = 13 TeV with hadronically decaying τ-leptons, b-jets and missing transverse momentum using the ATLAS detector

A search for pair production of bottom squarks in events with hadronically decaying τ -leptons, b -tagged jets, and large missing transverse momentum is presented. The analyzed dataset is based on proton-proton collisions at ﬃﬃﬃ s p ¼ 13 TeV delivered by the Large Hadron Collider and recorded by the ATLAS detector from 2015 to 2018, and corresponds to an integrated luminosity of 139 fb − 1 . The observed data are compatible with the expected Standard Model background. Results are interpreted in a simplified model where each bottom squark is assumed to decay into the second-lightest neutralino ˜ χ 02 and a bottom quark, with ˜ χ 02 decaying into a Higgs boson and the lightest neutralino ˜ χ 01 . The search focuses on final states where at least one Higgs boson decays into a pair of hadronically decaying τ -leptons. This allows the acceptance and thus the sensitivity to be significantly improved relative to the previous results at low masses of the ˜ χ 0 2 , where bottom-squark masses up to 850 GeV are excluded at the 95% confidence level, assuming a mass difference of 130 GeV between ˜ χ 02 and ˜ χ 01 . Model-independent upper limits are also set on the cross section of processes beyond the Standard Model.


Introduction
Although the Standard Model (SM) of particle physics is a very successful theory, it does not provide a natural explanation for the large hierarchy between the energy scale of electroweak interactions and the Planck scale related to the gravitational interaction.Nor does it have a viable candidate particle for dark matter, and it does not include a quantum description of gravity.Supersymmetry (SUSY) [1][2][3][4][5][6] is a theoretical framework that extends the SM by introducing partner states for the known particles, where the partners have the same quantum numbers as the respective SM particles but differ in spin by half a unit.This leads to new loop corrections to the Higgs boson mass that cancel out those involving SM particles, thereby solving the hierarchy problem [7][8][9][10].When conservation of -parity [11] is assumed, the lightest supersymmetric particle is stable and would be a viable candidate for dark matter if it is weakly interacting [12,13].However, SUSY must be a broken symmetry in order to allow the supersymmetric particles to be heavier than their SM partners and evade detection so far.Naturalness arguments [14,15] support the assumption that the partner states of the third-generation quarks, the top squarks t and the bottom squarks b, should be light and thus have relatively large production cross sections.They might even be the only strongly produced supersymmetric states within the current mass reach of the LHC.This paper presents a search for pair production of bottom squarks b that decay via the second-lightest neutralino χ0 2 to the lightest neutralino χ0 1 .The neutralinos χ0 1,2,3,4 together with the charginos χ± 1,2 are mixtures of the partner states of the electroweak gauge bosons (bino and winos) and Higgs bosons (higgsinos).The simplified model [16][17][18] of production and decay of supersymmetric particles considered in this search is shown in Figure 1.It is inspired by the Minimal Supersymmetric Standard Model [19,20] in scenarios where the branching ratio B ( χ0 2 → ℎ χ0 1 ) is enhanced, e.g. when the χ0 1 is bino-like and the χ0 2 a wino-higgsino mixture.The branching ratio B ( b →  χ0 2 ) is large compared to that of the direct decay B ( b →  χ0 1 ), which is studied elsewhere [21], when the mixture of the bottom squark is such that it is mostly the superpartner of the left-chiral bottom quark, the χ0 1 is mostly bino, and the χ0 2 mostly wino.A wino-or higgsino-like χ0 2 will be accompanied by a χ± 1 , which allows the decay b →  χ− 1 .This decay mode is relevant if the mass difference between the bottom squark and the chargino is larger than the top-quark mass.In the simplified model, B ( b →  χ0 2 ) and B ( χ0 2 → ℎ χ0 1 ) are assumed to be 100%.Moreover, the Higgs boson is assumed to have the same properties as in the SM, namely (ℎ) = 125 GeV, B (ℎ →  b) = 58%, and B (ℎ →  +  − ) = 6.3%.Only decays of the Higgs bosons into  b,  +  − ,  +  − and   are considered in the signal-model generation.Furthermore, the mass difference Δ( χ0 2 , χ0 1 ) between the χ0 2 and χ0 1 is set to 130 GeV such that the Higgs boson produced in the decay of the χ0 2 is on its mass shell.The free parameters of the model are chosen to be the masses ( b) and ( χ0 2 ).
The signal model illustrated in Figure 1 yields a final state with two bottom quarks, two Higgs bosons, and missing transverse momentum from the two χ0 1 particles that escape the detector without interacting.This analysis selects a final state with a pair of -leptons arising from the decay of one of the Higgs bosons, such that it complements a previous ATLAS search [22], which focuses on final states with multiple -jets.This particular decay mode of the Higgs boson has never been exploited by a bottom-squark search until now.The neutrinos from the -lepton decays provide a source of missing transverse momentum in addition to the pair of χ0 1 .This increases the acceptance of the search in the region of parameter space where the χ0 2 is relatively light and the χ0 1 moderately boosted, where the previous ATLAS analysis has limited sensitivity.The same simplified model has been employed by the CMS Collaboration in a search targeting ℎ →  decays [23].Using a dataset of 77.5 fb −1 , the CMS analysis excludes bottom-squark masses up to 530 GeV for an almost massless χ0 1 at the 95% confidence level, and bottom-squark masses up to at least 400 GeV for heavier masses of the χ0 1 .
The paper is structured as follows.After this introduction, Section 2 briefly describes the ATLAS detector, and Section 3 presents the dataset and simulated event samples.The reconstruction of physics objects is described in Section 4, and the signal selection and analysis discriminants are detailed in Section 5.
The procedures to derive the background estimate are explained in Section 6, followed by a summary of the systematic uncertainties in Section 7. Section 8 presents the results from the analysis and their interpretation, and conclusions are given in Section 9.

