Search for massive, long-lived particles using multitrack displaced vertices or displaced lepton pairs in pp collisions at √s = 8 TeV with the ATLAS detector

Many extensions of the Standard Model posit the existence of heavy particles with long lifetimes. This article presents the results of a search for events containing at least one long-lived particle that decays at a significant distance from its production point into two leptons or into five or more charged particles. This analysis uses a data sample of proton-proton collisions at ﬃﬃﬃ s p ¼ 8 TeV corresponding to an integrated luminosity of 20 . 3 fb − 1 collected in 2012 by the ATLAS detector operating at the Large Hadron Collider. No events are observed in any of the signal regions, and limits are set on model parameters within supersymmetric scenarios involving R -parity violation, split supersymmetry, and gauge mediation. In some of the search channels, the trigger and search strategy are based only on the decay products of individual long-lived particles, irrespective of the rest of the event. In these cases, the provided limits can easily be reinterpreted in different scenarios.


I. INTRODUCTION
Several extensions to the Standard Model (SM) predict the production at the Large Hadron Collider (LHC) of heavy particles with lifetimes of order picoseconds to nanoseconds (e.g., see Ref. [1] and references therein).At the LHC experiments, the decay of a long-lived particle (LLP) with lifetime in this range could be observed as a displaced vertex (DV), with daughter particles produced at a significant distance from the interaction point (IP) of the incoming proton beams.One such scenario is supersymmetry with R-parity violation (RPV) [2,3].The present (largely indirect) constraints on RPV couplings allow the decay of the lightest supersymmetric particle (LSP) as it traverses a particle detector at the LHC.In general gauge-mediated supersymmetry breaking (GGM) scenarios [4], the next-to-lightest supersymmetric particle (NLSP) decays into an SM particle and the LSP, which is a very light gravitino.The NLSP width is suppressed by the large supersymmetrybreaking scale, and may be such that its decay leads to the formation of a DV.Within split supersymmetry [5,6], gluino decay is suppressed by the high mass of the squarks.Long-lived gluinos then hadronize into heavy "R-hadrons" that may decay at a detectable distance from their production point.Additional scenarios with LLPs include hidden-valley [7], dark-sector gauge bosons [8], and stealth supersymmetry [9].Some of the models are disfavored [10] by the recent observation of a Higgs boson at m H ≈ 125 GeV [11,12].
This article presents the results of a search for DVs that arise from decays of long-lived, heavy particles, at radial distances of millimeters to tens of centimeters from the proton-proton IP in the ATLAS detector at the LHC.Two types of signatures are considered.In the dilepton signature, the vertex is formed from at least two lepton candidates (with "lepton" referring to an electron or a muon), with opposite electric charges.In the multitrack signature, the DV must contain at least five chargedparticle tracks.This signature is divided into four dif-ferent final states, in which the DV must be accompanied by a high-transverse-momentum (high-p T ) muon or electron candidate that originates from the DV, jets, or missing transverse momentum (E miss T ).These signatures are labeled DV+muon, DV+electron, DV+jets, and DV+E miss T , respectively.In all signatures, at least one DV is required per event.In all cases, the expected background is much less than one event.
The multitrack results improve on the previous ATLAS searches for this signature [13,14] in several ways.The LHC center-of-mass energy is increased to 8 TeV, and the integrated luminosity is more than four times larger.While the previous search required only a high-p T muon trigger, the current search also uses high-p T electron, jets, or E miss T triggers.Furthermore, the detector volume used for the search has been enlarged by more than a factor of three.This is the first search for high-mass, displaced lepton pairs at ATLAS.A previous ATLAS search [15] considered pairs of muons that were highly collimated due to the low mass of the decaying particle.ATLAS has also searched for long-lived particles that decay inside the hadronic calorimeter [16,17], the inner detector or the muon spectrometer [18], or that traverse the entire detector [19].
Related searches have been performed at other experiments.The CMS Collaboration has searched for decays of a long-lived particle into a final state containing two electrons, two muons [20,21], an electron and a muon [22], or a quark-antiquark pair [23].The LHCb Collaboration has searched for long-lived particles that decay into jet pairs [24].The Belle Collaboration has searched for long-lived heavy neutrinos [25], and the BABAR Collaboration has searched for displaced vertices formed of two charged particles [26].The D0 Collaboration has searched for displaced lepton pairs [27] and b b pairs [28], and the CDF Collaboration has searched for long-lived particles decaying to Z bosons [29].LLPs have also been searched for by the ALEPH Collaboration at LEP [30].
This article is organized as follows.First the ATLAS detector and event samples used are described in Secs.II and III, respectively.The event reconstruction and vertex selection criteria are given in Sec.IV, while the signal efficiency is detailed in Sec.V.The background estimation is given in Sec.VI, with the systematic uncertainties on background and signal in Sec.VII.Finally, the search results are given in Sec.VIII, along with their interpretations in various supersymmetric scenarios.

II. THE ATLAS DETECTOR
The ATLAS experiment [31][63] is a multipurpose detector at the LHC.The detector consists of several layers of subdetectors.From the IP outwards there is an inner tracking detector (ID), electromagnetic and hadronic calorimeters, and a muon spectrometer (MS).
The ID is immersed in a 2 T axial magnetic field, and extends from a radius of about 45 mm to 1100 mm and to |z| of about 3100 mm.It provides tracking and vertex information for charged particles within the pseudorapidity region |η| < 2.5.At small radii, silicon pixel layers and stereo pairs of silicon microstrip detectors provide high-resolution position measurements.The pixel system consists of three barrel layers, and three forward disks on either side of the IP.The barrel pixel layers, which are positioned at radii of 50.5 mm, 88.5 mm, and 122.5 mm are of particular relevance to this work.The silicon microstrip tracker (SCT) comprises four double layers in the barrel, and nine forward disks on either side.The radial position of the innermost (outermost) SCT barrel layer is 30.3 cm (52.0 cm).A further tracking system, a transition-radiation tracker (TRT), is positioned at larger radii, with coverage up to |η| = 2.0.This device has two hit thresholds, the higher of which is used to assist in the identification of electrons through the production of transition radiation within the TRT.
The calorimeter provides coverage over the pseudorapidity range |η| < 4.9.It consists of a lead/liquid-argon electromagnetic calorimeter, a hadronic calorimeter comprising a steel and scintillator-tile system in the barrel region and a liquid-argon system with copper and tungsten absorbers in the endcaps.
The MS provides muon identification and contributes to the muon momentum measurement.This device has a coverage in pseudorapidity of |η| < 2.7 and is a threelayer system of gas-filled precision-tracking chambers.The pseudorapidity region |η| < 2.4 is additionally covered by separate trigger chambers, used by the hardware trigger for the first level of triggering (level-1).The MS is immersed in a magnetic field that is produced by a set of toroid magnets, one for the barrel and one each for the two endcaps.
Online event selection is performed with a three-level trigger system.It is comprised of a hardware-based level-1 trigger that uses information from the MS trigger chambers and the calorimeters, followed by two software-based trigger levels.

