Search for long-lived neutral particles produced in $pp$ collisions at $\sqrt{s} = 13$ TeV decaying into displaced hadronic jets in the ATLAS inner detector and muon spectrometer

A search is presented for pair-production of long-lived neutral particles using 33 fb$^{-1}$ of $\sqrt{s} = 13$ TeV proton-proton collision data, collected during 2016 by the ATLAS detector at the LHC. This search focuses on a topology in which one long-lived particle decays in the ATLAS inner detector and the other decays in the muon spectrometer. Special techniques are employed to reconstruct the displaced tracks and vertices in the inner detector and in the muon spectrometer. One event is observed that passes the full event selection, which is consistent with the estimated background. Limits are placed on scalar boson propagators with masses from 125 GeV to 1000 GeV decaying into pairs of long-lived hidden-sector scalars with masses from 8 GeV to 400 GeV. The limits placed on several low-mass scalars extend previous exclusion limits in the range of proper lifetimes $c \tau$ from 5 cm to 1 m.


Introduction
Long-lived particles (LLPs) are predicted by many extensions of the Standard Model (SM), including various supersymmetric (SUSY) [1][2][3][4], hidden sector (HS) [5][6][7] and neutral naturalness [8][9][10] models that address the hierarchy problem. Decays of LLPs may go unnoticed in searches at collider experiments that are designed to identify promptly decaying particles. Searches for LLPs provide a promising avenue for the discovery of physics beyond the Standard Model (BSM). The search presented in this paper is sensitive to neutral LLPs that are pair-produced, with one LLP decaying in the ATLAS inner tracking detector (ID) and the other in the muon spectrometer (MS). This particular event topology provides sensitivity to LLPs with proper lifetimes (cτ) ranging from a few centimeters to several meters.
In HS models, a set of BSM particles is weakly coupled to the SM via a mediator particle. These models are intriguing because they can be built in multiple ways and can produce LLPs with little to no fine-tuning [6]. A SM Higgs boson mediator is of particular interest because the current experimental characterization of the Higgs boson allows sizable couplings of the Higgs boson to the BSM sector [11,12]. HS models are also compatible with SUSY [6,13] and with models of neutral naturalness [14]. The results of this search are interpreted in the context of a simplified HS model, in which the SM and HS are connected via a heavy mediator Φ, which decays into a pair of long-lived neutral scalar particles s as shown in Figure 1. The s-bosons then decay back into SM particles through their mixing with the mediator [15]. The HS model assumes an effective Yukawa coupling between the s-boson and the SM particles; therefore each s-boson decays primarily into a heavy fermion pair: bb, cc, τ + τ − . The branching ratio depends on the mass of the s-boson (m s ), but for m s > 25 GeV, the branching ratio is approximately 85:5:8.1 If the SM particles are quarks, they hadronize, resulting in jets that may be highly displaced from the interaction point (IP). The proper lifetime of the s-boson is relatively unconstrained aside from the upper limit imposed by Big Bang nucleosynthesis of cτ 10 8 m [18]. Two searches for displaced decays resulting from neutral LLPs in the HS model have been performed using the ATLAS Run 2 dataset. One analysis searched for pairs of displaced hadronic jets in the calorimeter [16] (the CR analysis) and the other searched for one or two displaced hadronic jets in the MS [17] (the MS analysis). For a SM Higgs boson mediator with m H = 125 GeV, decays of neutral scalars with masses between 8 and 55 GeV have been excluded by these two analyses for cτ between 7 cm and 220 m depending on the LLP mass (assuming a 10% branching ratio of the Higgs boson into ss pairs).
This analysis uses 33.0 fb −1 of √ s = 13 TeV proton-proton (pp) collision data collected by the ATLAS detector at the LHC and is an update to the results presented in the 8 TeV ATLAS search [21] for displaced hadronic jets in the ID and MS, and an extension of the MS analysis. In each event, one reconstructed decay vertex is required in the ID (IDVx) in addition to one in the MS (MSVx). Requiring the presence of an MSVx suppresses background, which allows looser selection requirements on the reconstructed mass and number of tracks associated with the IDVx than in other IDVx searches such as Ref. [28]. Additionally, requiring the presence of an IDVx suppresses background relative to the MS analysis, allowing greater sensitivity for LLPs with cτ < 1 m. This search thus increases the sensitivity to low-mass scalars with shorter proper lifetimes relative to the combined results of the CR and MS analyses published in Ref. [16].
hadronic endcap calorimeters that cover the region 1.5 < |η| < 3.2. A forward calorimeter using copper and tungsten absorbers with LAr completes the calorimeter coverage up to |η| = 4.9.
The MS consists of separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by superconducting air-core toroids. The muon tracking chamber system covers the region |η| < 2.7 with three layers of monitored drift tubes (MDT), complemented by cathode strip chambers (CSC) in the forward region. The MDT chambers consist of two multilayers, each of which consists of three or four layers of drift tubes. Three stations of resistive plate chambers (RPC) and thin gap chambers (TGC) are used for triggering and φ measurements in the MS barrel and endcaps, respectively. The muon trigger system covers the range |η| < 2.4.
The ATLAS detector selects events using a two-tiered trigger system [39]. The first level (L1), which is a hardware-based system, uses coarse data collected from the calorimeters and muon detectors to reduce the event rate from the LHC crossing frequency of 40 MHz to a design value of 100 kHz. The second level, known as the high-level trigger (HLT), is a software-based system that uses information from all of the ATLAS sub-detectors to reduce the rate of recorded events to approximately 1 kHz.