ATLAS detector
The ATLAS experiment [24][25][26][27] at the LHC is a multipurpose particle detector with a forward-backward symmetric cylindrical geometry and nearly 4 coverage in solid angle. 1 It consists of an inner tracking detector surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic and hadronic calorimeters, and a muon spectrometer.The inner tracking detector covers the pseudorapidity range || < 2.5.It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors.Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity.A steel/scintillator-tile hadronic calorimeter covers the central pseudorapidity range (|| < 1.7).The endcap and forward regions are instrumented with LAr calorimeters for EM and hadronic energy measurements up to || = 4.9.The muon spectrometer surrounds the calorimeters and is based on three large air-core toroidal superconducting magnets with eight coils each.The muon spectrometer includes a system of precision tracking chambers and fast detectors for triggering.A two-level trigger system is used to select events.The level-1 trigger is implemented in hardware and uses information from the calorimeters and the muon spectrometer to accept events at a maximum rate of 100 kHz.This is followed by a software-based high-level trigger (HLT) that reduces the event rate to 1 kHz on average depending on the data-taking conditions.
1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the -axis along the beam pipe.The -axis points from the IP to the center of the LHC ring, and the -axis points upwards.Cylindrical coordinates (, ) are used in the transverse plane,  being the azimuthal angle around the -axis.

Data and simulated event samples
The dataset used in this analysis consists of proton-proton collision data collected with the ATLAS detector during the second run of the LHC from 2015 to 2018 at a center-of-mass energy of √  = 13 TeV and with a minimum separation of 25 ns between consecutive crossings of proton bunches from the two beams.After applying data-quality requirements that ensure that all detector subsystems were operational, the total integrated luminosity of this data sample is 139 fb −1 with an uncertainty of 1.7% [28], obtained using the LUCID-2 detector [29] for the primary luminosity measurements.
The SUSY signal and SM background processes are modeled with Monte Carlo (MC) simulations, except for the multĳet background, which is estimated from data.The modeling of the two dominant SM background processes, namely top-quark production and production of  bosons with decays into -leptons ( ()), was improved by normalizing their contributions to data as described in Section 6. Simulated samples were produced using the ATLAS simulation infrastructure [30] with either a full simulation of the ATLAS detector in G 44 [31], or a faster variant that relies on a parameterized response of the calorimeters [32].The latter was only used for the simulation of bottom-squark signals and to evaluate systematic uncertainties associated with generator modeling.The effect of multiple interactions in the same and neighboring bunch crossings (pileup) was modeled by overlaying the hard-scattering event with simulated inelastic   collisions generated with P 8.186 [33] using the NNPDF2.3LOset of parton distribution functions (PDFs) [34] and the A3 set of tuned parameters (tune) [35].Simulated event samples were weighted to reproduce the distribution of the number of pileup interactions observed in the data.For all simulated samples except those generated with S [36], the E G [37] program was used to simulate the decays of bottom and charm hadrons.
The production of a top quark in association with a  boson was modeled using the P -B v2 generator [39][40][41]53] at NLO in QCD using the five-flavor scheme.Single-top-quark production in the -channel was modeled using the P -B v2 generator [39][40][41]54] at NLO in QCD using the four-flavor scheme.The -channel production was modeled using the P -B v2 generator [39][40][41]55] at NLO in QCD in the five-flavor scheme.For all three channels, the NNPDF3.0NLOPDF set was used for the matrix elements calculation.The events were interfaced with P 8.230 using the A14 tune and the NNPDF2.3LOPDF set.
Production of top-quark pairs in association with a ,  or Higgs boson (collectively denoted by  t ) was modeled using the M G 5_aMC@NLO v2.3.3 generator [56] at NLO in QCD with NNPDF3.0NLOPDFs.The events were interfaced to P 8.210 using the A14 tune and the NNPDF2.3LOPDF set.
The production of +jets ( = , ) was simulated with the S v2.2.1 generator [36] using NLO matrix elements for up to two jets, and leading-order (LO) matrix elements for up to four jets calculated with the Comix [57] and OpenLoops libraries [58,59].They were matched with the S parton showers [60] using the MEPS@NLO prescription [61][62][63][64] and the tune developed by the S authors.The NNPDF3.0NNLOPDF set [42] was used and the samples were normalized to a NNLO prediction [65].
The SUSY signal samples were generated with M G 5_aMC@NLO v2.2.3 [56] using NNPDF2.3LOPDFs, and the modeling of the parton showering, hadronization and underlying event was performed with P 8.210 with the A14 tune.The LO matrix elements include the emission of up to two additional partons.The matching between parton showers and matrix elements was done with the CKKW-L prescription [66,67], with a matching scale set to one quarter of the mass of the bottom squark.Signal samples were generated with bottom-squark masses ( b) ranging from 250 GeV to 1000 GeV, and masses of the second-lightest neutralino ( χ0 2 ) between 131 GeV and 380 GeV.Signal cross sections were calculated to approximate NNLO in QCD, adding the resummation of soft gluon emission at NNLL accuracy [68][69][70][71][72][73][74][75].The nominal cross sections and their uncertainties were derived using the PDF4LHC15_mc PDF set, following the recommendations of Ref. [76], and decrease from 24.8 ± 1.6 pb at ( b) = 250 GeV to 14.5 ± 1.5 fb at ( b) = 900 GeV.

