Search for neutral long-lived particles in pp collisions at √s = 13 TeV that decay into displaced hadronic jets in the ATLAS calorimeter

JHEP06(2022)005 Published for SISSA by Springer Received:March 3, 2022 Accepted:May 3, 2022 Published:June 1, 2022 Search for neutral long-lived particles in pp collisions at √s= 13 TeV that decay into displaced hadronic jets in the ATLAS calorimeter The ATLAS collaboration E-mail: [email protected] Abstract: A search for decays of pair-produced neutral long-lived particles (LLPs) is presented using 139 fb −1 of proton-proton collision data collected by the ATLAS detector at the LHC in 2015–2018 at a centre-of-mass energy of 13 TeV. Dedicated techniques were developed for the reconstruction of displaced jets produced by LLPs decaying hadronically in the ATLAS hadronic calorimeter. Two search regions are defined for different LLP kinematic regimes. The observed numbers of events are consistent with the expected background, and limits for several benchmark signals are determined. For a SM Higgs boson with a mass of 125GeV, branching ratios above 10% are excluded at 95% confidence level for values of c times LLP mean proper lifetime in the range between 20mm and 10m depending on the model. Upper limits are also set on the cross-section times branching ratio for scalars with a mass of 60GeV and for masses between 200 GeV and 1 TeV. Keywords: Hadron-Hadron Scattering ArXiv ePrint: 2203.01009 Open Access, Copyright CERN, for the benefit of the ATLAS Collaboration. Article funded by SCOAP3. https://doi.org/10.1007/JHEP06(2022)005 JHEP06(2022)005 Contents 1 Introduction 1 2 ATLAS detector 3 3 Data and simulation samples 4 4 Trigger and event selection 6 4.1 Triggers and event preselection 6 4.2 Displaced-jet-tagging neural network 10 4.3 Event selection 13 5 Background estimation 17 6 Systematic uncertainties 21 7 Results and statistical interpretation 23 8 Conclusion 27 The ATLAS collaboration 33 1 Introduction Many of the scenarios proposed to address some of the open questions of the Standard Model (SM) predict the existence of new non-SM particles whose lifetimes can be long enough for their decays to be significantly displaced from the interaction point but still within the ATLAS detector. Examples of theories involving such suitably long-lived particles (LLPs) are various supersymmetric (SUSY) models [ 1 – 7 ]; neutral naturalness models [ 8 – 11 ] which feature a hidden sector (HS) [ 12 – 14 ] that addresses the hierarchy problem; models that seek to incorporate dark matter [ 15 – 18 ], or explain the matter-antimatter asymmetry of the universe [ 19 ]; and models that lead to massive neutrinos [ 20 , 21 ] which provide an explanation for the origin of light neutrino masses and mixings. The decay of an LLP created in proton-proton collisions in the ATLAS detector could produce one of a variety of highly unconventional signatures, depending on the detector subsystem in which the LLP decays. Searches for promptly decaying particles often have very low sensitivity to such signatures and hence the study of LLPs requires dedicated analyses. This paper presents a search sensitive to neutral LLPs decaying chiefly in the calorimeters of the ATLAS detector. This allows the analysis to probe values of cτ (where c is the speed of light and τ is the mean proper lifetime of the LLP) ranging between a few centimetres and a few tens of metres. – 1 – JHEP06(2022)005 Φs s p pf ¯ f ¯ f f ' ' Figure 1. A diagram showing the Φ→ss →f¯ ff0¯ f0 decay used as the benchmark model. The s inherits Yukawa couplings to SM fermions from the Φ, and therefore decays primarily to heavy quarks. A HS benchmark model [ 12 – 14 , 22 , 23 ] is studied, in which the SM and HS are connected via a heavy neutral boson (Φ), which decays into two long-lived neutral scalar bosons ( s ). While Φcould be the SM Higgs boson, this analysis considers mediators with masses ( mΦ ) ranging from 60 GeV to 1000 GeV , and scalars with masses between 5 GeV and 475 GeV . The decay Φ→ss →f¯ ff0¯ f0 is considered (see figure 1), where f refers to fermions and ¯ f refers to anti-fermions. The branching ratio (BR, with value B ) of each decay mode depends on the mass of the scalar, with the dominant decay being to the heaviest quark that is kinematically accessible. In the hypothesised physics process with the largest scalar mass ms (475GeV), decays to top quarks dominate ( B > 99%). Conversely, in the hypothesis with the lightest ms (5GeV), decays to charm quarks dominate ( B∼ 75%), followed by decays to τ -leptons ( B∼ 25%). In the other cases, the relation among the BRs is approximately constant and typically 85:8:5 for b¯ b , c¯c , and τ+τ− , respectively. A single analysis strategy, described in section 4, is used for all mass hypotheses regardless of the scalar LLP’s decay mode. The cτ of LLPs in HS models are usually not constrained by theory, apart from a rough upper limit of cτ . 10 8 m given by the cosmological constraint of Big Bang Nucleosynthesis [ 24 ], and could be short enough for the LLPs to decay inside the ATLAS detector volume. The SM fermions from the LLP decay result in jets whose origins may be far from the interaction point (IP) of the colliding protons, leading to so-called displaced vertices or displaced jets. If the LLP decay occurs in the calorimeters, the decay products are collimated enough to be reconstructed as a single jet which is narrow, trackless and with an unusually high proportion of its energy in the hadronic calorimeter. Since pair-produced LLPs are considered, this analysis requires two such non-standard jets, with two selections targeting different LLP kinematic regimes. One is optimised for models with mΦ≤ 200 GeV (referred to as lowET models), and the other for models with mΦ> 200 GeV (highET models), where ET denotes transverse energy. The dominant background process that mimics this signal is SM multijet production, in cases where the jets are composed mainly of neutral hadrons or where some of the tracks are misreconstructed. Despite the low probability for a prompt jet to produce a signal-like jet, the SM multijet cross-section is high enough for this to be the dominant background in this search. Other contributions come from jets reconstructed from non-collision background consisting of cosmic rays and beam-induced background (BIB) [ 25 ]. The latter is composed of LHC beam-gas interactions and beam-halo interactions with the collimators upstream of the ATLAS detector, resulting – 2 – JHEP06(2022)005 in muons travelling parallel to the beam-pipe. This analysis makes use of a new per-jet neural network to discriminate signal-like jets from non-displaced jets or BIB-like jets, and a boosted decision tree to separate signal from background events. The per-jet neural network replaces a boosted decision tree used in the previous version of the analysis, using an adversarial training scheme to minimise the effect of mis-modelling in the input variables. This is the first time such a technique has been used in an ATLAS analysis. The background estimation is performed using a data-driven method. Previous searches for similar signatures (pair-produced neutral LLPs decaying hadronically) at hadron colliders have been performed at the Tevatron [ 26 , 27 ] and at the LHC. The search for displaced jets at LHCb in ref. [ 28 ] is sensitive to cτ values from ∼ 1mm to ∼ 0 . 