Data events
This analysis uses 33.0 fb −1 of data collected by the ATLAS detector during the 2016 data-taking period using pp collisions at √ s = 13 TeV. The analysis is performed using selected subsets of data which underwent special reconstruction of displaced tracks and vertices.
Two sets of data are used. One set consists of events that pass a signature-driven LLP trigger, referred to here as the Muon RoI Cluster trigger (described in Section 4). The Muon RoI Cluster trigger is used to collect events for the signal region; these events are also required to contain reconstructed displaced vertices in the MS and the ID, described in Sections 5 and 6. Events collected by the Muon RoI Cluster trigger are also used to define a validation region for the background estimation, as discussed in Section 7, in which case the event selection is agnostic to the presence of any reconstructed vertices in the MS.
The second set of data is used for the background estimation. Events are selected by a single-muon trigger that requires a muon with transverse momentum p T > 26 GeV at the HLT. To reduce the signal contamination, these events are also required to contain isolated muons. This requirement is further described in Section 7.
All of the events that pass the triggers used by the CR analysis [16], which select events with displaced hadronic jets decaying in the HCal, are vetoed in this analysis. This veto is imposed in order to facilitate the combination of the results of this search with the results of the CR and MS analyses (presented in Section 9).

Simulated events
The signal Monte Carlo (MC) samples were generated with a Φ mediator connecting the SM to a hidden sector in which Φ decays into pairs of long-lived neutral scalars ss. The neutral scalars s decay back into the SM via their coupling to the mediator, assuming a Yukawa coupling between the s-boson and the SM particles. The Φ → ss signal samples were generated using M G 5 [40]. Events were showered with P 8.210 [41] using the A14 set of tuned parameters (tune) [42] and the NNPDF2.3LO set [43] of parton distribution functions (PDF). Various mass points were generated corresponding to different combinations of the mass of the Φ (m Φ ) and m s , with m Φ ∈ [125, 1000] GeV and m s ∈ [8,400] GeV. The sensitivity of the analysis to models with s-boson mass smaller than 8 GeV is limited by the ID vertex reconstruction efficiency and selections to discriminate against vertices from background.
The LLP proper lifetime in each sample was tuned so that each mass point had an approximate mean lab-frame decay length of 5 m. The mean lab-frame decay length of 5 m is used so that there are approximately equal numbers of LLP decays in the ID and in the MS, and samples with this lab-frame decay length are used for the determination of the signal versus background selection for the IDVx, as well as the IDVx and overall efficiency studies. The overall efficiency for a range of proper lifetimes is estimated by reweighting the 5 m samples using an extrapolation method, as noted in Section 9. The LLP proper lifetimes for each mass point were also tuned to provide a set of samples with a mean lab-frame decay length of 9 m, and these samples are used to confirm the accuracy of the extrapolation method.
Multijet samples generated with P 8.186 are used to determine the systematic uncertainties (described in Section 8) in the displaced tracking and vertex reconstruction in the ID (described in Section 5). The A14 tune was used together with the NNPDF2.3LO PDF set.
The generated events for all MC samples described above were processed through a full simulation of the ATLAS detector geometry and response [44] using the G 4 [45] toolkit. To model the effect of multiple pp interactions per bunch crossing (pileup), additional simulated pp interactions were overlaid onto each simulated hard-scatter event. Pileup was simulated with P 8.186 using the A2 set of tuned parameters and the MSTW2008LO [46] PDF set. Per-event weights are applied to all simulated events such that the mean number of interactions per bunch crossing in simulation matches that in the data.