Event reconstruction
In this section, the reconstruction of the analysis objects from the detector data is described.The search presented in this paper is based on events which have -jets, hadronically decaying -leptons and large missing transverse momentum in the final state.In addition to these, selections are used where -leptons are substituted with muons to improve the background model.
Inner-detector tracks with  T > 500 MeV are used to reconstruct primary vertices [77].If several vertex candidates are found, the one with the largest sum of the squared transverse momenta of associated tracks Σ 2  T is treated as the hard-scattering vertex.An anti-  clustering algorithm [78,79] with a radius parameter of  = 0.4 is used to reconstruct jet candidates in the calorimeter.Jets are built from massless positive-energy topological clusters [80] of calorimeter cells containing energy above a noise threshold, measured at the electromagnetic energy scale.The jet candidates are calibrated using jet energy scale (JES) corrections derived from data and simulation [81].A global sequential calibration procedure is applied to improve the jet energy resolution (JER).Jets with  T > 20 GeV and || < 2.8 are selected, and a set of quality criteria are applied to reject jets not originating from   collisions [82].To suppress jets from pileup interactions, a jet-vertex-tagging algorithm [83] is employed for jets with  T < 120 GeV and || < 2.5.Jets containing -hadrons are tagged as -jets using a boosted decision tree (BDT) algorithm that exploits the impact parameters of tracks within the jet as well as secondary vertex information [84,85].The optimal working point for this analysis has an efficiency of 77%, with an approximate misidentification probability of 20% for jets arising from charm quarks, 6.7% for hadronically decaying -leptons, and 0.9% for light-flavor jets in simulated  t events.
The reconstruction of hadronically decaying -leptons [86] is seeded by anti-  jets ( = 0.4) built from topological clusters calibrated with a local hadronic weighting scheme [87].The -leptons are built from clusters and tracks found within Δ = 0.2 of the seed jet axis.The tracks are selected by a set of BDTs, and only the candidates with one or three associated tracks and a charge sum of ±1 are considered.The -leptons are required to have  T > 20 GeV and || < 2.5, and the transition region between barrel and endcap calorimeters (1.37 < || < 1.52) is excluded.The energy calibration is based on a boosted regression tree that exploits energy and shower-shape measurements from the calorimeter, information from particle-flow reconstruction [88] and the number of pileup interactions.A recurrent neural network algorithm [89] is used to distinguish between jets and -leptons.It uses as input a set of high-level variables combining tracking and calorimeter measurements, as well as low-level variables from individual tracks and clusters.The loose identification working point is applied, corresponding to efficiencies of 85% and 75% for 1-prong and 3-prong -leptons, respectively.To reduce background from electrons that are misidentified as -leptons, 1-prong -lepton candidates are discarded if a nearby electron passes the very loose working point of the likelihood-based algorithm used to identify electrons.This requirement is tuned to have an efficiency of 95% for hadronically decaying -leptons [90].
Muon candidates are reconstructed by combining information from the muon spectrometer and the inner tracking detectors [91].They are required to have  T > 10 GeV and || < 2.7, to satisfy the medium identification criteria, and to pass a | 0 sin | < 0.5 mm requirement on the longitudinal impact parameter. 3fter discarding the candidates failing the overlap-removal procedure described below, stricter requirements are applied: muons must have  T > 25 GeV, meet the loose isolation criteria and satisfy the requirement | 0 |/( 0 ) < 3 on the transverse impact parameter  0 and its uncertainty ( 0 ).
Electron candidates are reconstructed by matching energy clusters in the electromagnetic calorimeter to tracks from the inner tracking detector [92] and are required to have  T > 10 GeV and || < 2.47.A requirement on the longitudinal impact parameter | 0 sin | < 0.5 mm discards electrons not associated with the primary vertex.Electrons are included in the computation of missing transverse momentum and in the overlap-removal procedure, but are not used otherwise.
The missing transverse momentum vector ì  miss T is defined as the negative vector sum of the transverse momenta of all reconstructed objects mentioned above, with an additional soft term including all tracks from the primary vertex that are not associated with a reconstructed object [93].The magnitude of ì  miss T is denoted by  miss T .An overlap-removal procedure is performed after event reconstruction to resolve ambiguities when a single physical object is reconstructed as multiple final-state objects.If two electrons share the same track, the electron with lower transverse momentum is discarded.Any -leptons overlapping with an electron or a muon within Δ  ≡ √︁ (Δ) 2 + (Δ) 2 < 0.2 are removed.If an electron and a muon share the same inner-detector track, the muon is removed if it is tagged as a minimum-ionizing particle in the calorimeter, otherwise the electron is discarded.If a jet overlaps with an electron or a muon candidate within Δ  < 0.2, the jet is removed.An exception is when a jet that has more than two associated tracks overlaps with a muon within Δ  < 0.2, in which case the jet is kept and the muon is discarded.Finally, electron and muon candidates lying 0.2 < Δ  < 0.4 from a jet and jets within Δ  = 0.2 of a -lepton candidate are discarded.
The same reconstruction and identification algorithms are used for both data and simulation.Dedicated correction factors are applied to jet, -lepton, electron and muon candidates to account for differences in efficiencies and energy calibrations between data and simulation.