III. DATA AND SIMULATED EVENTS
The data used in this analysis were collected in 2012 at a pp center-of-mass energy of √ s = 8 TeV.After the application of detector and data-quality requirements, the integrated luminosity of the data sample is 20.3 fb −1 .The uncertainty on the integrated luminosity is ±2.8%.It is derived following the same methodology as that detailed in Ref. [32].With respect to the origin of the ATLAS coordinate system at the center of the detector, the mean position of the pp collision, averaged throughout the collected data sample is x = −0.3mm, y = 0.7 mm, z = −7.7 mm.The RMS spread of the z distribution of the collisions is σ z = 47.7 mm, and the spreads in the x and y directions are less than 0.1 mm.
Samples of simulated Monte Carlo (MC) events are used to study the reconstruction and trigger efficiency for signal events within RPV, split supersymmetry, and GGM scenarios.In each simulated event, two gluinos or two squarks are created in the pp collision.Both of these primary particles undergo decay chains described by the same set of effective operators.In the simulated GGM and RPV scenarios, the LLP is the lightest neutralino χ0 1 .In the split-supersymmetry scenario, the LLP is the gluino.Diagrams representing the simulated processes are shown in Fig. 1.
All samples are generated with the AUET2B ATLAS underlying-event tune [33] and the CTEQ6L1 parton distribution function (PDF) set [34].Events are generated consistently with the position of the pp luminous region and weighted so as to yield the correct z distribution of the collisions.Each generated event is processed with the Geant4-based [35] ATLAS detector simulation [36] and treated in the same way as the collision data.The samples include a realistic modeling of the effects of multiple pp collisions per bunch crossing observed in the data, obtained by overlaying additional simulated pp events generated using PYTHIA 8 [37], on top of the hard scattering events, and reweighting events such that the distribution of the number of interactions per bunch crossing matches that in the data.
In what follows, the notation P → A [L → F ] denotes an MC sample in which a primary particle P produced in the pp collision decays into a long-lived particle L and additional particles denoted A. The decay of the LLP into final state F is enclosed in square brackets.Samples where the primary particle is long-lived are denoted with [L → F ].In both cases, masses may be indicated with parentheses, as in [L(100 GeV) → F ].The symbol q indicates a u-or d-quark unless otherwise specified, and indicates an electron or a muon.Charge conjugation of fermions is to be understood where appropriate.
RPV samples of the type g → qq[ χ0 1 → ν] are produced with HERWIG++ 2.6.3 [38].Decays of the neutralino only into light leptons, which may be e + e − , The initial event selection is performed with a combination of triggers that require the presence of lepton candidates, jets, or E miss T .This selection is described in Sec.IV A.
Offline selection criteria for leptons, jets, and E miss T (see Sec. IV B) are used to further filter events for offline processing, as described in Sec.IV C.
Events satisfying the filter requirements undergo a CPU-intensive process termed "retracking", aimed at efficient reconstruction of tracks with large impact parameter (d 0 ) with respect to the transverse position of any primary vertex (PV) of particles formed from the pp collision.Retracking is described in Sec.IV D. At the final event-selection stage, events are first required to have a PV formed from at least five tracks and situated in the longitudinal range |z| < 200 mm, consistent with the IP.
The final selection is based on the reconstruction of a multitrack DV or dilepton DV, described in Secs.IV E and IV F, respectively.

A. Trigger requirements
Events must satisfy trigger requirements based on muon, electron, jets, or E miss T criteria.
Where muon triggers are used, a muon candidate is required by the trigger algorithm to be identified in the MS with transverse momentum p T > 50 GeV.Its pseudorapidity must be in the MS-barrel region |η| < 1.07, to reduce the trigger rate from fake muons due to beam background in the endcap region.
Photon triggers are used for channels requiring electron candidates, since the ID track of a high-d 0 electron may not be reconstructed.These require only a highenergy deposit in the electromagnetic calorimeter, and have no veto or selection based on ID tracks.Photon triggers provide significantly less background rejection than muon triggers.Therefore, the trigger used for final states involving electrons requires either a single photon candi-date with p T > 120 GeV or two photon candidates with p T > 40 GeV each.
The trigger requirement for the DV+E miss T search is E miss T > 80 GeV.The DV+jets trigger requires four jets with p T > 80 GeV, five jets with p T > 55 GeV, or six jets with p T > 45 GeV.

B. Offline object definition
The reconstruction and selection criteria for E miss T , muon, electron, and jet candidates are described in what follows.These object definitions are used by the offline filter (Sec.IV C) and the final analysis (Secs.IV E and IV F).

Muon selection
Muon candidates are required to be reconstructed in both the MS and the ID.The ID track associated with the muon candidate is required to have at least four SCT hits, but the number of required hits is reduced if the track crosses nonoperational sensors.Furthermore, the track must satisfy an |η|-dependent requirement on the number of TRT hits.No pixel hit requirement is applied to the muon-candidate track, which is different from the standard ATLAS muon-reconstruction algorithm [47].

Photon and electron selection
Photon and electron candidates are identified with criteria based on the fraction of the candidate energy deposited in the hadronic calorimeter and on the shape of the electromagnetic shower.In addition, electron candidates must be in the pseudorapidity region |η| < 2.47, and must satisfy requirements on the number of TRT hits associated with the ID track, the fraction of highthreshold TRT hits, and the pseudorapidity difference between the electron-candidate track and the associated calorimeter cluster.In contrast to the standard ATLAS electron-selection requirements [48], no requirement on the number of silicon hits is applied.Jet candidates are reconstructed using the anti-k t jet clustering algorithm [49,50] with a radius parameter R = 0.6.The inputs to this algorithm are the energies of clusters [51,52] of calorimeter cells seeded by those with energy significantly above the measured noise.Jet momenta are constructed by performing a four-vector sum over these cell clusters, treating each cell as a fourmomentum with zero mass.Jets are initially calibrated to the electromagnetic energy scale, which correctly measures the energy deposited in the calorimeter by electromagnetic showers [51].Further jet-energy scale corrections are derived from MC simulation and data, and used to calibrate the energies of jets to the scale of their constituent particles [51].Jets are required to satisfy |η| < 4.5 after all corrections are applied.
A special category of jets is termed "trackless" jets.These are reconstructed as above, except that the anti-k t radius parameter is R = 0.4, the jet pseudorapidity is in the range |η| < 2.5, and the scalar sum of the transverse momenta of the tracks in the jet is required to satisfy tr p T < 5 GeV.Trackless jets may arise from decays of LLPs that take place far from the PV, where trackreconstruction efficiency is low.
The measurement of the missing transverse momentum E miss T is based on the calibrated transverse momenta of all jet and lepton candidates, as well as all calorimeter energy clusters not associated with such objects [53,54].

C. Offline-filter requirements
Events are selected for retracking and subsequent offline analysis based on offline filters that require one of the following: • A muon candidate with p T > 50 GeV, an electron candidate with p T > 110 GeV, or a photon candidate with p T > 130 GeV.Electron candidates, and muon candidates that are associated with an ID track at this stage, are required to have |d 0 | > 1.5 mm.The sample selected by this criterion contains 8.5 × 10 6 events.
• A pair of candidate electrons, photons, or an electron-photon pair, with p T thresholds between 38 and 48 GeV per object, and electron impact parameter satisfying |d 0 | > 2.0 mm or |d 0 | > 2.5 mm depending on the channel.This criterion selects 2.4 × 10 6 events.
• Either two 50 GeV trackless jets and E miss T > 100 GeV (selecting 1.9×10 4 events), or one 50 GeV trackless jet and between four and six jets passing the same p T thresholds as those applied in the trigger, listed in Sec.IV A (selecting 4.6 × 10 5 events).