Trigger
Signal region events are selected with the Muon RoI Cluster trigger, which was developed to identify events with displaced hadronic decays outside the last active layer in the HCal [30].
Hadronic decays after the end of the HCal and before the first trigger plane in the MS are characterized by multiple muon regions of interest3 (RoIs) around the LLP line of flight. The trigger is seeded by an L1 trigger that searches for two RoIs in the MS each selecting a trajectory with p T > 10 GeV. At the HLT, the trigger requires clusters of muon RoIs, in which a cluster is defined as a ∆R = 0.4 region containing at least three (four) muon RoIs in the barrel (endcap) of the MS.
To correct for the differences in efficiency of the trigger on events in data compared with events in MC samples, scale factors are used and are determined to be 1.13 ± 0.01 for the barrel and 1.04 ± 0.02 for the endcaps [17]. The difference in the scale factors between the barrel and the endcaps derives from the differences in the trigger chambers used in the barrel (RPC) and the endcaps (TGC).

Reconstruction
To reconstruct the decay products and vertices of LLPs, dedicated reconstruction algorithms are used in both the ID and the MS. In the ID, large-radius tracking (LRT) [31] is employed after standard tracking is completed in order to reconstruct those tracks that do not point to the IP, and a displaced vertex reconstruction algorithm [28, 32] draws on the combined collection of standard and large-radius tracks to form displaced ID vertices.
In the MS, LLPs that decay hadronically after the last layer of the HCal are likely to produce narrow, high-multiplicity jets; several times as many hits are expected to be associated with the LLP decays compared with those associated with a muon. The standard algorithms in the MS are not optimized to operate in such dense environments. A special vertex reconstruction algorithm is employed for the reconstruction of MS vertices, which is described in Ref.

Reconstruction of standard jets
Jets are reconstructed in the ECal and HCal from energy deposits in neighboring calorimeter cells. Threedimensional topological clusters of the cells containing energy significantly above a noise threshold [47,48] are used as input to the anti-k t jet algorithm [49]. Jets are reconstructed with an R = 0.4 radius parameter using the F J 2.4.3 [50] software package. Jets energies are calibrated using the procedure described in Ref. [47].

Reconstruction of standard tracks
Tracks in the ID are reconstructed using the energy deposits, or hits, left by charged particles. The standard ATLAS tracking algorithm reconstructs inside-out tracks based on seeds made of three space points4 in the pixel and SCT detectors [51]. A window search is performed based on the seeds, and track candidates are formed by inputting the hits in the window into a Kalman filter [52]. A track candidate must pass selection requirements on the track parameters and the constituent hits, as outlined in Table 1. Track candidates are passed through an ambiguity solver [51] which evaluates the track candidates by using the hits, as well as the χ 2 of the track fit. Successful track candidates are extended into the TRT, and tracks are kept whether or not the TRT extension is successful.
After the completion of the inside-out tracking pass, an outside-in tracking pass is performed. Standalone TRT segments are created, seeded by energy deposits in the ECal. The standalone TRT segments are extended back into the SCT and pixel detectors, using hits that were not included in tracks reconstructed in the inside-out tracking. Standalone TRT segments that fail the extension into the silicon detectors are retained. Outside-in tracks must also pass the track impact parameter requirements in Table 1.

Reconstruction of large-radius tracks
The standard ATLAS tracking procedure is optimized for the reconstruction of tracks that originate very close to the IP and has strict restrictions on the impact parameters of reconstructed tracks to reduce the reconstruction of fake tracks. Tracks produced in displaced decays often have impact parameters that are larger than the maximum impact parameter allowed by the standard tracking reconstruction algorithm. In order to reconstruct these tracks, LRT is performed, taking as inputs the hits that are left over from the standard tracking. This iteration is performed with loosened requirements on the transverse (d 0 ) and longitudinal (z 0 ) track impact parameters, outlined in Table 1, in order to provide increased efficiency for displaced tracks. Additionally, in order to increase the efficiency of the reconstruction of the displaced decays, the requirement on the maximum number of unshared hits is relaxed.

Displaced vertex reconstruction in the MS
The dedicated MSVx reconstruction algorithm makes use of the two multilayers (ML) in each MDT chamber [33]. Straight-line segments are created from at least three MDT hits in each of the MLs using a minimum χ 2 fit. The segments from the two MLs are matched to form tracklets, which are used to reconstruct the MSVx positions. The vertex reconstruction algorithm proceeds separately in the barrel and the endcaps of the MS, extrapolating the tracklets through the magnetic field that is present in the barrel, and extrapolating tracklets as straight lines in the endcaps where the MDT chambers are not immersed in magnetic field. In the barrel, the χ 2 probability of the vertex is required to be ≥ 5%. If it is less than 5%, the tracklet with the largest contribution to the χ 2 is removed and the vertex is re-fit. This process is repeated until the χ 2 probability of the vertex is ≥ 5% or the vertex has fewer than three tracklets. In the endcap, all tracklets in the vertex must be within 30 cm of the calculated vertex position, otherwise the farthest tracklet from the vertex is removed and the vertex is re-fit. In both the barrel and the endcaps, each MSVx is required to have at least three tracklets.