Event selection
All selections used in this analysis require events to pass a  miss T trigger [94] or a combined  miss T + -jet trigger [95], except for specific selections used for the background estimate which rely on single-muon Table 1: Summary of the common analysis preselection.The requirements in the upper part of the table apply to all analysis regions, those in the lower part of the table to all but the  () control regions as discussed in Section 6. Events are rejected if no primary vertex with at least two tracks is found or if they contain a jet failing to meet the loose quality criteria described in Ref. [82].Furthermore, events are rejected if they contain muons with a large track-curvature uncertainty or muons which are likely to originate from cosmic rays as indicated by a large displacement from the primary vertex.
Events are required to have at least three jets, among which at least two must be -tagged unless stated otherwise.The leading and subleading jets are required to have  T > 140 GeV and  T > 100 GeV, respectively, and the leading -jet is required to have  T > 100 GeV.The  miss T requirement depends on the trigger considered: the  miss T + -jet trigger reaches maximum efficiency for  miss T > 160 GeV, while the  miss T trigger requires  miss T > 200 GeV to be fully efficient.
To suppress the multĳet background, events are vetoed if the angular separation in the transverse plane Δ(jet 1,2 , ì  miss T ) between one of the two leading jets and ì  miss T is less than 0.5.All analysis selections require the presence of at least one -lepton or one muon in the event.This common preselection is summarized in Table 1.In the following, the number of objects in an event is generically written as  object , and indices '1' and '2' refer to the leading and subleading objects, respectively, which are ordered by decreasing transverse momentum.
On top of the preselection from Table 1, a set of signal regions (SRs) are defined in order to target the bottom-squark signal processes illustrated in Figure 1.All SRs require at least two hadronically decaying -leptons with opposite electric charge (referred to as the OS criterion) and no muon to be present.
Additional kinematic selections are applied to suppress the SM background.These selections are described in the following and summarized in Table 2.They are optimized by maximizing the signal significance [96] in the previously nonexcluded parameter space of the targeted signal model.
To ensure compatibility with a Higgs boson decay, the visible invariant mass of the two leading -leptons must satisfy 55 GeV < ( 1 ,  2 ) < 120 GeV.The lower bound suppresses the  () background, while the upper bound reduces 'nonresonant' background contributions where the -leptons do not originate from the same resonance.Events are required to have  T > 1100 GeV, where is the scalar sum of the transverse momenta of all -leptons, muons and jets in the event.This variable exploits the fact that signals with large bottom-squark masses are expected to produce highly boosted particles in the final state.
The stransverse mass variable [97,98], denoted  T2 , is used to discriminate between the signal process and the top-quark production background.It is designed to have an endpoint for background processes such as top-quark production where the two -leptons originate from separate decay branches.For the signal process, the two -leptons originate from a resonant Higgs boson decay, and the  T2 spectrum has a pronounced tail towards larger values.The  T2 variable is computed as where ì   1 ,  2 T correspond to the transverse momenta of the two leading -leptons, and (, ) refers to two invisible particles assumed to be produced with transverse momentum ì  , T .The masses of the invisible particles are free parameters and set to   =   ≡  inv .The transverse mass  T is defined as  2 T ( ì where the -lepton mass is set to 0 GeV.The  T2 distribution peaks at 0 GeV for both the bottom-squark signal and the dominant  t background when setting  inv to 0 GeV, providing poor discrimination.The discrimination improves as  inv is increased, and a value of 120 GeV is found to result in an  T2 distribution that best separates the signal from the background.All SRs require  T2 > 140 GeV.Some of the CRs also make use of the transverse mass of a -lepton, which is computed as . The last discriminant is Θ min , defined as the smallest three-dimensional angle of the four combinations between either of the two leading -leptons and either of the two leading -jets.For the  t background, the smallest angle is expected from configurations where the -jet and the -lepton originate from the same top-quark decay, resulting in relatively low values of Θ min .For  () +  b events with a highly boosted  boson, the pair of -leptons recoils against the -jets, and large values of Θ min are expected.For signal events where b →  χ0 2 → ℎ() χ0 1 , the angle between the -jet and the -lepton pair increases with the b mass, and so does Θ min .A multi-bin SR with three Θ min bins (< 0.5, [0.5, 1.0], > 1.0) is defined in order to take advantage of these features.A single-bin SR requiring Θ min > 0.6 is used to provide cross-section limits on generic processes beyond the Standard Model (BSM).The probability for a signal event to enter the single-bin SR ranges between 6.4 • 10 Examples of signal and background kinematic distributions are shown in Figure 2. The three plots show the  T , ( 1 ,  2 ) and  T2 variables after the preselection.The estimated SM background is scaled by the normalization factors from the background fit described in Section 6, and the distributions for several signal models are overlaid.The "Other" contribution includes all the backgrounds not explicitly listed in the legend (+jets except  ()+jets, diboson/triboson, multĳet).The top-quark and  () background contributions are scaled with the normalization factors obtained from the background-only fit described in Section 6.The rightmost bin includes the overflow.The bottom panel shows the ratio of the observed data and the expected Standard Model background.