D. Retracking
In standard ATLAS tracking [31], several algorithms are used to reconstruct charged-particle tracks.In the silicon-seeded approach, combinations of hits in the pixel and SCT detectors are used to form initial track candidates (seeds) that are then extended into the TRT.Another algorithm starts from track segments formed of TRT hits, and extrapolates back into the SCT, adding any silicon hits that are compatible with the reconstructed trajectory.Both of these methods place constraints on the transverse and longitudinal impact parameters of track candidates that result in a low efficiency for tracks originating from a DV, many of which have large |d 0 |.
To recover some of these lost tracks, the siliconseeded tracking algorithm is rerun offline, using only hits that are not associated with existing tracks, for the events that satisfy the trigger and filter requirements (Secs.IV A and IV C).This retracking procedure is performed with the looser requirement |d 0 | < 300 mm and |z 0 | < 1500 mm.Furthermore, retracking requires a track to have at least five detector hits that are not shared with other tracks, while the corresponding requirement in standard silicon-seeded tracking is at least six hits.To reduce the rate of false seed tracks, it is required that these additional tracks have p T > 1 GeV, while the standard-tracking requirement is p T > 400 MeV.
The remainder of the analysis proceeds with both the standard-tracking tracks and retracking tracks.To realize the benefits of retracking for lepton candidates, the lepton-identification algorithms are rerun with the retracking tracks.

Multitrack vertex reconstruction
Tracks used for DV reconstruction must satisfy |d 0 | > 2 mm and p T > 1 GeV, and are required to have at least two SCT hits.
The tracks are rejected if they have no TRT hits and fewer than two pixel hits, in order to remove fake tracks.
The selected tracks are used to construct a multitrack DV by means of an algorithm based on the incompatibility-graph approach [55].
The algorithm starts by finding two-track seed vertices from all pairs of tracks.Seed vertices that have a vertex fit χ 2 of less than 5.0 (for one degree of freedom) are retained.If the seed vertex is inside the innermost pixel layer, both tracks must have a hit in this layer.If the vertex is between the first and second (second and third) pixel layers, both tracks must have a hit in either the second or third pixel layer (third pixel layer or the SCT).A seed vertex is rejected if any of its tracks has hits at radial positions smaller than that of the vertex.The interesting case of a charged LLP is not precluded by this selection, as the track formed by the LLP itself fails the |d 0 | > 2 mm requirement, and is therefore not included in the seed vertex.To ensure consistency between the position of the seed vertex and the direction p of the three-momentum vector of the seed-vertex tracks, the requirement d• p > −20 mm is applied, where d = r DV − r PV is referred to as the "distance vector" between the position of the DV and that of the first PV.The first PV is defined as the PV with the largest p 2 T , where the sum is over tracks associated with the PV.
Multitrack vertices are formed from combinations of seed vertices in an iterative process, as follows.If a track is assigned to several vertices, the vertex DV 1 with respect to which it has the largest χ 2 is identified.If this χ 2 is larger than 6, the track is removed from DV 1 .Otherwise, the algorithm finds the vertex DV 2 that has the smallest value of D/σ D , where D is the distance between DV 1 and DV 2 , and σ D is the estimated uncertainty on D. If D/σ D < 3, a single vertex is formed from all the tracks of both vertices.If this is not the case, the track is removed from DV 1 .This process continues until no track is associated with more than one vertex.Finally, vertices are combined and refitted if they are separated by less than 1 mm.No requirement is made on the total charge of the tracks forming a vertex.

Vertex selection
The reduced χ 2 of the DV fit is required to be smaller than 5.0.The DV position must be within the fiducial region r DV < 300 mm, |z DV | < 300 mm, where r DV and z DV are the radial and longitudinal DV positions with respect to the origin.To minimize background due to tracks originating from the PVs, the transverse distance ∆ xy = (x DV − x PV ) 2 + (y DV − y PV ) 2 between the DV and any of the PVs is required to be at least 4 mm.Here x and y are the transverse coordinates of a given vertex, with the subscripts PV and DV denoting the type of vertex.
DVs that are situated within regions of dense detector material are vetoed using a three-dimensional map of the detector within the fiducial region.The map is constructed in an iterative process, beginning with geometrically simple detector elements that are fully accounted for in the MC simulation.Subsequently, detailed structures, as well as the positioning and thickness of the simple elements, are obtained from the spatial distribution of vertices obtained from the data, taking advantage of the known φ periodicity of the detector to reduce statistical uncertainties.The vertices used to construct the map are required to be formed from fewer than five tracks, in order to avoid the signal region defined below.The invariant mass of these vertices, assuming massless tracks, must be greater than 50 MeV, to suppress vertices from photon conversions, which have low spatial resolution due to the small opening angle between the electrons, as well as electron scattering.Vertices arising from decays of K 0 S mesons are removed with an invariant-mass criterion.The transverse-plane projection of the positions of vertices that occur inside the material regions is shown in Fig. 2.
As the final step in multitrack DV selection, the number of tracks forming the DV is required to satisfy N tr ≥ 5, and the invariant mass m DV of all the tracks in the vertex to be greater than 10 GeV.In calculating m DV ,  The typical position resolution of the DV in the multitrack signal MC samples is tens of microns for r DV and about 200 µm for z DV near the IP.For vertices beyond the outermost pixel layer, which is located at a radius of 122.5 mm, the typical resolution is several hundred microns for both coordinates.

DV+lepton selection
In the DV+muon search, the muon candidate is required to have triggered the event and have transverse momentum p T > 55 GeV, which is well into the region where the trigger efficiency is approximately independent of the muon momentum.The muon candidate is further required to be in the pseudorapidity range |η| < 1.07 and have transverse impact parameter |d 0 | > 1.5 mm.A cosmic-ray muon traversing the entire ATLAS detector is reconstructed as two back-to-back muon candidates.To reject cosmic-ray background, events are discarded if they contain two muon candidates with ∆R cosmic = (π − ∆φ)) 2 − (η 1 + η 2 ) 2 ) < 0.04, where η 1 and η 2 are the pseudorapidities of the two reconstructed muon can-didates and ∆φ is their angular separation in the azimuthal plane.This has a negligible impact on the signal efficiency.
In the DV+electron search, the electron candidate is required to have triggered the event and satisfy p T > 125 GeV and |d 0 | > 1.5 mm.
To ensure that the lepton candidate is associated with the reconstructed DV, the distance of closest approach of the selected muon or electron candidate to the DV is required to be less than 0.5 mm.This requirement ensures that the reconstructed DV gave rise to the muon or electron candidate that triggered the event, and so the selection efficiency for each LLP decay is independent of the rest of the event.This facilitates a straightforward calculation of the event-selection efficiency for scenarios with different numbers of LLPs.The aforementioned selections are collectively referred to as the vertex-selection criteria.Events containing one or more vertices satisfying these criteria are accepted.The DV+jets selection requires one of the following: four jets with p T > 90 GeV; five jets with p T > 65 GeV; or six jets with p T > 55 GeV.All jets considered in these selection criteria are required to have |η| < 2.8.DV+jet candidate events are discarded if they contain any candidate jet failing to satisfy quality criteria designed to suppress detector noise and noncollision backgrounds [56,57].This has a negligible effect on the signal efficiency.In the DV+E miss T search, the requirement E miss T > 180 GeV is applied.For these selection criteria, the trigger efficiency is approximately independent of the E miss T and the jet transverse momenta.