Displaced vertex reconstruction in the ID
A displaced vertex reconstruction algorithm is used to reconstruct the LLP decays in the ID. The algorithm takes both the standard and large-radius tracks as input and selects tracks that meet the criteria listed in the upper section of Table 2. Number of pixel and TRT hits n pixel ≥ 2 or n TRT > 0 No hits on track may be present before the vertex Hits on track must be present in the layer following the vertex From this collection, a set of two-track vertices is formed from all possible pairs of intersecting tracks. The tracks making up these two-track vertices are required not to have any hits in pixel or SCT layers at smaller radii than the vertex position, and must have hits on the next possible pixel or SCT layer, unless the vertex is within a few mm of the layer. The two-track vertex seeds are merged into multi-track vertices if they are within d/σ d < 3 (where d is the distance between the two-track vertices and σ d is the uncertainty in the distance). Poorly associated tracks, with track χ 2 > 6, are removed from the multi-track vertices and the vertices are re-fit. This process is repeated until there are no more pairs of vertices satisfying d/σ d < 3. In the final step, all vertices within 1 mm are merged and the vertex fit is recalculated.

Event selection
All events used in the analysis are required to contain a primary vertex (PV), associated with the pp hard scatter [53]. The PV must have at least two tracks, each with p T > 400 MeV. If more than one vertex exists satisfying these criteria, the PV is chosen as the vertex with the largest sum of the squares of the p T of all tracks associated with the vertex. The events must pass the Muon RoI Cluster trigger, and pass the veto on the triggers from the CR analysis [16]. The events must contain a good MSVx (described in Section 6.1) matched within ∆R < 0.4 to the triggering muon cluster. Finally, events are required to have a good IDVx (described in Section 6.2), and the MSVx and IDVx must have an angular separation of ∆R > 0.4.5

MS vertex selection
The primary source of background that mimics LLP decays in the MS is jets that punch through the calorimeter. In order to reduce the background from these punch-through jets, each MSVx is required to pass certain isolation requirements developed in the MS analysis [17]. The MS vertices are required to be isolated by ∆R > 0.3 (∆R > 0.6) in the barrel (endcaps) from jets with p T > 30 GeV that are matched to the PV using a jet vertex tagger discriminant [54] and have log 10 (E HAD /E EM ) < 0.5.6 Isolation from these jets also reduces the contamination from multijet events. To further reduce the background from multijet events, each MSVx is required to be isolated from activity in the ID. The vector sum of the transverse momenta of tracks in a ∆R = 0.2 cone around the MSVx is required to be Σp T < 10 GeV, and in the barrel (endcaps) the MSVx must be ∆R > 0.3 (∆R > 0.6) from any tracks with p T > 5 GeV. The tracks used for this isolation must point back to the PV. Additionally, they are required to have at least seven silicon hits and no shared silicon hits, or at least ten silicon hits. To reduce the contribution from electronic noise, cosmic-ray muons, and machine-induced background, each MSVx is also required to have a minimum number of hits associated with the vertex in the MDT (n MDT ), RPC (n RPC ), and TGC (n TGC ), outlined in Table 3. A maximum n MDT selection is applied to reduce the background from coherent noise bursts in the MDTs. MS vertices are reconstructed by different algorithms in the barrel and the endcaps. When an LLP decays in the barrel-endcap transition region, 0.8 < |η| < 1.3, the resulting hits will be split between the two algorithms. This leads to a low reconstruction efficiency in the transition region, since neither algorithm has access to all hits, although occasionally two separate vertices will be reconstructed from a single LLP decay. The barrel-endcap transition region overlaps very closely with the barrel-endcap transition region in the HCal, 0.7 < |η| < 1.2, in which the probability of punch-through jets is higher. Thus, each MSVx is required to be contained in the barrel with |η MSVx | < 0.7 or in the endcap with |η MSVx | > 1.3 to remove vertices in the barrel-endcap transition region of the MS and HCal. A vertex that meets all of the necessary criteria is considered to be a good MSVx.