Background estimation
The largest backgrounds in the SRs are from  t and single-top-quark processes, referred to as top-quark background, and  () produced in association with -jets.Subdominant contributions arise from  t  processes, while other backgrounds such as multĳet or diboson and triboson production are found to be negligible.The normalization of the two dominant backgrounds is fitted to the data in dedicated control regions (CRs) kinematically close to the SRs but where little signal is expected.The normalization factors are derived with a likelihood fit based on the H F framework [99].The fit uses as input the observed data yields, the expected yields predicted from simulation, as well as the statistical and systematic uncertainties described in Section 7. Two main fit setups are employed in the analysis.The background-only fit refers to the configuration that only includes the CRs, and where no signal is considered.
The signal-plus-background fit includes both the CRs and the SRs, and it takes into account a possible signal contribution in the fitted regions.It is used to establish exclusion limits as discussed in Section 8.In both cases, the fit is performed simultaneously over all the relevant regions.Subdominant background contributions are normalized according to their cross sections and the integrated luminosity of the data.The multĳet background is determined from data.Validation regions (VRs) are defined in phase-space regions as close as possible to that of the SRs.The VRs are not included in the fit.They are used to validate the background-model extrapolation from the CRs to the SRs by comparing the observed data with the fitted background predictions.As such, they are designed to have little signal contribution.The methods used to estimate the various backgrounds are described in the following, together with the associated CRs and VRs.
Multĳet production is an important background at hadron colliders, but it is efficiently suppressed in this analysis by the requirement of two hadronically decaying -leptons, two -jets, large  miss T , and Δ(jet 1,2 , ì  miss T ) > 0.5.A data-driven jet-smearing method [100] is employed to estimate this background.Events recorded by single-jet triggers are processed through an energy-smearing procedure that emulates  miss T originating from resolution effects.The normalization of the smeared pseudo-data template is derived in events where one of the two leading jets is aligned with ì  miss T in the transverse plane.Except for that multĳet-enriched selection, the multĳet background is found to be negligible in all analysis selections.Therefore, its normalization is kept constant in the fits, for simplicity.
The design of the control regions for the top-quark and  () +  b backgrounds is driven by two main considerations.Firstly, the hadronically decaying -leptons selected in the analysis are either prompt -leptons from electroweak boson decays, or jets misidentified as -leptons.They are referred to as true -leptons ( true ) and fake -leptons ( fake ), respectively, and their contributions must be handled separately in the background model.No such distinction is made for -jets, as the fraction of misidentified -jets does not exceed 10% in the analysis phase space.The top-quark background in the SRs is composed of  true  true and  true  fake contributions of comparable magnitude, where one -lepton comes from a -boson decay, and the second -lepton either comes from the other -boson decay or from a jet misidentified as a -lepton.The  fake  fake contribution is negligible due to the large jet rejection provided by the -lepton identification algorithm.In the case of  () +  b events, only the  true  true contribution is found to be relevant.Secondly, the background normalization factors cannot be accurately determined using events containing two hadronically decaying -leptons ( had ) and two -jets, as the low event yields remaining after the preselection do not allow control regions with sufficient statistical power, high purity, and low signal contamination to be defined.
Because of these limitations the CRs are based on final states where either one or two -leptons are replaced with muons.The CR_Top_µ true and CR_Top_µ fake selections are defined to respectively target top-quark events with one muon plus either one  true or one  fake in the final state, where the muon replaces a  true from one of the -boson decays.The CR_Z_µµ2b region is defined to select  () +  b events.By trading  () for  () and  () for  (), the CRs target the desired background processes but benefit from larger yields due to the branching ratio B ( →  had   ) of 65% that does not apply to muons, and the reconstruction and identification efficiencies that are higher for muons.In the top-quark CRs, event yields are further increased by a combinatorial factor of two.
The normalization factors derived for background events with muons are not directly applicable to background events in the SRs that contain two hadronically decaying -leptons.The replacement of -leptons with muons has an impact on the reconstructed event kinematics and the selection efficiency of background processes, which needs to be accounted for.This is done by introducing additional CRs and normalization factors, two for the top-quark background and two for the  () +  b background, that allow  an extrapolation from muon to -lepton selections.As mentioned in Section 4, corrections are already applied to muons and -leptons in the simulation to match the efficiencies and energy calibration measured in data.The background normalization factors from the additional CRs thus mostly account for acceptance effects.
The definitions of the four control regions used to normalize the top-quark background are summarized in Table 3.The CR_Top_µ true and CR_Top_µ fake regions select events that contain exactly one muon and one -lepton of opposite electric charge.Like all control regions defined in this analysis, they use the  T range from 600 to 1000 GeV.For CR_Top_µ true , the -lepton transverse mass   T must be lower than 80 GeV, which results in a high purity of true -leptons.For CR_Top_µ fake ,   T has to be larger than 100 GeV, which gives a roughly equal mix of true and fake -leptons.The CR_Top_ true selection is identical to that of CR_Top_µ true except that events must not contain a muon.This region has a high purity in top-quark background events decaying semileptonically with a true -lepton in the final state.The CR_Top_µ selection is defined in a similar way, with one muon and no -lepton, selecting high-purity semileptonic top-quark processes with a muon in the final state.
The way the four CRs from Table 3 are used to derive normalization factors for the top-quark background processes is illustrated in Figure 3(a).The expected yields for top-quark production with true and fake To account for the different lepton flavors in the signal region (with two -leptons) and the control region (one -lepton and one muon), the top-quark production yields are further multiplied by additional freely floating normalization factors  1 and  1 , which are constrained mainly through the regions CR_Top_ true and CR_Top_µ.A transfer factor TF Top ≡  1 / 1 is used to correct for the difference between requiring a muon and a true -lepton.This means that a simulated top-quark event with one true and one fake -lepton in one of the signal regions receives a normalization factor   fake × TF Top , and a simulated top-quark event with two true -leptons a normalization factor   true × TF Top .
Figure 4 shows several examples of distributions from the four control regions associated with the top-quark background.In these plots, the predicted background contributions from simulation are scaled with the normalization factors obtained from the background-only fit.All of the CRs show good agreement between the SM prediction and the data.They also have high purity in the respective top-quark background processes except for CR_Top_µ fake , where the purity is only 43% because it is difficult to isolate the contribution of the top-quark background with fake -leptons.
The three control regions that target the  () background are summarized in Table 4.The CR_Z_µµ2b selection is defined using events with two muons of opposite electric charge, taken as proxies for two true -leptons, and two -jets.Since  ()+jets processes do not have large  miss T in the final state, the events are selected using a single-muon trigger, which has its efficiency plateau at  T () > 30 GeV.The invariant mass of the dimuon system is required to be within 10 GeV of the -boson mass, and  miss T to be lower than 100 GeV to increase the purity of the selection.To move the CR closer to the relevant phase space,  T must be in the range [600, 1000] GeV, and the transverse momentum of the muon pair  T ( 1 ,  2 ) must be larger than 200 GeV, which is a typical value found in simulation for the  T of the  boson in  () events after the preselection.The  () background is multiplied by the freely floating normalization factor  Zµµ2b , which is constrained through CR_Z_µµ2b.
The two additional control regions CR_Z_µµ0b and CR_Z_0b are used to correct for the difference in acceptance and efficiency when replacing the -leptons with muons to estimate the +jets background.The interplay of these CRs is illustrated in Figure 3 but with a -jet veto, whereas CR_Z_0b requires the presence of two -leptons with opposite electric charge and no -jet.The CR_Z_0b events are selected with an  miss T trigger and  miss T > 200 GeV as is done for the SRs, and muons are vetoed in this region.Additionally, the sum of -lepton transverse masses   1 T +   2 T has to be lower than 100 GeV to increase the purity in  () events.In all of these three CRs, All normalization and transfer factors are obtained from a simultaneous fit of the seven CRs for the top-quark and  () backgrounds.Table 5 lists the values of the normalization factors and transfer factors and their uncertainties, the names of the control regions that determine the normalization factors and the respective purities of the control regions in top-quark or +jets events.The transfer factors TF Top and TF  are computed from ratios of two normalization factors as explained above.For these, one row in the table ( 1 and  Zµµ0b ) gives the values forming the respective denominators of the ratios, showing how well the data and simulated events agree in these regions.The row below gives the transfer factor (TF Top and TF  , respectively).In these rows, the table lists the second control region (the numerator of the ratio) and its purity.
Three validation regions are defined to check the extrapolation from CR_Top_µ true , CR_Top_µ fake , and CR_Z_µµ2b in the  T variable.This is done by changing the requirement on  T that is applied in the CRs from 600 GeV <  T < 1000 GeV to 1000 GeV <  T < 1500 GeV in the VRs, while keeping all other requirements the same as for the respective CRs.Shifting the  T range moves the validation regions closer to the signal regions, which require  T > 1100 GeV.The VRs and the SRs are mutually exclusive due to the muon veto that is part of the signal-region selections.The names of the three VRs match those of the corresponding CRs.A fourth validation region, VR_Top_, is defined to validate the extrapolation from muons to -leptons in events with two -jets and two hadronically decaying -leptons which pass the  miss T trigger or the  miss T + -jet trigger and the corresponding trigger-plateau requirements.To avoid overlap of this VR with the SRs,  T is required to be within [600, 1000] GeV.In addition, the visible di- mass ( 1 ,  2 ) is required to be either lower than 40 GeV or larger than 90 GeV to reduce the contribution from a possible bottom-squark signal.The upper panel shows the expected number of SM background events and the number of events observed in data for each of the four validation regions.In the lower panel, the significance of the deviation of the observed yield from the expected yield is shown.The top-quark,  () and  () background contributions are scaled with the normalization factors obtained from the background-only fit described in Section 6.The hatched band indicates the total statistical and systematic uncertainty of the SM background.The "Other" contribution includes all the backgrounds not explicitly listed in the legend (+jets except  ()+jets,  t , diboson/triboson, multĳet).
Figure 5 shows that the expected background yields after the fit and the observed yields agree within one standard deviation for all four validation regions, demonstrating good modeling of the SM background.Figure 6 shows various kinematic distributions in the validation regions.Good agreement between the background model and the data is observed in VR_Z_µµ2b, VR_Top_µ fake and VR_Top_.In VR_Top_µ true , the modeling of kinematic distributions is reasonable.The contribution of a potential signal from the model in Figure 1 to the control regions does not exceed 7% at the low end of the range of bottom-squark masses covered by the signal models and quickly falls to below a percent at the high end.For the validation regions it is around 15% for low ( b) and again falls to a percent or less for larger ( b).Events