F. Dilepton selection
In the dilepton search, muon candidates are required to have transverse momentum p T > 10 GeV, pseudorapidity |η| < 2.5, and transverse impact parameter |d 0 | > 2 mm.For electron candidates, the requirements are p T > 10 GeV and |d 0 | > 2.5 mm.A lepton candidate is discarded if its ID track is in the pseudorapidity region |η| < 0.02, where the background-estimation procedure is observed to be unreliable (see Sec. VI).
To avoid double counting of vertices, lepton candidates used to form a dilepton DV must not have the same ID track as another lepton candidate.If two muon candidates or two electron candidates do share an ID track, the candidate that has the lower transverse momentum is discarded.If muon and electron candidates share an ID track, the electron candidate is discarded.Cosmic-ray muons, even those that interact while traversing the detector, are rejected by requiring that all lepton-candidate pairs satisfy ∆R cosmic > 0.04.
A dilepton DV is formed from at least two oppositecharge tracks identified as two electrons, two muons, or an electron and a muon.Any number of additional tracks may be included in the vertex.At this stage, it is verified that the dilepton selection criteria applied at the trigger and filter level (See Secs.IV A and IV C) are satisfied by the two lepton candidates forming the DV.Finally, the dilepton DV is required to satisfy the DV selection criteria specified in Sec.IV E 2, except for the requirement on the number of tracks, which is N tr ≥ 2. As in the DV+lepton case, the dilepton-DV selection relies only on the leptons in the DV, and is independent of the rest of the event.

V. SIGNAL EFFICIENCY
In the dilepton and DV+lepton searches, where the selection criteria rely only on the particles produced in the DV, the vertex-level efficiency DV is defined to be the product of acceptance and efficiency for reconstructing one signal DV, produced in the given search model, with all the trigger, filter, and final selection criteria.The event-level efficiency ev defined as the probability for an event containing two DVs to be identified with at least one DV satisfying all the selection criteria, is then obtained from the relation where B is the LLP branching fraction into the specific search channel.In the DV+jets and DV+E miss T searches, only the event-level efficiency is defined, since the selection criteria involve the entire event.
The efficiency for reconstructing a multitrack or dilepton DV with the above selection criteria depends strongly on the efficiencies for track reconstruction and track selection, which are affected by several factors: (1) The number of tracks originating from the DV and their total invariant mass increase with the LLP mass.(2) More tracks fail the minimal-|d 0 | requirement for small r DV , or when the LLP is highly boosted.(3) The efficiency for reconstructing tracks decreases with increasing values of |d 0 |.(4) When an LLP decays at a radius somewhat smaller than that of a pixel layer, many tracks share hits on that pixel layer, failing to meet the track-selection criteria.The resulting impact on efficiency can be seen in Fig. 3 at radii around 45 mm, 80 mm and 115 mm.
The efficiency for reconstructing a multitrack DV is reduced when the LLP decays to charm or bottom hadrons, resulting in two or more nearby DVs.Each of these DVs has a high probability of failing to meet the N tr and m DV criteria, resulting in low efficiency if these DVs are not merged.This happens less at large values of r DV , where DVs are more readily merged due to the worse position resolution.
However, the nature of the primary particle determines the number of jets, and hence impacts the event-level efficiency in the DV+jets and DV+E miss T channels.
Examples of the impact of LLP boost, mass, and heavy-flavor decays on the vertex-level efficiency are shown in Fig. 3 for q → q[ χ0 1 → µqq] samples.The dips correspond to efficiency losses for decays occurring immediately before a pixel layer, where many tracks from the vertex have shared pixel hits and therefore fail to meet the track-selection criteria.
Events in each MC sample are generated with a fixed value of the LLP lifetime τ MC .To obtain the vertex-level efficiency for a different lifetime τ , each LLP is given a weight where t is the true proper decay time of the generated LLP.The vertex-level efficiency is then the sum of weights for LLPs that satisfy all the criteria in the sample.The same procedure is applied when calculating the event-level efficiency, except that the entire event is weighted by where t 1 and t 2 are the true proper decay times of the two LLPs in the event.Examples of the resulting dependence of DV and ev on the average proper decay distance cτ are shown in Fig. 4. For most models considered in this analysis, the peak efficiency is typically greater than 5%, and it occurs in the range 10 < ∼ cτ < ∼ 100 mm.

VI. BACKGROUND ESTIMATION
The expected number of background vertices is estimated from the collision data for each channel.Since the number of events satisfying the final selection criteria is very small, the general approach is to first obtain a high-statistical-precision assessment of the probability for background-vertex formation using a large data control sample.That probability is then scaled by the size of the signal-candidate sample relative to that of the control sample.

A. Multitrack-vertex background estimation
Background vertices that are due to accidental spatial crossing of tracks in a jet, particle interactions with material, or heavy-flavor decays have low values of m DV and/or N tr and thus fail the selection requirements.Such vertices may contribute to high-m DV , high-N tr background vertices via two mechanisms.
• The dominant source of backgrounds are low-m DV vertices that are accidentally crossed by an unrelated, high-p T track at large angle (O(1 radian)) to the other tracks in the vertex.This is referred to as the accidental-crossing background.
• A much smaller background contribution is due to merged vertices.In this case, two low-m DV vertices are less than 1 mm apart, and thus may be combined by the vertex-reconstruction algorithm into a single vertex that satisfies the N tr and m DV criteria.
The expected background levels from the two sources are estimated from the data.In order for the background estimate to have high statistical precision, it is performed with a large sample containing all events that have undergone retracking.This includes the events selected for this search, as described in Sec.IV C, as well as events used for other ATLAS analyses.The sample is divided into three subsamples, referred to as the muon stream, the electron stream, and the jets+E miss T stream, with the name indicating the type of trigger used to select the events.The background level is estimated separately in each of these streams with the methods described below, and the results are used for the DV+muon, DV+electron, and DV+jets and DV+E miss T signal regions, respectively.To obtain the final background estimate in the signal region, the background estimate in each stream is multiplied by a final-selection scale factor F stream , which is the fraction of events in the given stream that satisfy the final event-selection criteria, other than the DV selection criteria.The values of these fractions are 0.08%, 5.0%, 1.45%, and 0.04%, for the DV+muon, DV+electron, DV+jet, and DV+E miss T searches, respectively.This use of F stream assumes that the number of vertices per event is independent of the selection criteria.Based on the variation in F stream as the selection criteria are sequentially applied, an upward bias correction of 60% is applied to the estimated background level in the DV+electron channel (the correction is included in the 5.0% value quoted above), and a 10% systematic uncertainty is estimated for all channels.