ID vertex selection
One of the primary sources of background for a search for displaced hadronic decays in the ID is vertices from interactions between particles and layers of detector material. Such hadronic interactions may result in reconstructed vertices that are indistinguishable from the reconstructed vertices of signal decays in the same region of space. In order to remove this source of background, a map is created using displaced vertices found in minimum-bias data in which the decays from known long-lived hadrons have been removed, as described in Refs. [55,56]. This map is used to create a material veto, which removes vertices in regions of space that were found to contain material. This material veto leads to a 42% loss in the fiducial volume of IDVx, R = x 2 + y 2 < 300 mm and |z| < 300 mm [28], but reduces the number of background events by more than a factor of 50. In addition to the material veto, a disabled-module veto is employed that accounts for the fact that a disabled module could cause a track not to have a hit immediately after a vertex, which causes the vertex to be rejected. This disabled-module veto is applied in simulation to mimic the effect in data, and operates by removing vertices in regions immediately before the location of the disabled modules.
The disabled-module veto leads to a minor loss in fiducial volume of 2.3% [28], and is applied in both data and simulation.
To reject poorly reconstructed vertices resulting from random track crossings, the χ 2 value of the vertex fit divided by the number of degrees of freedom is required to be less than 5.
In addition to the IDVx reconstruction requirement that the tracks forming the vertices have |d 0 | > 2 mm, a minimum radial distance of 4 mm is imposed between the IDVx and the reconstructed PV to further reduce the background contribution from b-hadrons.
ID vertices are required to have a separation of ∆R > 0.4 from the nearest selected MSVx in the event in order to reduce the probability that one high-energy hadronic jet could cause a background vertex simultaneously in the ID and in the MS.
The number of charged decay products from a hadronically decaying LLP is expected to be much higher than from vertices constructed from fake tracks or from random crossings of tracks. Thus, the number of tracks associated with the IDVx is an important discriminant between background and signal vertices. Figure 2(a) shows the distributions of the number of tracks associated with each IDVx (n trk ) for reconstructed vertices in signal MC samples compared with those reconstructed in data. In Figure 2, the signal MC events used have no additional selection requirements in order to reduce the statistical uncertainty. The background events in data are those events in the Bkg region of the background estimation method described in Section 7.
The reconstructed vertices in the signal MC samples are required to be dr = dx 2 + dy 2 + dz 2 < 5 mm of the LLP decay position, and have at least two tracks matched7 to particles produced in the LLP decay. The reconstructed IDVx distributions in the background events in data are dominated by vertices with n trk = 2, and when two-track vertices are removed, by n trk = 3. For an IDVx to be considered in the signal region, it is required to have n trk ≥ 4. Each IDVx is also required to pass a minimum vertex mass (m IDVx ) selection of 3 GeV, where the invariant vertex mass is computed assuming that the tracks originate from charged pions. Figure 2 Table 4. The heavier the mass of the LLP, the less impact the selection m IDVx > 3 GeV has on the IDVx selection efficiency. For the m Φ , m s = [1000, 400] GeV signal MC sample, this selection removes less than 4% of the reconstructed ID vertices that pass the other signal selections. In data, the selection on m IDVx removes 70% of reconstructed ID vertices which pass all the other selections.
The requirements on the signal region IDVx are summarized in Table 4.  Figure 3 shows the IDVx selection efficiency, including the reconstruction efficiency, as a function of the decay radius of the LLP for several mass points. The efficiency is defined as the fraction of LLP decay vertices in the fiducial volume R, |z| < 300 mm that are within 5 mm of reconstructed vertices that have at least two tracks matched to the decay products from the LLP and meet all the selection criteria listed in Table 4. Figure 3(a) shows that for a fixed mediator mass the IDVx selection efficiency increases with increasing LLP mass due to the larger impact of the selection on m IDVx and n trk at smaller LLP masses. For a fixed LLP mass, a higher boost leads to a decreased IDVx selection efficiency (Figure 3(b)) because decay products that point back to the IP are not included in the displaced vertex reconstruction, due to the selection of |d 0 | > 2 mm on associated tracks.
The structure in the IDVx selection efficiency as function of the LLP decay radius R is due to the impact of the material veto, as shown in Figures 3(a) and 3(b) for one mass point by the inclusion of the selection efficiency without the material veto.  seen in Figure 3). Events with higher LLP mass are also more likely to pass the trigger requirements and contain a good MSVx. The boost of the LLP is associated with a higher probability to pass the trigger requirements but a lower probability to contain a good MSVx, for events that pass the trigger.

Background estimation
Sources of background for ID vertices include reconstructed vertices from the interactions of particles with detector material, vertices created from fake tracks, and vertices from random track crossings. The incidence of vertices created from fake tracks and from random crossings is correlated with the jet activity in the events; events with a greater number of jets are more likely to include vertices from background. The background vertices are predominantly removed by the IDVx selection. A data-driven background estimation method is employed to determine the residual contribution to the events in the signal region from ID vertices from all sources of background.
The number of background events in the signal region is estimated by defining a set of background events that are designed to be approximately free of signal contamination and determining the fraction of those events that contain an IDVx that passes the full IDVx selection. This fraction is applied to events that pass the full event selection except for the requirement of an IDVx, to estimate how many background events contain an MSVx and an IDVx. Table 6: The data events used in the background estimation. These events include the background events, whose selection is defined in the text, divided into all background events (Bkg), and those that contain at least one IDVx that passes the full IDVx requirements (Bkg+IDVx). The other events making up the plane are the signal region events (Sig), and events that pass all signal region requirements except for the inclusion of an IDVx (Sig-IDVx).