Systematic uncertainties
The experimental uncertainties considered in this analysis comprise systematic uncertainties in the reconstruction, identification, calibration and corrections applied to the physical objects used in the analysis.They are assumed to be correlated across analysis regions and between the background processes and the signal.Theoretical uncertainties include contributions from generator modeling as well as cross-section uncertainties.They are assumed to be correlated across analysis regions but uncorrelated between different background processes.When assuming no correlation between analysis regions, the total background uncertainty increases by about 5 percentage points for the single-bin SR, and the exclusion contour does not change significantly.
The experimental uncertainties related to jets include uncertainties in the energy scale [81] and resolution [101], jet-vertex-tagging uncertainties [83] and flavor-tagging uncertainties [84,102,103].Flavor-related uncertainties come from the uncertainties in data-to-simulation correction factors for efficiencies and fake rates and from the extrapolation over jet  T .The -lepton uncertainties arise from the energy calibration, and reconstruction and identification efficiencies [86,90].The energy scale uncertainties include the nonclosure of the calibration and uncertainties in the detector response estimated from simulation, as well as uncertainties in the relative calibration of data and simulation measured in  (   had ) events.An uncertainty at high- T , based on single-particle response uncertainties, is taken into account.Muon-related uncertainties [91] are not relevant in the signal regions, as events with muons do not enter these, but they can be important in control regions with muons.Uncertainties related to electrons have a negligible impact on this analysis.The systematic uncertainties affecting the energy or momentum of calibrated objects are propagated to the  miss T calculation.Specific uncertainties in the soft-term contribution to the  miss T [93] are also considered.
The theoretical uncertainties related to variations of the PDFs [76], strong coupling constant  s and renormalization and factorization scales  r and  f [104] are evaluated from generator weights for all background samples.The sets include the nominal PDF as well as 100 variations.The PDF uncertainty is obtained as the envelope of all the variations.The uncertainty related to  s is evaluated by computing  s = 0.119 and  s = 0.117 parameterizations and averaging the difference between them.The PDF and  s uncertainties are then added in quadrature.In order to derive the scale uncertainties,  r and  f are varied up and down by a factor of two.Three independent nuisance parameters are used, two resulting from keeping one of the scales constant while varying the other one, and the third being the coherent variation of both scales.The variations are normalized to the nominal sum of weights so that the effect on the normalization included in the cross-section uncertainty is not double-counted.For all simulated processes that are not normalized to the data, uncertainties in the cross section and in the integrated luminosity of the data are applied.
For  t and single-top-quark production, generator uncertainties related to hard scattering and matching are evaluated by comparing P B +P with M G 5_aMC@NLO+P .Partonshowering uncertainties are estimated by comparison with P B +H 7. Uncertainties in the initial-state and final-state radiation are evaluated by simultaneously testing the impact of scale variations and eigenvariations of the A14 tune [45].For  t production, an additional comparison with the ℎ damp parameter set to 3 top is included.For single-top-quark production, an uncertainty in the treatment of the / t interference is considered by comparing samples produced with the nominal diagram-removal scheme [105] with alternative samples generated with a diagram-subtraction scheme [43,105].
For the +jets processes, additional uncertainties related to the resummation and CKKW matching scales [63,64] are considered.For the  ()+jets and  ()+jets backgrounds, the nominal S samples are compared with alternative samples produced with M G 5_aMC@NLO+P .For diboson and  t  samples, the PDF, scale and cross-section uncertainties are used.
For the bottom-squark signal samples, uncertainties in the acceptance related to the factorization and renormalization scales, merging scales, parton shower tuning and radiation uncertainties are considered.An additional uncertainty accounts for differences between samples produced with the full detector simulation and the parameterized calorimeter response.
A summary of the dominant systematic uncertainties in the background prediction for the signal regions is given in Table 6.The largest source of uncertainty is the generator modeling, and here in particular the modeling of the top-quark background, mainly the modeling of the hard-scatter process and initial state radiation uncertainties.Second-leading in size is the total uncertainty in the normalization and transfer factors, which is obtained from the fit.As the transfer factors are ratios of normalization factors, and a large part of the uncertainties cancel out in the ratio, the uncertainties in the transfer factors are comparatively small.Table 6: Dominant systematic uncertainties in the background prediction for the signal regions after the fit to the control regions.Generator modeling uncertainties refer to all theoretical uncertainties, and are largely dominated by the comparisons of MC event generators for top-quark processes."Other" includes the uncertainties arising from muons, jet-vertex tagging, modeling of pileup, the  miss T computation, multĳet background, and luminosity.The individual uncertainties can be correlated and do not necessarily add in quadrature to equal the total uncertainty.