Background from accidental vertex-track crossings
The accidental-crossing background is estimated separately in six radial regions, ordered from the inside out.Region 1 is inside the beampipe.Regions 2, 3, and 4 correspond to the volumes just before each of the three pixel layers.Regions 5 and 6 are outside the pixel layers.Region 5 extends outwards to r DV = 180 mm, where there is essentially no detector material, while Region 6 covers the volume from 180 < r DV < 300 mm.In each region, a study of the m DV distribution of N tr -track vertices, where N tr = 3 through 6, leads to identification of two types of background vertices, as follows.
The first type, which dominates the low-m DV range, is due to accidental track crossings in Region 1, and particle-material interactions in the other regions.This contribution to the m DV spectrum is referred to as collimated-tracks background, reflecting the typically small angle between the tracks.The m DV distribution P coll Ntr (m DV ) for this contribution is modeled from the N trtrack vertices for which the average three-dimensional angle between every pair of tracks is less than 0.5.In Fig. 5, P coll 3 (m DV ) is seen to fully account for 3-track vertices with m DV less than about 3 GeV.However, it does not account for vertices with higher masses, particularly the signal region, m DV > 10 GeV.
The high-m DV part of the m DV distribution is dominated by the second contribution, referred to as "DV+track".In this case, a (N tr − 1)-track vertex is crossed by an unrelated track at a large angle with respect to the momentum vector of the vertex tracks.To construct a model of the DV+track m DV distribution of N tr -track vertices, every (N tr − 1)-track vertex, referred to as an "acceptor" vertex, is paired with a "donated" track that is taken from a "donor" vertex in another event.This is done for N tr − 1 in the range 2 − 5, where acceptor vertices with five tracks are required to have mass below 10 GeV, to avoid the signal region.
The pairing of a vertex and a track is performed with the following procedure.The donor vertex must satisfy all the DV selection criteria, except that the requirement on its mass is not applied, and it may have as few as two tracks.To ensure that the donated track is able to accurately model the effects of a large-angle crossing, it is required that the donor vertex be from the same radial region as the acceptor vertex, and that there is a large angle between the direction of the donated track and the distance vector of the donor vertex.
In all regions apart from Region 1, the momentum vector of the donated track is then rotated, so that its azimuthal and polar angles with respect to the distance vector of the acceptor vertex match those that it originally had with respect to the donor vertex.
Then, the four-momentum of the acceptor vertex and the rotated four-momentum of the track are added, obtaining the m DV value of the N tr -track vertex that would have been formed from an accidental crossing of the acceptor vertex and the rotated donated track.The resulting m DV distribution for the N pairs DV+track pairs found in each region is denoted h Ntr (m DV ), such that Tracks from donor vertices in Region 1 are treated differently, since they tend to have high pseudorapidity, which impacts their DV-crossing probability more than their ∆η donor and ∆φ donor values.Therefore, a Region-1 track is not rotated before its four-momentum is added to that of the acceptor vertex.
The high-m DV distribution for N tr -track vertices is then modeled by where is the scale factor that normalizes the model to the data, and N 10 GeV The model describes the high-m DV background distribution in data well, as seen in Fig. 5 for jets+E miss T stream 3-track and 4-track vertices in Region 6.Also shown is the collimated-track contribution, which accounts for the low-m DV part of the distribution.Using 4-track vertices to validate Eq. ( 7), the prediction for each of the three streams and six regions is compared with the observed number of vertices.The comparison, summarized in Fig. 6, shows good agreement within the statistical precision.
The final numbers of expected background vertices, after multiplying N stream Ntr by the scale factor F stream , are shown in Table I.  7).In Region 1, the prediction includes the contribution from merging of two 2-track vertices (see Sec. VI A 2).The error bars on the prediction are too small to be visible, and in some bins no events are observed.

Background due to merged vertices
To estimate the background arising from merging of vertices, the distribution of the distance d 2DV between two 2-track or 3-track vertices is studied.Each of the selected vertices is required to satisfy the DV selection criteria of Sec.IV E 2 except the m DV and N tr requirements, and their combined mass is required to be greater than 10 GeV.To obtain a sufficient number of vertices for studying the d 2DV distribution, the distribution is reconstructed from a much larger sample of vertex pairs, where each vertex in the pair is found in a different events.This is referred to as the "model" sample.
To validate the d 2DV distribution of the model sample, it is compared to that of vertices that occur in the same event, referred to as the "same-event" sample.It is found that the z positions of vertices in the same event are correlated, since more vertices are formed in high-trackmultiplicity regions corresponding to jets.This effect is absent in the model sample.As a result, the distributions of the longitudinal distance between the vertices in the model and the same-event samples differ by up to 30% at low values of d 2DV .To correct for this difference, each vertex pair in the model sample is weighted so as to match the z component distribution of the sameevent sample.After weighting, the model distribution of the three-dimensional distance d 2DV agrees well with that of the same-event sample in the entire study range of d 2DV < 120 mm.This is demonstrated in Fig. 7 for pairs of 2-track vertices and for the case of a 2-track vertex paired with a 3-track vertex.
The background level for the analysis requirement of N tr ≥ 5 tracks is estimated from vertex pairs where one vertex has two tracks and the other has three tracks.The area under the model distribution in the range d 2DV < 1 mm yields a background prediction of 0.02±0.02events in each of the DV+lepton channels, and 0.03±0.03events in the DV+jets and DV+E miss T channels.After multiplication by F stream , this background is negligible relative to the accidental-crossing background, described in Sec.VI A 1. Background from the merging of two 3-track vertices or a 2-track and a 4-track vertex is deemed much smaller still.

B. Dilepton-vertex background estimation
Background DVs in the dilepton search may arise from two sources: • The dominant background is due to accidental spatial crossings of unrelated lepton candidates that happen to come close enough to satisfy the vertexreconstruction criteria.
• Minor backgrounds, due to tracks originating from the PV wrongly associated with a DV, decays of SM long-lived particles, or cosmic-ray muons.The levels of background from these sources are determined to be negligible relative to the accidentalcrossing background.

Background from accidental lepton crossing
The level of the accidental-crossing background is estimated by determining the crossing probability, defined as the probability for two unrelated lepton-candidate tracks to be spatially nearby and reconstructed as a vertex.Pairs of opposite-charge lepton candidates are formed, where each lepton candidate in a pair is from a different event and satisfies the lepton-selection criteria.The momentum vector of one of the two lepton candidates, selected at random, is rotated through all azimuthal angles by a step δφ.At each rotation step, the two lepton candidates are subjected to a vertex fit and the DV selection criteria.If the pair satisfies the selection criteria, it is assigned a weighted probability δφ/2π.Averaging the weighted probabilities over all pairs gives the probability for a lepton-candidate pair to accidentally form a vertex.The probability is observed to be independent of δφ for δφ < 0.03.To obtain the final background estimate, this probability is multiplied by the number N of data events containing two opposite-charge lepton candidates that satisfy the lepton-selection criteria.This procedure yields the background predictions shown in Table II.Compared with these predictions, the background level for a 3-track-vertex, where at least two of the tracks are lepton candidates, is negligible.
The validity of this method for estimating the number of dilepton DVs is verified in several ways.Using Z → µ + µ − and t t MC samples, the procedure is applied to vertices formed from two lepton candidates, a lepton candidate and another track, or two tracks that are not required to be lepton candidates.It is observed that the method correctly predicts the accidental-crossing background to within about 10%.The background-estimation method is tested also on pairs of tracks in the data, excluding pairs of lepton candidates, with a variety of se- e ± µ ∓ 2.4 ± 0.9 +0.8 lection criteria.The predicted and observed numbers of background vertices are again found to agree to within 10% for all selection criteria.The method also reproduces well the distributions of m DV , r DV , z DV , d • p, and the azimuthal angle between the two lepton candidates, in both MC simulation and data.As an example, Fig. 8 shows the m DV and r DV distributions observed for data vertices composed of two nonlepton tracks and the distributions predicted by pairing two tracks in different events.Some differences between the model and the data are seen at certain radii (e.g.r DV < 50 mm and 250 < r DV < 270 mm), but these do not substantially affect the total number of DVs and are covered by the assigned systematic uncertainty (see Sec. VII A 2).The prediction is accurate down to DV masses of 6 GeV, well below the DV selection criterion of 10 GeV.At smaller masses, contributions from other background sources become significant.