1m. The most recent CMS searches at 13 TeV [ 29 – 32 ] involve jets with displaced vertices in the tracking system, and are sensitive to cτ values from ∼ 1mm to ∼ 1m. Previous ATLAS searches at 13 TeV looked for displaced vertices in the tracking system [ 33 , 34 ], pairs of reconstructed vertices in the muon spectrometer [ 35 ], or the combination of one displaced vertex in the muon spectrometer and one in the inner tracking detector [ 36 ]. These ATLAS searches are complementary, and together provide coverage of cτ values extending from effectively prompt to ∼ 200 m. This analysis is an update of a search for pairs of displaced hadronic jets in the ATLAS calorimeters [ 37 ], with significant improvements to the displaced-jet identification, and using the full LHC Run 2 dataset with 139fb −1 of 13TeV data instead of only data from 2016. It is sensitive to long-lived particle cτ values between approximately 20 mm and 10m, depending on the model. The paper is structured as follows. The ATLAS detector is described in section 2. The collection of the data and generation of samples of simulated events are then discussed in section 3. The trigger and event selection are detailed in section 4, followed by a discussion of the estimation of the background yield in the search regions in section 5. The systematic uncertainties are summarised in section 6. The statistical interpretation of the data is described in section 7, and the conclusions are given in section 8. 2 ATLAS detector The ATLAS detector [ 38 ] at the LHC covers nearly the entire solid angle around the collision point. 1 It is a multipurpose detector consisting of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and a muon spectrometer incorporating three large superconducting toroidal magnets. The inner-detector system is immersed in a 2T axial magnetic field and provides charged-particle tracking in the range |η|<2.5. The high-granularity silicon pixel detector covers the vertex region and typically provides four measurements per track. The layer closest to the interaction point is known as the 1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point in the centre of the detector and the z -axis along the beam pipe. The x -axis points from the IP to the centre of the LHC ring, and the y -axis points upwards. Cylindrical coordinates ( r, φ )are used in the transverse plane, φ being the azimuthal angle around the z -axis. The pseudorapidity is defined in terms of the polar angle θ as η=−ln tan(θ/2). Angular distance is measured in units of ∆R≡p(∆η)2+ (∆φ)2. – 3 – JHEP06(2022)005 insertable B-Layer [ 39 – 41 ]. It was added in 2014 and provides high-resolution hits at small radius to improve the tracking performance. The pixel detector is surrounded by the silicon microstrip tracker, which usually provides four three-dimensional measurement points per track. These silicon detectors are complemented by the transition radiation tracker, with coverage up to |η|= 2.0. The calorimeter system covers the pseudorapidity range |η|< 4 . 9. Within the region |η|< 3 . 2, electromagnetic calorimetry is provided by barrel and endcap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters (together referred to as the ECal), with an additional thin LAr presampler covering |η|< 1 . 8to correct for energy loss in material upstream of the calorimeters. The ECal extends from 1 . 5m to 2 . 0m in radial distance r in the barrel and from 3 . 6m to 4 . 25 m in |z| in the endcaps. Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter (HCal), segmented into three barrel structures within |η|< 1 . 7, and two copper/LAr hadronic endcap calorimeters covering |η|> 1 . 5. The HCal covers the region from 2 . 25 m to 4 . 25 m in r in the barrel (although the HCal active material extends only up to 3 . 9m) and from 4 . 3m to 6 . 05 m in |z| in the endcaps. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules optimised for electromagnetic and hadronic measurements, respectively. The calorimeters have a highly granular lateral and longitudinal segmentation. Including the presamplers, there are seven sampling layers in the combined central calorimeters (the LAr presampler, three in the ECal barrel and three in the HCal barrel), and the endcap regions provide up to eight sampling layers (the presampler, three in ECal endcaps and four in HCal endcaps). The forward calorimeter modules provide three sampling layers in the forward region. The total amount of material in the ECal corresponds to 24–35 radiation lengths in the barrel and 35–40 radiation lengths in the endcaps. The combined depth of the calorimeters for hadronic energy measurements is more than 9 hadronic interaction lengths nearly everywhere across the full detector acceptance. The muon spectrometer comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in the magnetic field generated by the superconducting air-core toroids. The field integral of the toroids ranges between 2.0 and 6.0Tm across most of the detector. The ATLAS detector selects events using a tiered trigger system [ 42 ]. The level-1 (L1) trigger is implemented in custom electronics and reduces the event rate from the LHC crossing frequency of 40MHz to a design value of 100 kHz. The second level, known as the high-level trigger (HLT), is implemented in software running on a commodity PC farm that processes the events and reduces the rate of recorded events to 1kHz. An extensive software suite [ 43 ] is used in the reconstruction and analysis of real and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment. 3 Data and simulation samples Data collected by the ATLAS detector during the period 2015–2018 from proton-proton ( pp ) collisions at √s = 13 TeV are used in this search. Only data collected during stable beam conditions in which all detector subsystems were operational are considered [ 44 ]. These – 4 – JHEP06(2022)005 Trigger Collected integrated luminosity [fb−1] 2015 2016 2017 2018 Total High-ETCalRatio trigger with ET>60 GeV 3 33 41 40 117 High-ETCalRatio trigger with ET>100 GeV — — 44 59 103 Low-ETCalRatio trigger (2016 version) — 11 43 — 54 Low-ETCalRatio trigger (2018 version) — — — 59 59 Table 1. CalRatio triggers which were available during the LHC Run 2 data-taking, and corresponding integrated luminosity collected in each period. The highET CalRatio trigger with ET> 60 GeV was disabled in 2017 for instantaneous luminosities higher than 1 . 4 × 10 34 cm−2s−1 . Two versions of the lowET CalRatio trigger were used, with slight differences in their algorithms. The details are reported in section 4. data were collected with a set of dedicated LLP signature-driven triggers and separated into four datasets, defined according to the triggers used to collect them. The search is performed on the main dataset, composed of all data events passing at least one of the two types of CalRatio triggers [ 45 ] running on bunch crossings where protons were present in both beams. The name “CalRatio” refers to the ratio of energies deposited in the hadronic and electromagnetic calorimeters. As described in detail in section 4, these include the lowET CalRatio triggers and highET CalRatio triggers. Different versions of these triggers ran during the full data-taking period. The amount of data collected in each case is summarised in table 1, with at least one of these triggers running at any given time during the entire data-taking. Two additional datasets were collected for the study of non-collision backgrounds. The BIB dataset, used for the study of BIB events faking signal events, was collected from events failing the CalRatio trigger BIB-removal algorithm. The cosmics dataset, used for the estimation of cosmic-ray events passing the analysis selection, was collected from events recorded during empty bunch crossings, as described in section 4. Finally, a dijet dataset is selected using a single-jet-based trigger and vetoing on the CalRatio triggers to make it orthogonal to the main dataset. This dataset is used in the neural network training described in section 4.2 and in the calculation of some of the systematic uncertainties involved in the analysis. The HS Φ→ss signal samples were generated using the MadGraph5_aMC@NLO v2.6.2 [ 46 ] generator at leading order (LO) with the NNPDF2.3lo parton distribution function (PDF) set [ 47 ]. In these samples, Φis produced via gluon-gluon fusion. The Φtransverse momentum distribution for the samples is reweighted to match that obtained for corresponding next-to-leading-order (NLO) predictions using the same event generator. A production cross-section of 48 . 