Background Muon RoI Cluster trigger events events with a good MSVx Has IDVx passing full signal selection Bkg+IDVx Sig Agnostic to IDVx
Bkg Sig-IDVx The selection of background events is designed to limit the possibility of signal contamination. The background events (Bkg), shown in the lower left in Table 6, are required to pass the single-muon trigger described in Section 3 and are required to pass a veto on the Muon RoI Cluster trigger used to collect events in the signal region. The background events are also required to contain two isolated muons with p T > 25 GeV and p T > 20 GeV. When applied to events in the signal MC samples, the requirements used to define the Bkg events select fewer than 0.1% of events for any given mass point, without including the requirement of reconstructing and selecting both an MSVx and an IDVx.
The selection for the Bkg events is agnostic to the presence of an IDVx. The Bkg+IDVx events, shown in the upper left in Table 6, are required to pass the same trigger and isolated muon background requirements as the Bkg events, but are also required to contain at least one IDVx that passes all of the IDVx selections outlined in Table 4. The number of events in regions Bkg+IDVx and Bkg (N Bkg+IDVx and N Bkg ) are used to calculated a factor F = N Bkg+IDVx /N Bkg , which represents the probability that a given event will contain an IDVx from background that meets the selection criteria.
Signal region events (Sig) in the upper right of Table 6 are those which pass the full signal selection described in Section 6. Events that pass the full signal selection but are not required to contain an IDVx (Sig-IDVx) are in the lower right of Table 6. The number of events in the signal region (N Sig ) which contain an IDVx from background can be estimated using the number of Sig-IDVx events (N Sig−IDVx ) and the factor F defined above. Hence, the number of Sig region events which are expected to contain an IDVx from background is estimated as N bkg pred. Sig There are 45 events in the Bkg+IDVx region out of 6,099,660 events in the Bkg region, giving a factor F = N Bkg+IDVx /N Bkg = (7.4 ± 1.1 (stat.)) × 10 −6 . The Sig-IDVx region contains 156,805 events; the predicted number of background events in the signal region is then N pred The validation of the background estimation is performed using two sets of validation regions, in which the predicted and observed numbers of events are compared in regions containing vertices similar to those passing the IDVx signal selection (Table 7). This validation serves as a cross-check that the fraction of background events that contain an IDVx is not significantly different from the fraction of events passing the Muon RoI Cluster trigger, with or without a selected MSVx, that contain an IDVx from background.
The first set of validation regions, the Bkg, 2-trk and Val, 2-trk regions, are similar to the Bkg+IDVx and Sig regions except that instead of containing an IDVx that meets the full IDVx selection criteria, the selection on n trk is changed from n trk ≥ 4 to n trk = 2. Vertices with n trk = 2 are chosen because the IDVx distribution in background events is dominated by two-track vertices, as shown in Figure 2(a), and the signal contamination is small. This allows the fraction of vertices to be examined in events that otherwise pass all signal region selections.  The sources of background that contribute primarily to ID vertices with n trk = 2 are not exactly the same as those that contribute to higher n trk ID vertices, thus a second set of validation regions is studied. The signal contamination is non-negligible for ID vertices with n trk > 2 in events that pass the Muon RoI Cluster trigger and also contain an MSVx. In order to study higher n trk vertices, the requirement of the MSVx is removed (Trig and Trig, 3-trk regions) in the second set of validation regions. In order to further reduce the signal contamination for ID vertices with higher n trk , the requirement on m IDVx is modified to select an m IDVx range adjacent to that used for the final signal selection. The Bkg, 3-trk and Trig, 3-trk regions contain background events and events passing the Muon RoI Cluster, respectively, that have ID vertices which pass the full signal selection with the exceptions that the m IDVx selection is changed to 1 GeV < m IDVx < 3 GeV, and the n trk selection is changed to n trk = 3.
The predicted and observed numbers of events in the Val, 2-trk and Trig, 3-trk regions are listed in Table 8. The predicted and observed numbers of events in the Val, 2-trk regions agree within 2%, and the kinematic distributions for the two-track vertices in the Val, 2-trk and Bkg, 2-trk regions are also found to be in good agreement. The predicted and observed numbers of events in the Trig, 3-trk regions agree within 25%.
The event selection used to populate the different regions impacts the jet multiplicity in each region. The probability to find an IDVx from background is highly correlated with the jet activity in the events, and the effect is more pronounced for higher n trk ID vertices than for two-track ID vertices. It is found that scaling to adjust for the differences in the jet multiplicities reduces the difference in the predicted and observed numbers of events in the Trig, 3-trk region. However, the impact of applying the same scaling to the predicted number of background events in the final signal region changed the final background estimate by less than the statistical uncertainty, so this scaling was not ultimately applied.
The largest difference in all background systematic uncertainty studies is observed to be within 25%, so this value is taken to be the systematic uncertainty of the background estimation. The sensitivity of the results to this choice is tested by doubling the systematic uncertainty on the background; the resulting change in the predicted and observed limits is negligible, as the number of predicted background events is small. With a 25% systematic uncertainty, the predicted number of background events passing the final signal selection is 1.16 ± 0.18 (stat.) ± 0.29 (syst.).