Results
The event yields for all signal regions are reported in Table 7.The SM background prediction is based on the background-only fit described in Section 6.To illustrate the order of magnitude of the contribution of signal events, the expected yields for three benchmark signal models are included in the table.The single-bin SR and the first two bins of the multi-bin SR are dominated by top-quark production, whereas for Θ min > 1.0 the  () background is the largest contribution.Other SM processes contribute very little to the signal regions.Figure 7 shows a comparison of data and background yields in the SRs together with the corresponding significances quantifying the deviation of the observed yields from the SM expectation in the bottom panel.No significant excess of data above the expected yields from the SM background processes is observed in any of the signal regions.The -value for the event yield in the single-bin signal region to fluctuate to at least the observed value under the background-only hypothesis is ( = 0) = 0.44.
Exclusion contours at the 95% confidence level (CL) are derived from the yields in the multi-bin signal region for the two-dimensional parameter space of ( b) and ( χ0 2 ) in the simplified model from Figure 1.A fixed mass difference of 130 GeV between the second-lightest neutralino χ0 2 and lightest neutralino χ0 1 is assumed for all signal models.The probabilities that the data are compatible with the background-only and signal-plus-background hypotheses are evaluated using a one-sided profile-likelihood-ratio test statistic and the CL s prescription [106].The computations rely on asymptotic properties of the profile-likelihood ratio [96].Systematic uncertainties are treated as nuisance parameters with Gaussian probability densities in the likelihood function.The resulting observed and expected exclusion contours are shown in Figure 8.The uncertainties in the cross section of the supersymmetric signal are not included in the fit but shown as an uncertainty band around the observed limit contour.Since the observed data yield is larger than the expected total background in the highest Θ min bin, which is most sensitive to models with large ( b), the observed exclusion contour deviates inwards from the expected contour with increasing ( b), but it stays within the uncertainty band of the expected limit.The search is optimized for the low-( χ0 2 ) region and has sensitivity to models with ( χ0 2 ) up to 300 GeV.Bottom squarks with masses up to 850 GeV are excluded in this region.For ( χ0 2 ) below about 200 GeV, the softer  miss T spectrum of the signal results in a lower 2 ) 20 GeV cannot be excluded as the bottom-squark decay products are not boosted enough, and the stringent kinematic requirements in the SRs result in low signal acceptance.These results are overlaid on the observed exclusion contour from a previous ATLAS search [22] to demonstrate the complementarity of the two approaches.The new results have unique sensitivity to a previously uncovered region of parameter space at low χ0 2 masses, where the previous search quickly loses sensitivity.
The results from the single-bin signal region can be interpreted in terms of model-independent upper limits on the event yields from potential BSM processes.The fit is performed simultaneously over the CRs and the single-bin SR, assuming no signal contribution in the CRs.The profile-likelihood-ratio test statistic is evaluated using pseudo-experiments.An upper limit of 0.05 fb is derived for the visible cross section  vis , defined as the product of the cross section, acceptance and selection efficiency of such processes.In addition, Table 8 summarizes the expected and observed 95% CL upper limits on the number of BSM events, as well as the confidence level of the background-only hypothesis CL b .The -value and the corresponding significance for the background-only hypothesis to fluctuate to at least the observed values are also included.Table 8: Upper limits at 95% CL on the visible cross section  vis , on the number of signal events ( 95  obs ), and on number of signal events given the expected number (and ±1 excursions of the expectation) of background events ( 95  exp ).The last two columns indicate the CL b value, i.e. the confidence level observed for the background-only hypothesis, the discovery -value (( = 0)), and its associated significance . in the final state.The observed exclusion limit from a previous ATLAS search [22] that requires -jets and  miss T in the final state is also displayed.The region ( b) < 400 GeV is excluded by a previous search from CMS [23].

Conclusion
A search for bottom-squark pairs in events with -jets, hadronically decaying -leptons and large missing transverse momentum is presented.A simplified SUSY model assuming b →  χ0 2 → ℎ χ0 1 is considered, where at least one Higgs boson decays into a pair of -leptons.This analysis has unique sensitivity at low χ0 2 masses due to the presence of hadronically decaying -leptons, which mitigates the Standard Model background, and to the associated   -neutrinos that add to the  miss T originating from the χ0 1 .A multi-bin signal region exploiting angular correlations between the -jets and the hadronically decaying -leptons is used to search for a b signal, and a single-bin signal region is employed for a model-independent statistical interpretation.The data observed in the signal regions are compatible with the expected Standard Model background.Exclusion limits are placed on the bottom-squark mass at the 95% confidence level.For ( χ0 2 ) ranging from 130 GeV to 180 GeV, bottom-squark masses below 775 GeV to 850 GeV are excluded.This extends significantly beyond the reach of a previous ATLAS search [22], which was performed in final states with -jets and large  miss T , in this challenging region of parameter space.

1 hFigure 1 :
Figure 1: Simplified model of bottom-squark pair production and the decay chain targeted by this analysis.
or single-jet triggers as described in Section 6.The -jet and muon objects reconstructed by the trigger algorithms are required to geometrically match the corresponding reconstructed analysis objects defined in Section 4, otherwise the event is discarded.The HLT threshold of the  miss T trigger increased from 70 to 110 GeV over the data-taking period.The  miss T + -jet trigger had HLT thresholds of 60 GeV on  miss T and 80 GeV on the transverse momentum of the -jet, and the efficiency of the online -jet identification algorithm determined for simulated  t events was 60% in 2016 and 50% in 2017 and 2018.This trigger increases the acceptance for low- miss T signals expected from low-mass bottom squarks.The dataset associated with the  miss T + -jet trigger has a reduced integrated luminosity of 127 fb −1 because this trigger was not active in 2015, and stricter data-quality requirements are applied to -jet triggers in 2016 and 2017 to ensure a valid beam-spot determination.
−6 at ( b) = 250 GeV and (χ02 ) = 150 GeV and 1.4 • 10 −3 at ( b) = 900 GeV and ( χ0 2 ) = 150 GeV, taking into account the Higgs boson and -lepton branching ratios, the SR acceptance, and particle reconstruction and identification efficiencies.The requirement responsible for the largest decrease in signal acceptance is the presence of two hadronically decaying -leptons in the final state.