6pb, taken from a next-to-next-to leading-order calculation [ 48 ], is assumed when normalising results for the case where the mediator is the SM Higgs boson (the mass of which was set to 125 GeV). Parton showering and hadronisation was modelled using Pythia 8.230 [ 49 ] with the A14 set of tuned parameters (tune) [ 50 ]. Several sets of samples were generated, with different assumptions for the masses of the – 5 – JHEP06(2022)005 mediator ( mΦ∈ [60 , 1000] GeV ) and LLPs ( ms∈ [5 , 475] GeV ). These mass ranges ensure an extensive LLP boost spectrum, allowing a wide variety of topologies to be studied. The LLP mean proper lifetime at which each of the signal samples was generated ( τgen ) was determined so as to maximise the fraction of decays in the ATLAS hadronic calorimeter and muon system, and is quoted in relevant tables and figures throughout this document. Some of the samples were generated for two assumptions about the LLP generated lifetime: one sample is used to study the signal throughout the analysis, while the other sample (with the alternative lifetime assumption but exactly the same mass choices) is used to validate the procedure for extrapolating limits to different mean proper lifetimes of the long-lived scalar. The dominant SM background in this analysis is SM multijet production. Although a data-driven method is used to perform the background estimation, Monte Carlo (MC) simulated multijet events are needed to train the per-jet neural network to discriminate between signal jets and the multijet background, and to evaluate some of the systematic uncertainties. The samples were generated at LO with Pythia 8.186 [ 51 ] using the A14 tune for parton showering and hadronisation. The NNPDF2.3lo PDF set [47] was used. The effect of multiple interactions in the same and neighbouring bunch crossings (pile-up) was modelled by overlaying the simulated hard-scattering event with inelastic pp collision events generated with Pythia 8.186 [ 51 ] using the NNPDF2.3lo PDF set and the A3 tune [52]. The detector geometry and response were simulated with Geant4 [ 53 , 54 ]. The standard ATLAS reconstruction software is used for both simulation and collision data. 4 Trigger and event selection This section describes how the data were collected, processed and selected for the analysis. The main dataset was collected with dedicated CalRatio triggers, and auxiliary datasets are also defined so as to be enriched in background events such as BIB, cosmic rays, or SM dijets. Using a combination of data and simulated samples, per-jet neural networks are trained to distinguish three classes of objects: signal-like jets, BIB-like jets, and non-displaced jets. The neural network training architecture involves an adversarial network, which is used to ensure that differences between data and simulation in the training samples are not exploited. Details are provided in section 4.2. Per-event boosted decision trees (one each for lowET and highET signals) make use of the per-jet neural network scores as well as several other event-level variables to construct discriminants which separate signal from all sources of background. Some additional requirements are applied to maximise the sensitivity of the final selection. Finally, the data-driven ABCD method, explained in detail in section 5, is used to estimate the remaining background in the final selection. In this method the boosted decision tree score is used as one of two axes which define the ABCD plane. 4.1 Triggers and event preselection Events are selected by the CalRatio triggers [ 45 ], which are designed to identify jets that result from neutral LLPs decaying near the outer radius of the ECal or within the HCal. The combined L1 and HLT selections make use of the main characteristics of jets resulting – 6 – JHEP06(2022)005 0 100 200 300 400 500 [GeV] T LLP p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency T L1 seed: 60GeV-high-E T L1 seed: 100GeV-high-E v2016 T L1 seed: low-E v2018 T L1 seed: low-E ATLAS Simulation )=(125,35) GeV s ,m Φ (m =2.63m gen τc =2.63m gen τc (a) 0 100 200 300 400 500 [GeV] T LLP p 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency T L1 seed: 60GeV-high-E T L1 seed: 100GeV-high-E v2016 T L1 seed: low-E v2018 T L1 seed: low-E ATLAS Simulation )=(600,150) GeV s ,m Φ (m =3.31m gen τc =3.31m gen τc (b) Figure 2. Trigger efficiency for simulated signal events as a function of the LLP pT for (a) one of the lowET signal samples and (b) one of the highET signal samples for HLT CalRatio triggers seeded by the highET L1 triggers with ET thresholds of 60GeV and 100GeV and by the two versions of the low-ETL1 triggers. Only statistical uncertainties are shown. from the decay of a neutral LLP in the calorimeters: due to the late development of these jets, they appear narrower than standard jets, they have a high fraction of their energy deposited in the HCal, and they are isolated from tracks. Two types of such triggers are used, differing only in the L1 trigger selection. At L1, two different triggers are used. The highET L1 triggers select narrow jets with energy deposits above certain thresholds (either ET> 60 GeV or ET> 100 GeV ) in a 0 . 2 × 0 . 2 (∆ η× ∆ φ )region of the ECal and HCal combined [ 55 ]. The lowET L1 trigger makes use of the L1 topological trigger system [ 56 ] by accepting events where the largest energy deposit, with totalET threshold at 30GeV, does not geometrically overlap in the η – φ plane with any energy deposits with ET> 3 GeV in the ECal. The veto on ECal deposits ensures a high value of the ratio at L1 of energy deposited in the HCal to energy deposited in the ECal, EH/EEM > 9, rejecting a large portion of the background with typical values of EH/EEM <1, and allowing the ET threshold to be kept low. This looser ET requirement increases the efficiency for lowerpT LLPs. In its 2016 version, the trigger requires that if there is more than one HCal deposit, the second-most energetic one is also isolated from energy deposits in the ECal. This condition was removed in 2018, which helped to increase the trigger efficiency as seen in figures 2and 3. At the HLT, a two-step selection algorithm is applied to CalRatio triggers, regardless of the L1 selection. In the first step, calorimeter deposits are clustered into jets using the antikt algorithm [ 57 , 58 ] with radius parameter R = 0 . 4. The standard jet-cleaning requirements [ 59 ] applied offline in most ATLAS analyses reject jets with high values of EH/EEM , one of the key characteristics of the displaced hadronic jets, and are therefore not included in these triggers. A dedicated cleaning algorithm (referred to as CalRatio jet – 7 – JHEP06(2022)005 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 [m] xy LLP L 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency ECal inner radius ECal outer radius HCal inner radius HCal outer radius T L1 seed: 60GeV-high-E T L1 seed: 100GeV-high-E v2016 T L1 seed: low-E v2018 T L1 seed: low-E ATLAS Simulation )=(125,35) GeV s ,m Φ (m =2.63m gen τc (a) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 [m] xy LLP L 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Efficiency ECal inner radius ECal outer radius HCal inner radius HCal outer radius T L1 seed: 60GeV-high-E T L1 seed: 100GeV-high-E v2016 T L1 seed: low-E v2018 T L1 seed: low-E ATLAS Simulation )=(600,150) GeV s ,m Φ (m =3.31m gen τc (b) Figure 3. Trigger efficiency for simulated signal events as a function of the LLP decay position in the x – y plane ( Lxy ) for LLPs decaying in the barrel ( |η|< 1 . 4) for (a) one of the lowET signal samples and (b) one of the highET signal samples for HLT CalRatio triggers seeded by the highET L1 triggers with ET thresholds of 60GeV and 100 GeV and by the two versions of the lowET L1 triggers. Only statistical uncertainties are shown. cleaning and applied starting in 2016) is applied instead. This algorithm is based on the standard jet cleaning described in ref. [ 59 ] but with the requirements on the jet EH/EEM substituted by a condition to reject any jet with more than 85% of its energy associated with a single calorimeter sampling layer and with an absolute value of its negative energy higher than 4GeV, calculated as the sum of the energy in all cells with negative energy, caused by electronic and pile-up noise. At least one of the HLT jets passing the CalRatio jet cleaning is required to satisfy ET> 30 GeV, |η|< 2 . 