Systematic uncertainties in signal predictions
Several sources of systematic uncertainty in the signal selection efficiency are considered. The dominant uncertainty is due to the difference in performance of the LRT and ID displaced vertex reconstruction algorithms between data and MC simulation.

Systematic uncertainties in large-radius tracking and displaced vertex reconstruction
To assess the systematic uncertainty of the ID vertex reconstruction efficiency due to the modeling of the large-radius tracking and vertex reconstruction, the rates of displaced vertices consistent with K 0 S → π + π − decays are compared between data and multijet simulation. The uncertainty is estimated by examining the variations between data and simulation in the K 0 S yield as function of vertex radius. Events in data and MC samples are selected by requiring the presence of a PV. The events used in data are in the selected subset of events that underwent the reconstruction of displaced tracks and vertices. The same reconstruction is performed on the multijet MC sample, and the simulated events are reweighted to correctly reproduce the distribution of the mean number of interactions per bunch crossing in the data. To minimize the statistical uncertainty, no additional event-level requirements are applied. From the selected events, candidate K 0 S vertices are identified by requiring that the vertices have a decay length greater than 15 mm, have exactly two tracks, and have an invariant mass in the region 450 to 550 MeV. After the last two selection criteria are applied, the vast majority of selected vertices originate from K 0 S decays and the possibility of signal contamination is minimized. The kinematic distributions of candidate K 0 S vertices are compared between data and MC and are found to have good agreement within statistical uncertainties.
The number of K 0 S candidate vertices found in data and simulation are binned by their decay radius R. To achieve a better estimate of the number of K 0 S in each bin the background contribution is computed from the sidebands of the invariant mass distribution, from 350 to 450 MeV and from 550 to 650 MeV, and subtracted from number of K 0 S candidates in the region 450 to 550 MeV. Tracks originating from a K 0 S decay can be reconstructed by either the standard tracking or the LRT algorithm. The data are normalized such that the number of K 0 S vertices with two standard tracks is the same between data and simulation. This accounts for any differences that may exist between data and simulation in the total number of K 0 S decays. The vertex yields of K 0 S with two large-radius tracks are compared between data and MC simulation, and the largest difference in the ratio of data to MC is found to be 20%. For vertices in the signal region, the effect of this tracking inefficiency is reduced due to the high multiplicity of tracks present in the vertices. The uncertainty in the vertex reconstruction efficiency is taken to be 20% and is applied as an uncertainty of the global selection efficiency.

Other systematic uncertainties
The uncertainty of the integrated luminosity measurement is 2.2% [57], obtained using the LUCID-2 detector [58] for the primary luminosity measurements.
The systematic uncertainties of the Muon RoI Cluster trigger efficiency and the MSVx reconstruction efficiency are examined in Ref. [17]. The systematic uncertainty due to the trigger scale factors is evaluated by varying the scale factors up and down by the uncertainty of the scale factor fit, and comparing the trigger efficiency resulting from the modified scale factors with the trigger efficiency from the nominal scale factor. The systematic uncertainties are evaluated separately in the barrel and the endcaps. Similar methods are used to determine the impact of the pileup uncertainty and the systematic uncertainty from the PDF used to generate the signal MC events on the trigger efficiency. The largest relative uncertainty in the trigger efficiency in any given mass point used in this analysis is found to be 4.8%.
These methods are also used to evaluate the impact of the pileup and PDF uncertainties on the MSVx reconstruction efficiency, and the largest relative uncertainty for any mass point in the barrel or endcap is found to be 5.5%.