Minor backgrounds
Backgrounds from the following sources are found to be negligible relative to the accidental-crossing background, and are therefore neglected.
A potential source of background is prompt production of hard lepton pairs, notably from Z → + − decays.Requiring ∆ xy < 4 mm and removing the m DV > 10 GeV requirement yields no dilepton-vertex candidates, so the data show no evidence for prompt background.Therefore, MC simulation is used to estimate the probability for leptons originating from Z → + − decays to satisfy the minimum-|d 0 | requirements, the probability for such leptons to satisfy the vertex requirements, and the probability for a Z → + − event to pass the analysis kinematic requirements.Multiplying the product of these probabilities by the number of Z → + − events produced at AT-LAS yields an estimate of 10 −5 Z → µ + µ − events and 10 −4 Z → e + e − events in the ∆ xy < 4 mm sideband.Thus, the background from this source is negligible.
Background from cosmic-ray muons is studied with the ∆R cosmic distribution of the two highest-p T muon candidates in each event, which satisfy the selection criteria except the ∆R cosmic > 0.04 requirement.The distribution drops rapidly as ∆R cosmic increases, with the highest pair having ∆R cosmic = 0.014.The pairs that also satisfy the DV selection criteria constitute less than 7% of this sample and have a similar ∆R cosmic distribution, terminating at ∆R cosmic ∼ 0.0045.Therefore, it is concluded that the rate for cosmic-ray background muons satisfying the ∆R cosmic > 0.04 requirement is several orders of magnitude below the accidental-crossing background.In the case of a partially reconstructed cosmic-ray muon crossing a reconstructed lepton candidate from a pp collision, the two tracks are uncorrelated and any contribution to the background is already accounted for in the results shown in Table II.
Background from decays of known long-lived hadrons is studied from vertices in which only one track is required to be a lepton candidate.It is found to be negligible, due to the small probability for a hadron to be misidentified as a lepton candidate and the mass resolution of the detector.

VII. SYSTEMATIC UNCERTAINTIES AND CORRECTIONS
A. Background-estimation uncertainties

Multitrack DV background uncertainties
The choice of the m DV > 10 GeV mass range for determining the scale factor f (see Sec. VI A 1), as well as differences between the m DV distribution of the vertices and that of the model, are a source of systematic uncertainty on the background prediction.To estimate this uncertainty, f is obtained in the modified mass ranges m DV > 5 GeV and m DV > 15 GeV.The resulting 10% change in the background prediction for DVs passing the final selection requirements is used as a systematic uncertainty.An additional uncertainty of 10% is estimated from the variation of F stream as the selection criteria are varied (see Sec. VI A 1). Compared with these uncertainties, the uncertainty on the much smaller merged-vertex background level is negligible.

Dilepton background uncertainties
The background-estimation procedure for the dilepton search (see Sec. VI B 1) normalizes the background to the number N of events containing two lepton candidates that could give rise to a DV that satisfies the selection criteria.Contrary to the underlying assumption of the background estimation, the two lepton candidates may be correlated, impacting their probability for forming a high-m DV vertex.To study the impact of such correlation, N is recalculated twice, placing requirements on the azimuthal angle between the two lepton candidates, ∆φ , of 0.5 < ∆φ < π and 0 < ∆φ < π −0.5.The resulting variation yields the relative uncertainty estimates on N of +0% −54% , +19% −49% , and +13% −50% for the µ + µ − , e ± µ ∓ , and e + e − channels, respectively.
An uncertainty of 15% on the background prediction is estimated from the validation studies performed using MC simulation and data, described in Sec.VI B 1. The resulting systematic uncertainties are shown in Table II.

Trigger efficiency
The muon trigger efficiency is studied with a "tag-andprobe" method, in which the invariant-mass distribution of pairs of tracks is fitted to the sum of a Z → µ + µ − peak and a background contribution.To reduce the background, one of the muon candidates (the "tag") is required to be identified as a muon.The muon-trigger efficiency is determined from the fraction of Z → µ + µ − decays in which the other muon candidate (the "probe") satisfies the trigger criteria.Based on the results of this study in data and MC simulation, a correction of ∆ = −2.5% is applied to the MC-predicted trigger efficiency.A total uncertainty of σ = 1.7% is estimated by comparing the trigger efficiency as a function of the muon candidate p T in data and MC simulation, and by comparing the results of the tag-and-probe method with MC generator-level information.Similar studies of the trigger selections used for the electron channels lead to ∆ = −1.5% and σ = 0.8% for the p T > 120 GeV photon trigger, and ∆ = −0.5%,σ = 2.1% for the twophoton p T > 40 GeV trigger.The jets and E miss T triggers are fully efficient after the offline cuts.

Offline track-reconstruction efficiency
The uncertainty associated with the reconstruction efficiency for tracks that originate far from the IP is estimated by comparing the decay radius distributions for K 0 S mesons in data and MC simulation.The comparison is carried out with the ratio where i = 1, . . ., 4 labels four radial regions between 5 mm and 40 mm, and N data/MC i (K 0 S ) is the number of K 0 S mesons in radial region i in data/MC simulation, obtained by fitting the two-track mass distributions.The K 0 S candidates in MC are weighted so that their pseudorapidity and transverse-momentum distributions match those seen in the data.The ratio ρ i (K 0 S ) is constructed separately for the pseudorapidity regions |η| < 1 and |η| ≥ 1.The difference ∆ρ i (K 0 S ) = ρ i (K 0 S ) − ρ 1 (K 0 S ) quantifies the radial dependence of the data-MC discrepancy.The discrepancy is largest in the outermost radial region, with ∆ρ 4 (K 0 S ) = −0.03for |η| < 1 and ∆ρ 4 (K 0 S ) = −0.2 for |η| ≥ 1.To propagate this maximal discrepancy into a conservative uncertainty on the signal efficiency, DV daughter tracks are randomly removed from signal-MC vertices before performing the vertex fit.The single-track removal probability is taken to be ∆ρ 4 (K 0 S )/2 in each of the two pseudorapidity regions.The resulting change in the DV efficiency is taken as the tracking-efficiency systematic uncertainty.This uncertainty is evaluated separately for each value of cτ , and is generally around 1%.

Offline lepton-identification efficiency
The lepton-identification efficiency uncertainty is determined in ATLAS using Z → decays, and is typically less than 1%.For this analysis, an additional uncertainty associated with identification of high-|d 0 | leptons is evaluated.
For muons, this is done by comparing a cosmic-raymuon simulation to cosmic-ray muon candidates in data.The events are required to pass the muon trigger and to have two muon candidates that fail the muon veto (see Sec. IV B 1).The MC muons are weighted so that their η and φ distributions are in agreement with those of the data.Comparing the ratio of the muon candidate d 0 distributions in data and in MC simulation yields a d 0dependent efficiency correction that is between 1% and 2.5%, with an average value of 1.5%.The uncertainty associated with this procedure is taken from the statistical uncertainty, and is 2% on average.
Unlike in the case of cosmic-ray muons, there is no easily identifiable, high-rate source of large-|d 0 | electrons.Therefore, the performance of the simulation is validated by comparing the electron-identification efficiency e (z 0 ) as a function of the longitudinal impact parameter z 0 of the electron candidate in data and MC simulation, measured with the tag-and-probe method using Z → e + e − events.It is observed that e (z 0 ) is consistent in data and in MC simulation to better than 1% for |z 0 | < 250 mm, beyond which there are too few events for an accurate measurement.Furthermore, the value of e obtained with the tag-and-probe method is consistent to within 1% with that determined from MC generator-level information.This data-MC agreement in e (z 0 ) is taken as an indication that the d 0 dependence of the efficiency, e (d 0 ), is also well described by simulation.In signal MC samples, the function e (d 0 ) varies by about 10% due to kinematic correlations between d 0 and factors that affect the efficiency, such as the value of r DV and the boost of the LLP.To account for the possibility of an additional d 0 dependence that may not be well simulated, a systematic uncertainty of 10% on the electron-identification efficiency is assigned.The impact on the signal efficiency of uncertainties in the jet-energy scale calibration and jet-energy resolution are evaluated following the methods described in Ref. [57] and Ref. [58], respectively.An additional uncertainty on the jet p T is evaluated for jets that originate from the decay of an LLP, by linearly parameterizing the p T mismeasurement in MC simulation as a function of r DV and z DV .
The only significant dependence observed is a relative p T mismeasurement of (4 ± 1) × 10 −5 (r DV / mm), which is propagated to the jet-selection efficiency as a systematic uncertainty.To account for possible mismodeling of trackless jets, an uncertainty is obtained by varying the requirement on tr p T for these jets.Systematic uncertainties in the E miss T measurement are evaluated with the methods described in Refs.[53,54] and propagated to the efficiency uncertainty.The impact of uncertainties in the simulation of initial-state radiation is estimated by varying the p T distribution of the primary particles according to the distribution observed in MADGRAPH5 [59] samples.The resulting efficiency uncertainty varies between 2% and 10%.