5and log10(EH/EEM)> 1 . 2. Jets satisfying these requirements are used to determine 0 . 8 × 0 . 8regions in ∆ η× ∆ φ centred on the jet axis in which to perform charged-particle reconstruction (tracking). Triggering jets are required to have no tracks with pT>2GeV within ∆R= 0.2of the jet axis. In the second step, events passing the CalRatio triggers are required to pass a BIBremoval algorithm. Events which pass the first step but fail this algorithm are collected to form the BIB dataset. Muons from BIB enter the HCal horizontally and may radiate a photon via bremsstrahlung, generating an energy deposit that may be reconstructed as a signal-like jet. BIB deposits are more likely to be aligned in φ since they travel parallel to the LHC beam pipe. Furthermore, muons from BIB leave these energy deposits in the calorimeter earlier than particles resulting from a collision in the same bunch crossing. The BIB-removal algorithm applied at the HLT therefore identifies events as containing BIB if the triggering jet has at least four HCal-barrel cells close together in φ and in the same calorimeter layer but not belonging to the same jet and requiring that every cell’s timing be consistent with that of a BIB deposit [ 60 ]. This algorithm has been estimated to have an efficiency of approximately 70% in BIB identification. – 8 – JHEP06(2022)005 samples in the HS model is used to train the per-event BDT against BIB data. As in the NN training, only part of each signal sample is used for training, leaving the other part for interpretation. Four CalRatio jet candidates are defined as the two clean jets with the highest lowET signal-NN-score and the two clean jets with the highest highET signal-NN-score in the event ( jetsig1l , jetsig2l , jetsig1h , jetsig2h ). Analogously, four BIB jet candidates are defined as the two clean jets with the highest lowET BIB-NN-score and the two clean jets with the highest highET BIB-NN-score in the event ( jetBIB1l , jetBIB2l , jetBIB1h , jetBIB2h ). The NN outputs of these jets are used as input variables for the per-event BDTs. Other event-level variables are used in the training: examples include the distance ∆ R between the two highET CalRatio jet candidates ( jetsig1h , jetsig2h ) and Hmiss T/HT , where HT is the scalar sum of the transverse momenta of the jets. Following the same strategy as used for the per-jet NN and to obtain optimal signal-tobackground discrimination at any jet pT , two versions of the per-event BDT are trained: the highET BDT is trained for the analysis of the high-mass ( mΦ = 400 to 1000 GeV) signal samples, with a high jetpT distribution, and the lowET BDT is trained for low-mass (mΦ= 125 to 200GeV) signal samples, with a softer jet-pTdistribution. The two versions use the same set of input variables and the same BIB background sample. They differ only in the signal samples used during training. Only signal events where at least one of the LLPs decays after passing through the inner detector are considered in the training. Figure 7 shows the distribution of the per-event BDT outputs from five signal samples, as well as from the main data and BIB data. The BDT output in the BIB dataset peaks at slightly lower values than in the main data. Using the jet’s time, measured as the energy-weighted average of the timing for each calorimeter cell related to the jet and corrected by the corresponding time-of-flight from the interaction point, and z -coordinate measurements of the jets, it was checked that events with low BDT values (lowET BDT <− 0 . 2or highET BDT <− 0 . 35) have the typical characteristics of BIB, while events with intermediate values ( − 0 . 2 < lowET BDT < 0 . 05 or − 0 . 35 < highET BDT < 0 . 0) are most like multijet events. Taking this separation between BIB and multijets into account, the per-event BDT serves two purposes in the analysis: first, it is used as part of the event cleaning described below in this section to reject BIB; second, it is used in the data-driven background estimation in the search region (see section 5). The simulated distributions of the per-jet NN and other inputs to the per-event BDTs show mostly good agreement with data. A dedicated procedure to evaluate the impact of residual mismodelling of NN and BDT input variables on the signal efficiency is described in section 6. Two selections are defined, referred to as the highET selection and the lowET selection, which are optimised to give maximum sensitivity for highET models and lowET models, respectively. Event-cleaning selections are applied to remove as much BIB and detector-related background as possible: the per-event BDT output must satisfy lowET BDT > 0 . 05 and highET BDT > 0 . 0in the lowET and highET selections, respectively; trigger matching, where at least one of the CalRatio jet candidates must be matched to the jet that fired the – 15 – JHEP06(2022)005 0.4−0.2−0 0.2 0.4 BDT T Low-E 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Fraction of events Main data BIB data )=(200,50) GeV s ,m Φ (m =1.26m gen τc )=(125,55) GeV s ,m Φ (m =1.05m gen τc ATLAS -1 =13 TeV, 139 fbs (a) 0.4−0.2−0 0.2 0.4 BDT T High-E 0 0.05 0.1 0.15 0.2 0.25 Fraction of events Main data BIB data )=(1000,275) GeV s ,m Φ (m =2.40m gen τc )=(600,150) GeV s ,m Φ (m =1.84m gen τc )=(400,100) GeV s ,m Φ (m =1.61m gen τc ATLAS -1 =13 TeV, 139 fbs (b) Figure 7. Distribution of the (a) lowET per-event BDT and (b) highET per-event BDT outputs in main data, BIB data and some of the benchmark signal samples after preselection. Only statistical uncertainties are shown. trigger and fulfil the requirements applied at trigger level; a timing window of − 3 <t< 15 ns , where t is the jet time for any of the CalRatio jet candidates or BIB jet candidates (this selection helps to remove remaining BIB jets and jet candidates produced by detector noise while retaining signal jets originating from relatively slowly moving LLPs with timing up to 15ns); a veto on events where one of the CalRatio jet candidates falls in the transition region between the ECal barrel and endcaps (1 . 45 <|η|< 1 . 55), where poor coverage by the electromagnetic calorimeter produces jets with artificially low fractions of energy in the ECal; and a veto on events where one of the CalRatio jet candidates or BIB jet candidates has log10(EH/EEM)<− 1 . 5. These requirements ensure that in the final selection, the only remaining source of background is multijet events, as described in section 5. The final selections are optimised to maximise the signal-to-background ratio in each search region. Variables with good signal-to-background discrimination at event level are used, such as Hmiss T/HT and the product of the NN signal scores of the two relevant CalRatio jet candidates. The quantity Hmiss T/HT has high values for BIB events but it has a softer distribution for signal. Hence it is a good discriminator, especially in the highpT regime. Making a selection based on the product of the NN signal scores of the two relevant CalRatio jet candidates helps to further reduce the background while keeping most signal events where one of the LLPs decays in the ATLAS calorimeters and the other one decays between the IP and the outer edge of the calorimeters. The lowET NN product is defined as the product of the two highest lowET NN signal-scores for clean jets in a given event. The highET NN product is defined analogously. The requirements shown in table 2are applied for the low-ETand high-ETselections. The signal efficiency for signal events to pass the lowand highET selections depends on the momenta, decay positions and decay products of the two LLPs in the event. For – 16 – JHEP06(2022)005 Low-ETselection High-ETselection Hmiss T/HT<0.6Hmiss T/HT<0.6 (Pjetsig1l,jetsig2llog10(EH/EEM)) >2 (Pjetsig1h,jetsig2hlog10(EH/EEM)) >1 pT(jetsig1l)>80 GeV pT(jetsig1h)>70 GeV pT(jetsig2l)>80 GeV pT(jetsig2h)>80 GeV low-ETNN product >0.7high-ETNN product >0.5 Table 2. Final selection requirements in the low-ETand high-ETselections. the benchmark HS models which are analysed using the lowET selection, the efficiencies range between 0.5% and 0.005%. Benchmark models analysed using the highET selection have signal efficiencies varying between nearly 9.3% and 1.3%. The efficiencies typically increase with the mean LLP pT in the sample. Further, the efficiencies are highest for samples where most decays take place in the calorimeter. Finally, the efficiency depends on what particles the LLPs decay to. LLP decays to bottom quarks are typically dominant in the samples considered by this analysis. Hence, the efficiency for events where the LLPs decay to b -quarks lead to similar efficiencies to the ranges mentioned above. Events where LLPs decay to c -quarks also have a similar efficiency. LLP decays to pairs of taus typically have an efficiency around half of the nominal efficiency. Finally samples where the LLPs decay to top quarks lead to a reduction in efficiency by about an order of magnitude. The signal efficiencies parameterized as a function of kinematic quantities and the decay mode are available in HEPData [66]. 5 Background estimation A data-driven ABCD method is used to estimate the contribution from the dominant background (SM multijet events) to the final selection. The ABCD method relies on the assumption that the distribution of background events can be factorised in the plane of two relatively statistically independent variables. In this plane, the method uses three control regions (B, C and D) to estimate the contribution of background events in the search region (A). In the case of no signal contamination in regions B, C and D, the number of background events in region A can be predicted using NA = ( NB·NC ) /ND , where NX is the number of background events in region X . In reality, there is non-zero signal contamination in the control regions. This is accounted for by using a modified ABCD method, which involves fitting to background and signal models simultaneously. The background component of the yield in each of the regions A, B, C and D is constrained to obey the standard ABCD relation, within the bounds of the ABCD method uncertainty (described below), while a signal strength parameter uniformly scales the signal yield in each region. Events passing the highET and lowET selections defined in the previous section are divided into four subregions according to two variables: P∆Rmin (jet, tracks) and highET BDT or lowET BDT, depending on the selection. The variables are uncorrelated (Pearson – 17 – JHEP06(2022)005 0 1 2 3 4 5 min R∆ ∑ 0 0.2 0.4 0.6 BDT T High-E 2− 10 1− 10 1 Number of events BIB data ATLAS -1 =13 TeV, 139 fbs AB CD (a) 0 1 2 3 4 5 min R∆ ∑ 0 0.2 0.4 0.6 BDT T High-E 1− 10 1 10 Number of events main data ATLAS -1 =13 TeV, 139 fbs AB CD (b) 0 1 2 3 4 5 min R∆ ∑ 0 0.2 0.4 0.6 BDT T High-E 1− 10 1 10 Number of events =1.84m gen τ)=(600,150) GeV; c s ,m Φ (m ATLAS Simulation =13 TeVs AB CD (c) 0 1 2 3 4 5 min R∆ ∑ 0 0.1 0.2 0.3 0.4 0.5 BDT T Low-E 1− 10 1 10 Number of events BIB data ATLAS -1 =13 TeV, 139 fbs AB CD (d) 0 1 2 3 4 5 min R∆ ∑ 0 0.1 0.2 0.3 0.4 0.5 BDT T Low-E 1 10 2 10 3 10 Number of events main data ATLAS -1 =13 TeV, 139 fbs AB CD (e) 0 1 2 3 4 5 min R∆ ∑ 0 0.1 0.2 0.3 0.4 0.5 BDT T Low-E 2− 10 1− 10 1 10 Number of events =1.23m gen τ)=(200,50) GeV; c s ,m Φ (m ATLAS Simulation =13 TeVs AB CD (f) Figure 8. The distributions of P∆Rmin (jet, tracks) vs highET BDT for (a) BIB events, (b) main data and (c) a signal sample after event cleaning for the highET selection. Panels (d,e,f) show the equivalent distributions for the lowET selection. The signal sample with mΦ = 600 GeV and ms = 150 GeV is shown for the highET selection, while the sample with mΦ = 200 GeV and ms= 50 GeV is shown for the low-ETselection. correlation coefficient |r|< 0 . 03 in the main dataset after the event cleaning, with additional tests for correlations described below) and have good separation between signal and multijet background, as shown in figure 8. Region A is defined by high-ETBDT ≥ 0 . 36 and P∆Rmin ≥ 1 . 5for the highET analysis and by low-ETBDT ≥ 0 . 27 and P∆Rmin ≥ 1 . 0for the lowET analysis. Regions B, C, and D are obtained by reversing one or both of these selections. In cases where more than one background population is included in the final selection, the condition that the two variables defining the plane are statistically independent is only guaranteed if their contributions have the same shape in the ABCD plane. In this search there are three major sources of background (BIB, cosmics and SM multijets) with different distributions in the plane, which results in the two variables defining it having some correlation. It is therefore necessary to make sure that the selection above has a high rejection power for two of the three sources. Specifically, the contribution from BIB and cosmics in the ABCD plane must be negligible after the object and event selection requirements, leaving only the contribution of SM multijet events to be estimated by the ABCD method. Two checks were performed to confirm that the contribution of background events from non-collision background is negligible after the selection. – 18 – JHEP06(2022)005 First, the number of events satisfying each stage of the selection for the main dataset and the BIB dataset is shown in table 3for the highET and lowET selections, along with the fraction of signal events passing each cut for several benchmark samples. For both the highET and lowET selections, the number of BIB events satisfying all selection criteria is well within the uncertainty in the number of events passing all selections in the main dataset. Considering that the efficiency of BIB identification in this dataset is approximately 70%, the BIB contamination in the main dataset can be considered negligible. Furthermore, the events from the BIB dataset that pass the selection were checked and found to display properties of multijet events. In particular, their φ and z vs time distributions do not show the typical shape of BIB. The events from the main dataset that pass the event cleaning were also checked and were found not to display the properties of BIB. The second check is to confirm that the contamination from cosmic rays in the ABCD plane is negligible. This is done using the cosmics dataset. The number of events in this dataset passing the full selections is checked after weighting by the following two factors. The first factor takes into account the difference between the number of bunch crossings where protons are present in both beams while the CalRatio triggers were enabled, and the number of empty bunch crossings, during which the cosmics dataset was collected. The protons-toempty live-time ratio depends on the beam conditions, and its value lies in the range 2 to 3.5. The second factor takes into account the fact that events in the cosmics dataset will have no related collision activity, and therefore will be largely trackless: events in the cosmics dataset will be far more likely than events from the main dataset to pass the requirements on jet ∆ Rmin at the HLT and in the analysis preselection. The second factor is calculated as the ratio of the number of events entering the ABCD plane in the main dataset to the number passing the selection if all tracks in the event are ignored. This factor is < 0 . 1in all data-taking periods. The final estimated number of events in the ABCD plane is 2 . 5 ± 0 . 8 (none of which are in region A) in the highET selection and 1 . 8 ± 0 . 5(0 . 3 ± 0 . 