Results
One event is observed that passes the full signal selection, consistent with the estimated background of 1.16 ± 0.18 (stat.) ± 0.29 (syst.) events.
Upper limits at the 95% confidence level (CL) are set on the production cross section times branching ratio, for various signal mass hypotheses, following the CL S prescription [59] with a profile likelihood ratio used as the test statistic. An asymptotic approach [60] is used to compute the CL S value. This method was tested and found to give results consistent with those obtained from ensemble tests. A Poisson probability term describing the total number of observed events is used, and the systematic uncertainties of the signal efficiency, background estimation, and luminosity are treated as nuisance parameters and are assigned Gaussian constraints.
To evaluate the efficiency of the full event selection as a function of the proper lifetime of the LLP, a reweighting procedure is used, following the method described in Ref. [16]. The extrapolated efficiency from the 5 m mean lab-frame decay length sample agrees with the efficiency from the 9 m mean lab-frame decay length sample within the combined statistical uncertainty from the efficiency and extrapolation computations.
The observed limits for all benchmark models considered are summarized in Figure 4. For the m H = 125 GeV mediator, the SM Higgs boson gluon-gluon fusion production cross section of 49 pb [61] at 13 TeV is assumed and limits on the branching ratio B H→ss are shown. The observed limits are consistent with the expected limits within ±1σ and extend the limits set by previous displaced jet searches [16,17] significantly for low scalar masses and short lifetimes.

Combination of results with other displaced jets searches
The results presented in this paper are complementary to the CR [16] and MS [17] analyses, which set limits on the same benchmark models as used in this analysis. The results derived above are combined with the results from the CR and MS analyses to provide increased sensitivity over a greater range of proper lifetimes.
The orthogonality of the search presented in this paper (the ID analysis) and the CR analysis is ensured by vetoing on the CR triggers in both the data and signal MC events as described in Section 6. The MS analysis is separated into the 1-MSVx plus missing transverse momentum (MS1) and 2-MSVx (MS2) channels. To ensure orthogonality between the ID and MS analyses, only the 2-MSVx channel is used in the combination. Across all MC signal samples in this channel, only a few events are found which contain both an IDVx and two MS vertices passing all selections used by the respective analyses, and these events are explicitly vetoed for the combination. There are no events found in data which pass the full selection of both the ID and MS2 analyses. The orthogonality between the CR and MS analyses has been verified in Ref. [16]. This ensures that the final selected MC signal events and data events in all three analyses used in the combination are statistically independent.
The combination is performed using a simultaneous fit of the likelihood functions of each analysis. The signal strength is correlated between all three likelihoods, as is the nuisance parameter for the luminosity uncertainties. The signal uncertainties are treated as uncorrelated, since they are dominated by different experimental uncertainties in each search. The background estimates in each analysis are derived using independent data-driven methods and are therefore not correlated.
As in the individual searches, the asymptotic approach is used to compute the CL S value, and the limits are defined by the region excluded at 95% CL. The limits are calculated using a global fit, where the overall likelihood function is the product of the individual likelihood functions of the searches to be combined. The limits are calculated separately at each cτ point, and at each point the signal efficiency is scaled by the result of the lifetime extrapolation procedure. Figures 5 and 6 show the observed and expected limits for the ID analysis, as well as the combination of the CR and MS analyses both with and without their combination with the ID analysis. For the models with m H = 125 GeV or m Φ = 200 GeV and 8 GeV < m s ≤ 55 GeV, the ID analysis has greater sensitivity than the combination of the CR and MS analyses for proper lifetimes ranging from 0.05 m up to 0.7 m. Although the IDVx reconstruction efficiency diminishes with decreasing LLP masses, requiring both a good MSVx and a good IDVx suppresses the background in the final signal region and allows stronger limits to be set at low cτ for these mass points. Table 9 summarizes the proper lifetime ranges excluded by the combinations for the m H = 125 GeV mediator, assuming a 10% branching ratio for H → ss and using the SM Higgs boson gluon-gluon fusion production cross section.

Conclusion
This paper presents a search for pairs of long-lived particles decaying in the ATLAS inner tracking detector and muon spectrometer, using 33.0 fb −1 of √ s = 13 TeV proton-proton collision data which were collected at the LHC in 2016. Benchmark HS models are studied, using a scalar mediator that ranges in mass from 125 to 1000 GeV, decaying into pairs of long-lived scalars ranging in mass from 8 to 400 GeV, depending on the mass of the mediator. The search presented focuses on the topology consisting of one displaced hadronic decay in the inner detector and one in the muon spectrometer. The search employs dedicated techniques to reconstruct both the displaced inner detector and muon spectrometer hadronic vertices. A data-driven background estimation is performed, which predicts approximately one event in the signal region from background sources. One event is found in the signal region, and limits are set on the various signal mass points. This search has a greater sensitivity for low-mass, long-lived scalars at shorter lifetimes than previously published searches. The limits resulting from the combination of this search with the previous ATLAS searches for long-lived particles are the most stringent thus far on the branching ratios from the Higgs boson to several low-mass scalars, and on the cross section times branching ratio for a 200 GeV mass Φ decaying into long-lived scalars with masses of 25 and 50 GeV.