Multiple pp interactions
The dependence of the reconstruction efficiency on the number of pp interactions per bunch crossing is studied by varying the average number of interactions per LHC bunch crossing in the simulation by 4%.This value reflects uncertainties in the detector acceptance, trigger efficiency, and modeling of additional pp interactions.The resulting relative uncertainty is typically of order 1% or less.

VIII. RESULTS
Fig. 9 shows the distribution of m DV versus the number of associated lepton candidates in the selected data sample before the final selection requirements on these variables are applied.The distributions of m DV versus the number of tracks in the vertex obtained for the multitrack-DV search are shown in Figs. 10 and 11.No events are seen in the signal region for any of the seven channels.In addition, no same-charge dilepton vertices are seen with m DV > 10 GeV.The distributions expected for some of the signal samples are also shown for comparison.
Given the lack of a signal observation, 95% confidencelevel upper limits on the total visible cross-section for new physics are shown in Table III.
Furthermore, for each of the physics scenarios considered, 95% confidence-level upper limits on the signal yields and production cross-sections are calculated for different values of the proper decay distance cτ of the LLP, and presented in the figures in this section.The limits are calculated using the CL S prescription [60] with the profile likelihood used as the test statistic, using the HistFitter [61] framework.Uncertainties on the signal efficiency and background expectation are included as nuisance parameters, and the CL S values are calculated by generating ensembles of pseudoexperiments corresponding to the background-only and signal-plus-background hypotheses.Since less than one background event is expected in all cases and no events are observed, the observed limits are very close to the expected limits.
In the case of the dilepton and DV+lepton searches, where the trigger and reconstruction depend almost exclusively on the signal DV, upper limits on the number of vertices produced in 20.3 fb −1 of data are presented for each channel, accounting for the vertex-level efficiency at each value of cτ .Fig. 12 shows these number limits for the DV+lepton search signatures.The limits are given separately for different masses of the long-lived neutralino and the primary squark or gluino, as well as for  shown in Fig. 13 for the final states ee, µµ, eµ, as well as for the combination of Z → ee, Z → µµ and Z → τ τ .
In addition, limits on the production cross-sections for events are presented for the different simulated scenarios.
Figures 14 and 15 show cross-section upper limits obtained with the dilepton-DV search.Upper limits are shown for gluino-pair production in the RPV scenario, with neutralino decays determined by the choice of nonzero RPV coupling λ 121 or λ 122 , as well as within the GGM scenario with leptonic decays of the Z boson.For example, the RPV scenario is excluded for gluino mass m g = 600 GeV, neutralino mass m χ0 1 = 400 GeV, and neutralino proper decay distance in the range 0.7 < cτ < 3 × 10 5 mm.
Cross-section upper limits obtained with the multitrack-DV search are shown in the remaining figures.These limits are calculated up to proper decay distances of cτ = 1 m, to avoid inaccuracies associated with reweighting events to very high lifetimes when the efficiency depends on both LLPs in the event.
Fig. 16 shows the upper limits on the production crosssection of two squarks in the RPV scenario, with different squark and neutralino masses, as well as different λ parameters governing the neutralino decay.These limits are obtained with the DV+jets search, which results in tighter limits than the DV+lepton searches for this scenario.These results exclude a m q = 1 TeV squark for m χ0 1 = 108 GeV and 2.5 < cτ < 200 mm with either light-or heavy-quark neutralino decays.Fig. 17 shows the cross-section upper limits for gluino-pair production within the GGM scenario, using hadronic Z decays.The scenario is excluded, for instance, for m g = 1.1 TeV and m χ0 1 = 400 GeV in the proper decay distance range 3 < cτ < 500 mm.Fig. 18 shows the upper limits on gluino-pair production cross-section in the split-supersymmetry model.These limits are obtained from the results of the DV+E miss T and DV+jets searches.The sensitivity is greater for the cases with m χ0 1 = 100 GeV than for those with m χ0 1 = m g − 480 GeV, and the DV+E miss T search performs better than DV+jets in these scenarios, excluding m g < 1400 GeV in the range of proper decay lengths 15 mm < cτ < 300 mm.
In Figs.19 and 20, the region of gluino mass vs. proper decay distance that is excluded by these limits is shown.The limit for each point in parameter space is taken from the channel that is expected to yield the most stringent limit, which is DV+E miss T for most points.For the region of parameter space where the sensitivity is greatest, 20 mm < cτ < 250 mm and m χ0 1 = 100 GeV, gluino masses of m g < 1500 GeV are excluded.This range of masses is comparable or slightly larger than those excluded by prompt searches [62], searches for long-lived R-hadrons stopped in the ATLAS calorimeter [17], or searches for stable, massive, charged particles [19].
[mm] τ c FIG. 14: 95% confidence-level upper limits, obtained from the dilepton search, on the production cross-section for a pair of gluinos of different masses that decay into two quarks and a long-lived neutralino in different models: (a) the RPV scenario with a pure λ121 coupling, (b) the RPV scenario with a pure λ122 coupling.All relevant final-state lepton-flavor combinations are used.The shaded bands around the observed limits indicate ±1σ variations in the expected limit, while the horizontal bands show the theoretical cross-sections and their uncertainties.In some cases limits are terminated for cτ < ∼ 1 mm due to limited statistical precision.
[mm] τ c    95% confidence-level excluded regions lie below the curves shown in the mass-vs-cτ plane for the splitsupersymmetry samples, with the gluino decaying into a gluon or light quarks, plus a 100 GeV neutralino.The shaded bands indicate ±1σ variations in the expected limit, while the dotted lines indicate the effect of varying the production cross-section by one standard deviation.The expected and observed limits are identical.95% confidence-level excluded regions lie below the curves shown in the mass-vs-cτ plane for the splitsupersymmetry samples, with the gluino decaying into (a) a top quark pair and a 100 GeV neutralino, or (b) a top quark pair and a neutralino with a mass that is 480 GeV smaller than the gluino mass.The shaded bands indicate ±1σ variations in the expected limit, while the dotted lines indicate the effect of varying the production cross-section by one standard deviation.The expected and observed limits are identical.

IX. SUMMARY AND CONCLUSIONS
This article reports on a search for long-lived particles decaying into two leptons or five or more charged particles.In the latter case, events are selected using associated lepton candidates, jets or missing transverse momentum.The main signature of the search is a displaced vertex with an invariant mass greater than 10 GeV.The search uses a data sample of pp collisions obtained by the ATLAS detector at the LHC with a center-of-mass energy of √ s = 8 TeV and an integrated luminosity of 20.3 fb −1 .Less than one background event is expected in each of the channels, and no events are observed.Upper limits are provided on the number of long-lived particle decays in the data sample and on the cross-section for production of particles that give rise to the search signatures in a variety of supersymmetric models.