2in region A) in the lowET selection. These yields are negligible in comparison with the expected number of data events in the ABCD plane in the main dataset, which is over 300 in both selections. The validity of the ABCD method is tested by applying it to a number of validation regions (VRs), which are orthogonal to region A. A first set of validation regions is defined using the nominal event selections but looking only into part of regions B, C and D. Restricting the VR ABCD plane to intermediate values of the BDT output (using part of nominal regions C and D) allows a test of the background estimation method in the whole P∆Rmin range in the absence of signal contamination. Likewise, restricting the VR ABCD plane to low values of P∆Rmin and allowing any BDT output value (using part of nominal regions B and D) permits a test of the method at large values of the BDT output. As an example, the nominal highET event selection is validated in region VRCDhigh-ET , defined using the nominal highET selection but restricted to the range 0 . 0 <high-ETBDT < 0 . 3 and 0 . 5 <P∆Rmin < 5 . 0. First, the ABCD method is tested by dividing this region into four subregions defined by the boundaries of high-ETBDT = 0 . 15 and P∆Rmin = x , where the value of x is varied from 1 to 4. Then the ABCD method is tested again in this same region by setting the P∆Rmin (jet, tracks) boundary at 1.5 and allowing the highET BDT boundary to take values from 0.05 to 0.25. – 19 – JHEP06(2022)005 High-ETselection: Main data BIB mΦ= 1000GeV mΦ= 600GeV mΦ= 400GeV ms= 275GeV ms= 150GeV ms= 100GeV (cτgen = 2.40 m) (cτgen = 1.84 m) (cτgen = 1.61 m) Preselection: trigger, 2 clean jets 40743 867 2 200 854 24% 19% 15% P∆Rmin >0.528248 024 1399 351 23% 19% 15% Event cleaning: high-ETBDT>0.075 224 3141 23% 19% 14% Trigger matching 58190 2026 21% 17% 14% −3< t < 15ns 54108 1837 20% 17% 13% log10(EH/EEM)>−1.5for jetsig1,jetsig2,jetbib1,jetbib250 516 1733 19% 16% 13% |η|/∈[1.45,1.55] for jetsig1,jetsig247037 1627 18% 15% 12% High-ETselection: Hmiss T/HT<0.640464 1295 14% 13% 11% pT(jetsig1h)>70GeV 39 266 1270 14% 13% 11% pT(jetsig2h)>80GeV 21 787 531 13% 11% 8.5% Pjetsig1h,jetsig2hlog10(EH/EEM)>113 183 341 12% 9.6% 6.8% High-ETNN product >0.5393 15 9.3% 6.9% 4.2% Region A: 22 1 7.4% 4.8% 2.6% Region B: 7 0 0.63% 0.54% 0.30% Region C: 233 7 1.1% 1.4% 1.2% Region D: 131 7 0.10% 0.14% 0.15% Low-ETselection: Main data BIB mΦ= 200GeV mΦ= 125GeV mΦ= 60GeV ms= 50GeV ms= 55GeV)ms= 5GeV (cτgen = 1.25 m) (cτgen = 1.05 m) (cτgen = 0.22 m) Preselection: trigger, 2 clean jets 40743 867 2 200 854 7.1% 1.1% 0.79% P∆Rmin >0.528248 024 1399 351 6.9% 1.1% 0.73% Event cleaning: low-ETBDT >0.05 1 288596 44 035 6.3% 0.93% 0.51% Trigger matching 1138 961 36 266 6.0% 0.86% 0.47% −3< t < 15ns 1123 239 35245 5.9% 0.84% 0.45% log10(EH/EEM)>−1.5for jetsig1,jetsig2,jetbib1,jetbib21 038019 33 100 5.5% 0.79% 0.43% |η|/∈[1.45,1.55] for jetsig1,jetsig2976805 31 292 5.1% 0.73% 0.39% Low-ETselection: Hmiss T/HT<0.6965748 30 712 5.0% 0.71% 0.38% pT(jetsig1l)>80GeV 315 530 10048 4.0% 0.54% 0.23% pT(jetsig2l)>80GeV 73 484 2810 1.8% 0.25% 0.10% Pjetsig1l,jetsig2llog10(EH/EEM)>23375 93 0.59% 0.060% 0.02% Low-ETNN product >0.7307 10 0.53% 0.04% 0.006% Region A: 23 0 0.46% 0.03% 0.003% Region B: 3 0 0.01% 0% 0% Region C: 220 7 0.06% 0.01% 0.002% Region D: 61 3 0% 0% 0% Table 3. Sequential impact of each requirement on the number of events passing the selection for the highET (top table) and lowET (bottom table) selections. The signal columns represent the cumulative fraction of events passing the selection than the number of events. The ABCD plane defined in this VR can be seen in figure 9for VRCDhigh-ET and the lowET selection, VRCDlow-ET , along with the level of agreement between the expected and observed numbers of events in region A in all the tested boundary selections. It should be noted that the tests in each VR are statistically correlated. Therefore, statistical fluctuations can affect several tests. A second set of VRs is defined by inverting the selection on the product of the signal NN scores of the two CalRatio jets in the analysis selections. – 20 – JHEP06(2022)005 0 1 2 3 4 5 min R∆ ∑ 0 0.2 0.4 0.6 BDT T High-E 2− 10 1− 10 1 Number of events T high-E VRCD main data ATLAS -1 =13 TeV, 139 fbs Nominal A A B CD (a) 0.5 1 1.5 2 2.5 3 3.5 4 4.5 min R∆ ∑ 0 20 40 60 80 100 120 140 Number of events T high-E VRCD observed A expected A ATLAS -1 =13 TeV, 139 fbs (b) 0 0.05 0.1 0.15 0.2 0.25 0.3 BDT T High-E 0 20 40 60 80 100 120 140 160 180 200 Number of events T high-E VRCD observed A expected A ATLAS -1 =13 TeV, 139 fbs (c) 0 1 2 3 4 5 min R∆ ∑ 0 0.1 0.2 0.3 0.4 0.5 BDT T Low-E 2− 10 1− 10 1 Number of events T low-E VRCD main data ATLAS -1 =13 TeV, 139 fbs Nominal A AB CD (d) 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 min R∆ ∑ 0 20 40 60 80 100 120 140 Number of events T low-E VRCD observed A expected A ATLAS -1 =13 TeV, 139 fbs (e) 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 BDT T Low-E 0 50 100 150 200 250 300 350 Number of events T low-E VRCD observed A expected A ATLAS -1 =13 TeV, 139 fbs (f) Figure 9. (a) The per-event BDT vs P∆Rmin (jet, tracks) distribution for the main dataset in the VRCDhigh-ET validation region. Region A in the nominal highET selection is shown for reference. Also shown is a comparison of the observed and expected events in region A of this VR. The x -axis shows the different (b) P∆Rmin (jet, tracks) and (c) BDT boundaries used to test the ABCD method. Statistical uncertainties are shown in (b) and (c). Panels (d,e,f) show the equivalent distributions in the VRCDlow-ETvalidation region. Given that signal contamination is low in all the validation regions, the plain ABCD method assuming no signal is applied. The statistical precision of this closure test is better than the final statistical uncertainty of the number of events observed in region A. Good closure, within one standard deviation, is observed in all the validation regions defined in this section. 6 Systematic uncertainties The uncertainty in the data-driven ABCD method for the background estimate is studied in the dijet control region. In this control region, an alternative ABCD plane is defined using the same variables as in the analysis, but adjusting the boundaries in regions A, B, C and D to reduce the effect of statistical fluctuations in the estimation of the number of dijet events in region A by this method. The observed number of events in region A is compared with the estimate given by the ABCD method for both the highET and the lowET ABCD planes. In all the tests performed, the observed and expected numbers of events agree within the statistical uncertainties. This confirms that the two variables – 21 – JHEP06(2022)005 forming the plane are statistically independent and therefore no systematic uncertainty is added for the background estimation method. The uncertainty in the combined 2015–2018 integrated luminosity is 1.7% [ 67 ], obtained using the LUCID-2 detector [68] for the primary luminosity measurements. Events in MC simulation are reweighted to obtain the correct pile-up distribution. The uncertainty in the pile-up reweighting of the reconstructed events in the MC simulation is estimated by comparing the distribution of the number of primary vertices in the MC simulation with the distribution in data as a function of the instantaneous luminosity. Differences between these distributions are reduced by scaling the mean number of pp interactions per bunch crossing in the MC simulation and the ± 1 σ uncertainties are assigned to these scaling factors [ 67 , 68 ]. The effect on the signal event yields varies between 2% and 8% depending on the signal model. The jet energy scale and jet energy resolution introduce uncertainties in the signal yield of < 1% to 5% and 1% to 6%, respectively, depending on the signal model. These uncertainties are calculated using the procedure detailed in ref. [ 69 ]. Since the jets used in this analysis are required to have a low fraction of calorimeter energy in the ECal, the jet energy uncertainties are rederived as a function of ECal energy