Figure 2 : 2 )
Figure 2: Kinematic distributions of data and SM background for events that pass the preselection and have at least two hadronically decaying -leptons.Predictions from three signal models are also shown, where the masses ( b) and ( χ0 2 ) are given in GeV in the legend.Distributions are displayed for the (a)  T , (b) ( 1 ,  2 ) and (c)  T2 variables.The hatched band indicates the total statistical and systematic uncertainty of the SM background.The "Other" contribution includes all the backgrounds not explicitly listed in the legend (+jets except  ()+jets, diboson/triboson, multĳet).The top-quark and  () background contributions are scaled with the normalization factors obtained from the background-only fit described in Section 6.The rightmost bin includes the overflow.The bottom panel shows the ratio of the observed data and the expected Standard Model background.

Figure 3 :
Figure 3: Schematic representation of the control region setup that is used to constrain the normalization of the (a) top-quark and (b)  ()+jets backgrounds in the signal regions.The arrows represent the transfer factors associated with the replacement of muons with true -leptons, which correct for acceptance.For the top-quark background, the sketch illustrates the normalization strategy for the  true  true contribution.A similar strategy is employed for the  true  fake contribution, where the  fake can originate from a jet from a hadronically decaying  boson, a -jet, or a jet from initial-state radiation.

Figure 4 :
Figure 4: Kinematic distributions from the four control regions associated with the top-quark background, showing (a)  miss T in CR_Top_µ true , (b)  T () in CR_Top_µ fake , (c)  T (jet 1 ) in CR_Top_µ, and (d)   T in CR_Top_ true .The hatched band indicates the total statistical and systematic uncertainty of the SM background.The top-quark and  () background contributions are scaled with the normalization factors obtained from the background-only fit.The "Other" contribution includes all the backgrounds not explicitly listed in the legend (+jets,  t , diboson/triboson, multĳet).The rightmost bin includes the overflow.The bottom panel shows the ratio of the observed data and the expected Standard Model background.

Figure 5 :
Figure5: The upper panel shows the expected number of SM background events and the number of events observed in data for each of the four validation regions.In the lower panel, the significance of the deviation of the observed yield from the expected yield is shown.The top-quark,  () and  () background contributions are scaled with the normalization factors obtained from the background-only fit described in Section 6.The hatched band indicates the total statistical and systematic uncertainty of the SM background.The "Other" contribution includes all the backgrounds not explicitly listed in the legend (+jets except  ()+jets,  t , diboson/triboson, multĳet).

Figure 6 :
Figure 6: Kinematic distributions from the four validation regions, showing (a) Θ min in VR_Top_, (b)  T2 in VR_Top_µ fake , (c)  T2 in VR_Top_µ true , (d) Θ min in VR_Top_µ true , (e)  T ( 1 ,  2 ) in VR_Z_µµ2b, (f)  T in VR_Z_µµ2b.The hatched band indicates the total statistical and systematic uncertainty of the SM background.The top-quark and  () background contributions are scaled with the normalization factors obtained from the background-only fit.The "Other" contribution includes all the backgrounds not explicitly listed in the legend (+jets,  t , diboson/triboson, multĳet).The rightmost bin includes the overflow.The bottom panel shows the ratio of the observed data and the expected Standard Model background.

Figure 7 : 2 )
Figure 7: Comparison of the expected and observed event yields in the signal regions defined in Table 2.The top-quark and  () background contributions are scaled with the normalization factors obtained from the background-only fit.The "Other" contribution includes all the backgrounds not explicitly listed in the legend (+jets except  ()+jets, diboson/triboson, multĳet).The hatched band indicates the total statistical and systematic uncertainty of the SM background.The contributions from three signal models to the signal regions are also displayed, where the masses ( b) and ( χ0 2 ) are given in GeV in the legend.The lower panel shows the significance of the deviation of the observed yield from the expected background yield.

Table 2 :
Definition of the single-bin and multi-bin signal regions.The requirements are applied in addition to the preselection from Table1.The single-bin and multi-bin SRs only differ by the Θ min requirement.

Table 3 :
Definition of the control regions used for the top-quark background.The requirements are applied in addition to the preselection.A dash means that no requirement on this variable is applied.CR_Top_µ CR_Top_ true CR_Top_µ true CR_Top_µ fake

Table 4 :
Definition of the control regions used for the +jets background.The requirements are applied in addition to the set of preselection criteria reported in the upper part of Table1.A dash means that no requirement on this variable is applied.-leptonsfrom Monte Carlo simulation are respectively multiplied by normalization factors   true and   fake , that float freely in the fit and are constrained by data mainly through CR_Top_µ true and CR_Top_µ fake .

Table 5 :
Values of normalization and transfer factors with their statistical and systematic uncertainties as obtained from the background-only fit, in the top part of the table for top-quark background processes, and in the bottom part for +jets.The control regions that primarily affect the normalization factors are listed, together with the purity of the CR in the relevant background process.As TF Top and TF  are ratios of two normalization factors, one of which (the denominator) is listed in the row directly above, the table lists the respective second control region (the numerator of the ratio) and its purity in top-quark or  () +  b events.
T is again required to be within [600, 1000] GeV.From these two auxiliary control regions, the freely floating normalization factor  Zµµ0b and transfer factor TF  ≡  Z 0b / Zµµ0b are derived in the background fit.The background normalization in CR_Z_µµ0b is absorbed into  Zµµ0b .The transfer factor TF  transfers the normalization from CR_Z_µµ0b to CR_Z_0b, and from CR_Z_µµ2b to the SRs, i.e.  () +  b events in the SRs are scaled by  Zµµ2b • TF  .

Table 7 :
The observed event yields in data, the total expected yields from SM processes obtained from the backgroundonly fit and breakdown of individual contributions, and the expected signal contributions for three benchmark models are shown for the single-bin signal region and the three bins of the multi-bin signal region.Total uncertainties combining the statistical and systematic uncertainties are quoted for the background processes.For the signal, the quoted uncertainties are only statistical."Other" combines all SM background contributions that are not listed explicitly, covering +jets except for  ()+jets, multĳet, diboson and triboson contributions.The dash means that no events pass the selection.