FIG. 1 :
FIG. 1: Diagrams representing some of the processes under study, corresponding to the simulated event samples.In RPV scenarios, the long-lived neutralino may decay via the (a) λ ijk or (b) λ ijk couplings.(c) Long-lived neutralino decay in a GGM scenario.(d) Long-lived R-hadron decay in a split-supersymmetry scenario.The quarks and leptons shown may have different flavors.Filled circles indicate effective interactions.

3 .
Jet and E miss T selection

FIG. 2 :
FIG.2: Transverse-plane density (in arbitrary units) of vertices with fewer than five tracks in material regions that are excluded by the material veto in the region |z| < 300 mm.The innermost circle corresponds to the beampipe.This is surrounded by the three pixel layers.The octagonal shape and outermost circles are due to support structures separating the pixel and SCT detectors.
each track is taken to have the mass of the charged pion.Candidate vertices that pass (fail) the m DV > 10 GeV requirement are hereafter referred to as being high-m DV (low-m DV ) vertices.

4 .
DV+jets and DV+E miss T selection
FIG. 4: (a) The event-level efficiency as a function of cτ for split-supersymmetry [g → g/qq χ0 1 (100 GeV)] samples with various gluino masses, reconstructed in the DV+E miss T channel.(b) The vertex-level efficiency for the RPV g → qq[ χ0 1 → eµν] samples with combinations of gluino and neutralino masses, reconstructed in the eµ dilepton channel.The total uncertainties on the efficiencies are shown as bands (see Sec. VII).

3P
is the number of 3-track vertices with m DV > 10 GeV.The model-predicted number of N trtrack background vertices with m DV > 10 GeV for a given stream and region is given by Ntr (m DV )dm DV .

FIG. 5 : 29 FIG. 6 :
FIG. 5:The mass distribution for (a) 3-track and (b) 4-track vertices (data points) from the jets+E miss T stream in Region 6, overlaid with the model f h3(mDV) of Eq. (5) (yellow-shaded histogram) at high mass.The lower panel of each plot shows the ratio of the data to this model.The model for the collimated-track contribution P coll

FIG. 7 :
FIG. 7: The distribution of the distance d2DV between (a) two 2-track vertices and (b) a 2-track vertex and a 3-track vertex with a combined mass above 10 GeV for the jets+E miss T stream data (data points) and in the model sample, in which the two vertices are in different events (histogram).A conservative 100% uncertainty on the model is shown in the data/model ratio plot.The inset shows the d2DV distance up to values of 120 mm.The merged-vertex background estimate is determined from the area under the model distribution in the range d2DV < 1 mm in (b).

FIG. 8 :
FIG.8: Distributions of the (a) vertex mass and (b) vertex position radius for vertices composed of two nonlepton tracks in the data sample (data points), and the predicted model distribution obtained from vertices formed by combining tracks from two different data events (shaded histograms).The ratio of the data to the model distributions is shown below each plot.The gray bands indicate the statistical uncertainties for the predicted distributions.The inset shows the mass distribution in the low-mass region, elsewhere mDV > 10 GeV is required.In (a), the highest bin shows the histogram overflow.

4 .
Jets and E miss T reconstruction

FIG. 9 :
FIG. 9:The distribution of dilepton-vertex candidates in terms of the vertex mass versus the number of lepton candidates in the vertex, in the (a) µ + µ − , (b) e ± µ ∓ , and (c) e + e − search channels.The data distributions are shown with red ovals, the area of the oval being proportional to the logarithm of the number of vertex candidates in that bin.The gray squares show the g(600 GeV) → qq[ χ0 1 (50 GeV) → µµν/eµν/eeν] signal MC sample.The shape of the background mDV distribution arises partly from the lepton-candidate pT requirements.The signal region defined by the two-lepton and mDV > 10 GeV requirements is indicated.

FIG. 10 :FIG. 11 :
FIG. 10:The distribution of (a) DV+muon and (b) DV+electron candidates in terms of the vertex mass versus the number of tracks in the vertex.The data distribution is shown with red ovals, the area of each oval being proportional to the logarithm of the number of vertex candidates in that bin.The gray squares show the q(700 GeV) → q[ χ0 1 (494 GeV) → qq] RPV signal MC sample.The signal region Ntr ≥ 5, mDV > 10 GeV is indicated.

FIG. 12 :
FIG. 12: RPV-scenario upper limits at 95% confidence level on the number of neutralinos in 20.3 fb −1 that decay into (a) µqq (with q indicating a u-or d-quark), (b) µqb and µcb (indicated by the nonzero RPV couplings λ 213 and λ 223 , respectively), (c) eqq, and (d) eqb and ecb (λ 113 and λ 123 , respectively).The upper limits account for the vertex-level efficiency for each value of the neutralino proper decay distance cτ .The different curves show the results for different masses of the primary gluino or squark and of the long-lived neutralino, while the shaded bands indicate ±1σ variations in the expected limit.

FIG. 13 :
FIG.13: Upper limits at 95% confidence level on the number of neutralinos in 20.3 fb −1 that decay into (a) eeν in the RPV model, (b) eµν in the RPV model, (c) µµν in the RPV model, and (d) Z G in the GGM model.The upper limits account for the vertex-level efficiency for each value of the neutralino proper decay distance cτ .The different curves show the results for different masses of the primary gluino and of the long-lived neutralino, while the shaded bands indicate ±1σ variations in the expected limit.In some cases limits are terminated for cτ < ∼ 1 mm due to limited statistical precision.

FIG. 15 :FIG. 16 :
FIG.15: 95% confidence-level upper limits, obtained from the dilepton search, on the production cross-section for a pair of gluinos of mass 1.1 TeV that decay into two quarks and a long-lived neutralino in the GGM scenario for two values of the neutralino mass..For further details see Fig.14.

FIG. 17 :
FIG. 17: 95% confidence-level upper limits, obtained from the (a) DV+E miss T and (b) DV+jets searches, on the production cross-section for a pair of gluinos of mass 1.1 TeV that decay into two quarks and a long-lived neutralino in the GGM scenario.For further details see Fig.14.

FIG. 18 :
FIG. 18: 95% confidence-level upper limits, obtained from the (a, c, e) DV+E miss T and (b, d, f) DV+jets searches, on the cross-section for gluino pair production in the split-supersymmetry model, with the gluino decaying to a neutralino plus either (a, b) a gluon or a light-quark pair or (c, d, e, f) a pair of top quarks.The mass of the neutralino is 100 GeV in (a, b, c, d) and is 480 GeV smaller than the gluino mass in (e, f).For further details see Fig. 14.
FIG. 19:95% confidence-level excluded regions lie below the curves shown in the mass-vs-cτ plane for the splitsupersymmetry samples, with the gluino decaying into a gluon or light quarks, plus a 100 GeV neutralino.The shaded bands indicate ±1σ variations in the expected limit, while the dotted lines indicate the effect of varying the production cross-section by one standard deviation.The expected and observed limits are identical.
FIG. 20:95% confidence-level excluded regions lie below the curves shown in the mass-vs-cτ plane for the splitsupersymmetry samples, with the gluino decaying into (a) a top quark pair and a 100 GeV neutralino, or (b) a top quark pair and a neutralino with a mass that is 480 GeV smaller than the gluino mass.The shaded bands indicate ±1σ variations in the expected limit, while the dotted lines indicate the effect of varying the production cross-section by one standard deviation.The expected and observed limits are identical.

TABLE II :
Estimated numbers of background vertices satisfying all of the dilepton signal selection criteria, arising from random combinations of lepton candidates.In each entry, the first uncertainty is statistical, and the second is systematic (see Sec. VII).

TABLE III :
Model-independent 95% confidence-level upperlimits on the visible cross-section for new physics in each of our searches.