fraction as well as η . The additional jet energy uncertainties are found to have an effect of 1% to 6% on the signal yield, and are conservatively taken in quadrature with the regular jet-energy uncertainties. The lowET models are more sensitive to all jet energy uncertainties than the high-ETmodels. The uncertainty in the signal trigger efficiency is estimated by studying how well modelled the three most important trigger variables (jet ET , log10(EH/EEM) , and pT of tracks within the jet) are between HLT-reconstructed quantities and offline-reconstructed quantities in data and MC simulation. A tag-and-probe technique is applied to a pure sample of multijet events obtained using standard jet triggers in both data and MC simulation. Scale factors that represent the degree of mismodelling in each variable are derived and then applied in an emulation of the CalRatio triggers. The change in yield relative to the nominal (unscaled) trigger emulation after the full analysis selection is taken as the size of the systematic uncertainty, which is between 1% and 7% depending on the signal model. A systematic uncertainty is included to account for potential mismodelling of input variables used in the machine-learning techniques applied in the analysis. Using the same control sample of dijet events defined for the evaluation of the systematic uncertainty in the data-driven background estimate, the distributions of the inputs and outputs of the per-jet NNs and the per-event BDTs are studied. They are found to agree fairly well between data and MC simulation. The residual differences are translated into a systematic uncertainty in the signal efficiency, using the following procedure. For each mis-modeled variable, the residual differences are quantified through a transfer factor between simulation and data. In an ensemble of pseudo-experiments, the NN and BDT input variables for each signal event are varied by this transfer factor; in each pseudo-experiment the transfer factor is modulated by a random Gaussian, with a mean of zero and a width determined by measurements in the control region. The final per-event BDTs are then re-evaluated, and the overall signal – 22 – JHEP06(2022)005 efficiency of the sample is evaluated for each pseudo-experiment. This sequence of steps allows for the statistical determination of the systematic uncertainty in the final signal efficiency. The value of the resulting uncertainty can thus be obtained from the distributions of efficiencies for the ensemble, and can be as large as 6% depending on the signal model. Finally, an uncertainty due to the NLO-reweighting of the signal samples is obtained by comparing the NLO MadGraph predictions for a 125 GeV Higgs boson mediator with predictions at next-to-next-to-leading-order accuracy in QCD from Powheg Box v2 [ 70 – 74 ]. This results in an additional signal efficiency uncertainty of 1%–7% for most samples. 7 Results and statistical interpretation A data-driven background estimation and signal hypothesis test is performed simultaneously in all regions. The procedure for the simultaneous fit is explained in detail in the previous iteration of this analysis [ 37 ] and is summarised in the following. A profile likelihood function is constructed from the product of the probabilities of observing a given number of events in each region of the ABCD plane, given the expected number of events in that region. This expected number of events is given by the sum of the predicted signal yield in that region (scaled by a parameter of interest called the signal strength) and the expected number of background events. The background component of the expected yield in each region is constrained to satisfy the ABCD relation introduced in section 5. The introduction of a signal component will therefore dynamically modify the remaining allowed background prediction in this set-up. Additionally, a nuisance parameter which represents the total uncertainty in the signal efficiency, and consequently the signal yield, is introduced. The background estimates before (a priori) and after (a posteriori) unblinding region A are shown in table 4. After unblinding, the modified ABCD method takes account of the observed number of events in region A when making the final fit. As a consequence, the background estimate changes relative to the a priori case, since the fit now uses all available information to determine the expected background in each region. As shown in the table, there is a slight excess in the observed number of events in region A over the a priori expected background in both the highand lowET selections. In the a priori fit, these excesses correspond to background-only hypothesis p -values of 0.083 and 0.076 in the highET and lowET selections, respectively. The significance is reduced to slightly under one standard deviation in the a posteriori (background-only fit) estimate. The CLs method [ 75 ], using the “alternative test statistic” ˜q [ 76 ] is used to set upper limits on the production cross-section times BR of the LLP signals considered. The pyhf [ 77 , 78 ] framework is used to implement the likelihood function and extract the upper limits. An asymptotic approximation [ 76 ] is used for these results. This approximation was tested against the full frequentist pseudo-experiment-based method for a variety of signal samples and was found to give consistent limits. Since each signal sample was generated for a given lifetime assumption, it is necessary to extrapolate the limits across lifetimes. This extrapolation is performed using a reweighting method, which is described in detail in the previous iteration of this analysis [ 37 ] and summarised briefly here. LLPs follow an exponential decay distribution, where the decay constant is given by the mean lifetime τgen – 23 – JHEP06(2022)005 High-ETselection A B C D Observed data 22 7 233 131 a priori Estimated background 12.4±4.7 7 ±2.6 233 ±15 131 ±11 a posteriori (background-only fit) Fitted background 18.8±3.5 10.2±3.2 236 ±15 128 ±11 a posteriori (signal-plus-background fit) Fitted background 10.0±6.0 5.7±2.4 230 ±15 131 ±11 Fitted signal ((mΦ, ms) = (600,150) GeV)12.2±8.7 1.4±1.0 3.4±2.5<1 Low-ETselection A B C D Observed data 23 3 220 61 a priori Estimated background 10.8±6.6 3 ±1.7 220 ±15 61 ±7.8 a posteriori (background-only fit) Fitted background 20.6±4.0 5.4±2.3 222 ±15 59 ±7.7 a posteriori (signal-plus-background fit) Fitted background 8.4±7.7 2.4±1.5 217 ±15 61 ±7.8 Fitted signal ((mΦ, ms) = (125,55) GeV)14.6±9.9<1 3.2±2.2<1 Table 4. Application of the modified ABCD method to the final highET and lowET selections. The a priori estimate refers to the ‘pre-unblinding’ case, where the data in region A are ignored by removing the Poisson constraint in that region and the signal strength is fixed to zero. This matches the simple Nbkg A = ( Nbkg B·Nbkg C ) /Nbkg D relation. The a posteriori estimate refers to the ‘post-unblinding’ case, including the observed data in region A in the background-only global fit, obtained by fixing the signal strength to 0 (background-only fit) or allowing it to float (signalplus-background fit). The table also shows one set of representative signal yields in each selection for the signal-plus-background fit. Only statistical uncertainties are included in the quoted error of the background, while the uncertainties in the signal include those from both statistical and experimental sources. in a given sample. To extrapolate to a different mean proper lifetime τnew , a weight w is calculated as a function of the given particle’s proper decay time t: w(t) = τgen exp(−t/τgen)·exp(−t/τnew) τnew . The per-event weight is the product of the weights obtained for each LLP in a given event. Figure 10 shows a summary of the observed limits for the samples where the mediator is assumed to be the SM Higgs boson, with mass 125 GeV . SM Higgs boson BRs to long-lived neutral scalars above 10% are excluded for cτ values between a few centimetres and about 20 metres, depending on the mass of the LLP. Figure 11 shows a summary of observed limits – 24 – JHEP06(2022)005 [51] T. Sjöstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1,Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE]. [52] ATLAS collaboration, The PYTHIA 8 A3 tune description of ATLAS minimum bias and inelastic measurements incorporating the Donnachie-Landshoff diffractive model, ATL-PHYS-PUB-2016-017 (2016). 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Berta140, I.A. Bertram89, O. Bessidskaia Bylund178, S. Bethke113, A. Betti42, A.J. Bevan92, S. Bhatta152, – 33 – JHEP06(2022)005 D.S. Bhattacharya173, P. Bhattarai26, V.S. Bhopatkar6, R. Bi136, R. Bi29, R.M. Bianchi136, O. Biebel112, R. Bielski129, N.V. Biesuz71a,71b, M. Biglietti74a, T.R.V. Billoud139, M. Bindi53, A. Bingul21b, C. Bini72a,72b, S. Biondi23b,23a, A. Biondini90, C.J. Birch-sykes99, G.A. Bird20,141, M. Birman176, T. Bisanz36, J.P. Biswal2, D. Biswas177,j, A. Bitadze99, K. Bjørke131, I. Bloch46, C. Blocker26, A. Blue57, U. Blumenschein92, J. Blumenthal98, G.J. Bobbink117, V.S. Bobrovnikov 119b,119a , M. Boehler 52 , D. Bogavac 13 , A.G. Bogdanchikov 119b,119a , C. Bohm 45a , V. Boisvert 93 , P. Bokan 46 , T. Bold 83a , M. Bomben 5 , M. Bona 92 , M. Boonekamp 142 , C.D. Booth 93 , A.G. Borbély57, H.M. Borecka-Bielska108, L.S. Borgna94, G. Borissov89, D. Bortoletto132, D. Boscherini23b, M. Bosman13, J.D. Bossio Sola36, K. Bouaouda35a, J. Boudreau136, E.V. 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Frattari72a,72b, – 35 – JHEP06(2022)005 A.C. Freegard92, P.M. Freeman20, W.S. Freund80b, E.M. Freundlich47, D. Froidevaux36, J.A. Frost 132 , Y. Fu 60a , M. Fujimoto 124 , E. Fullana Torregrosa 170 , J. Fuster 170 , A. Gabrielli 23b,23a , A. Gabrielli36, P. Gadow46, G. Gagliardi55b,55a, L.G. Gagnon17, G.E. Gallardo132, E.J. Gallas132, B.J. Gallop141, R. Gamboa Goni92, K.K. Gan125, S. Ganguly160, J. Gao60a, Y. Gao50, F.M. Garay Walls144a,144b, B. Garcia29, C. García170, J.E. García Navarro170, J.A. García Pascual14a, M. Garcia-Sciveres17, R.W. Gardner37, D. Garg77, R.B. Garg150, S. Gargiulo52, C.A. Garner163, V. Garonne29, S.J. Gasiorowski145, P. Gaspar80b, G. Gaudio70a, P. Gauzzi72a,72b, I.L. Gavrilenko109, A. Gavrilyuk121, C. Gay171, G. Gaycken46, E.N. Gazis10, A.A. Geanta27b, C.M. Gee143, J. Geisen96, M. Geisen98, C. Gemme55b, M.H. Genest58, S. Gentile 72a,72b , S. George 93 , W.F. George 20 , T. Geralis 44 , L.O. Gerlach 53 , P. Gessinger-Befurt 36 , M. Ghasemi Bostanabad172, A. Ghosal148, A. Ghosh167, A. Ghosh7, B. Giacobbe23b, S. Giagu 72a,72b , N. Giangiacomi 163 , P. Giannetti 71a , A. Giannini 60a , S.M. Gibson 93 , M. Gignac 143 , D.T. Gil83b, B.J. Gilbert39, D. Gillberg34, G. Gilles117, N.E.K. Gillwald46, L. Ginabat133, D.M. Gingrich2,af, M.P. Giordani66a,66c, P.F. Giraud142, G. Giugliarelli66a,66c, D. Giugni68a, F. Giuli 73a,73b , I. Gkialas 9,h , P. Gkountoumis 10 , L.K. Gladilin 111 , C. Glasman 97 , G.R. Gledhill 129 , M. Glisic129, I. Gnesi41b,d, Y. Go29, M. Goblirsch-Kolb26, D. Godin108, S. Goldfarb103, T. Golling54, M.G.D. Gololo33g, D. Golubkov120, J.P. Gombas105, A. Gomes137a,137b, A.J. Gomez Delegido170, R. Goncalves Gama53, R. Gonçalo137a,137c, G. Gonella129, L. Gonella20, A. Gongadze79, F. Gonnella20, J.L. Gonski39, S. González de la Hoz170, S. Gonzalez Fernandez13, R. Gonzalez Lopez90, C. Gonzalez Renteria17, R. Gonzalez Suarez168, S. Gonzalez-Sevilla54, G.R. Gonzalvo Rodriguez170, R.Y. González Andana50, L. Goossens36, N.A. Gorasia20, P.A. Gorbounov121, H.A. Gordon29, B. Gorini36, E. Gorini67a,67b, A. Gorišek91, A.T. Goshaw49, M.I. Gostkin79, C.A. Gottardo116, M. Gouighri35b, V. Goumarre46, A.G. Goussiou145, N. Govender 33c , C. Goy 4 , I. Grabowska-Bold 83a , K. Graham 34 , E. Gramstad 131 , S. Grancagnolo 18 , M. Grandi153, V. Gratchev135, P.M. Gravila27f, F.G. Gravili67a,67b, H.M. Gray17, C. Grefe24, I.M. Gregor46, P. Grenier150, K. Grevtsov46, C. Grieco13, A.A. Grillo143, K. Grimm31,l, S. Grinstein13,t, J.-F. Grivaz64, S. Groh98, E. Gross176, J. Grosse-Knetter53, C. Grud104, A. Grummer115, J.C. Grundy132, L. Guan104, W. Guan177, C. Gubbels171, J.G.R. Guerrero Rojas170, F. Guescini113, D. Guest18, R. Gugel98, A. Guida46, T. Guillemin4, S. Guindon36, F. Guo14a, J. Guo60c, L. Guo64, Y. Guo104, R. Gupta46, S. Gurbuz24, G. Gustavino36, M. Guth54, P. Gutierrez126, L.F. Gutierrez Zagazeta134, C. Gutschow94, C. Guyot142, C. Gwenlan132, C.B. Gwilliam90, E.S. Haaland131, A. Haas123, M. Habedank46, C. Haber17, H.K. Hadavand8, A. Hadef98, S. Hadzic113, M. Haleem173, J. Haley127, J.J. Hall146, G.D. Hallewell100, L. Halser19, K. Hamano172, H. Hamdaoui35e, M. Hamer24, G.N. Hamity50, J. Han 60b , K. Han 60a , L. Han 14c , L. Han 60a , S. Han 17 , Y.F. Han 163 , K. Hanagaki 81,r , M. Hance 143 , D.A. Hangal39, M.D. Hank37, R. Hankache99, E. Hansen96, J.B. Hansen40, J.D. Hansen40, P.H. Hansen40, K. Hara165, D. Harada54, T. Harenberg178, S. Harkusha106, Y.T. Harris132, P.F. Harrison174, N.M. Hartman150, N.M. Hartmann112, Y. Hasegawa147, A. Hasib50, S. Haug19, R. Hauser105, M. Havranek139, C.M. Hawkes20, R.J. Hawkings36, S. Hayashida114, D. Hayden105, C. Hayes104, R.L. Hayes171, C.P. Hays132, J.M. Hays92, H.S. Hayward90, F. He60a, Y. He161, Y. He133, M.P. Heath50, V. Hedberg96, A.L. Heggelund131, N.D. Hehir92, C. Heidegger52, K.K. Heidegger52, W.D. Heidorn78, J. Heilman34, S. Heim46, T. Heim17, B. Heinemann46,ad, J.G. Heinlein134, J.J. Heinrich129, L. Heinrich36, J. Hejbal138, L. Helary46, A. Held123, C.M. Helling143, S. Hellman45a,45b, C. Helsens36, R.C.W. Henderson89, L. Henkelmann32, A.M. Henriques Correia36, H. Herde150, Y. Hernández Jiménez152, H. Herr98, M.G. Herrmann112, T. Herrmann48, G. Herten52, R. Hertenberger112, L. Hervas36, N.P. Hessey164a, H. Hibi82, E. Higón-Rodriguez 170 , S.J. Hillier 20 , I. Hinchliffe 17 , F. Hinterkeuser 24 , M. Hirose 130 , S. Hirose 165 , D. Hirschbuehl178, B. Hiti91, O. Hladik138, J. Hobbs152, R. Hobincu27e, N. Hod176, – 36 – JHEP06(2022)005 M.C. Hodgkinson146, B.H. Hodkinson32, A. Hoecker36, J. Hofer46, D. Hohn52, T. Holm24, M. Holzbock113, L.B.A.H. Hommels32, B.P. Honan99, J. Hong60c, T.M. Hong136, Y. Hong53, J.C. Honig52, A. Hönle113, B.H. Hooberman169, W.H. Hopkins6, Y. Horii114, L.A. Horyn37, S. Hou 155 , J. Howarth 57 , J. Hoya 88 , M. Hrabovsky 128 , A. Hrynevich 107 , T. Hryn’ova 4 , P.J. Hsu 63 , S.-C. Hsu145, Q. Hu39, S. Hu60c, Y.F. Hu14a,14d,ah, D.P. Huang94, X. Huang14c, Y. Huang60a, Y. Huang14a, Z. Hubacek139, M. Huebner24, F. Huegging24, T.B. Huffman132, M. Huhtinen36, S.K. Huiberts16, R. Hulsken58, N. Huseynov12,z, J. Huston105, J. Huth59, R. Hyneman150, S. Hyrych 28a , G. Iacobucci 54 , G. Iakovidis 29 , I. Ibragimov 148 , L. Iconomidou-Fayard 64 , P. Iengo 36 , R. Iguchi160, T. Iizawa54, Y. Ikegami81, A. Ilg19, N. Ilic163, H. Imam35a, T. Ingebretsen Carlson45a,45b, G. Introzzi70a,70b, M. Iodice74a, V. Ippolito72a,72b, M. Ishino160, W. Islam177, C. Issever18,46, S. Istin21a,ai, H. Ito175, J.M. Iturbe Ponce62a, R. Iuppa75a,75b, A. Ivina176, J.M. Izen43, V. Izzo69a, P. Jacka138, P. Jackson1, R.M. Jacobs46, B.P. Jaeger149, C.S. Jagfeld112, G. Jäkel178, K. Jakobs52, T. Jakoubek176, J. Jamieson57, K.W. Janas83a, G. Jarlskog96, A.E. Jaspan90, T. Javůrek36, M. Javurkova101, F. Jeanneau142, L. Jeanty129, J. Jejelava156a,x, P. Jenni52,e, S. Jézéquel4, J. Jia152, X. Jia59, Z. Jia14c, Y. Jiang60a, S. Jiggins50, J. Jimenez Pena113, S. Jin14c, A. Jinaru27b, O. Jinnouchi161, H. Jivan33g, P. Johansson146, K.A. Johns7, C.A. Johnson65, D.M. Jones32, E. Jones174, R.W.L. Jones89, T.J. Jones90, J. Jovicevic15, X. Ju17, J.J. Junggeburth36, A. Juste Rozas13,t, S. Kabana144e, A. Kaczmarska84, M. Kado72a,72b, H. Kagan125, M. Kagan150, A. Kahn39, A. Kahn134, C. Kahra98, T. Kaji175, E. Kajomovitz157, N. Kakati176, C.W. Kalderon29, A. Kamenshchikov163, N.J. Kang143, Y. Kano114, D. Kar33g, K. Karava132, M.J. Kareem164b, E. Karentzos52, I. Karkanias159, S.N. Karpov 79 , Z.M. Karpova 79 , V. Kartvelishvili 89 , A.N. Karyukhin 120 , E. Kasimi 159 , C. Kato 60d , J. Katzy46, S. Kaur34, K. Kawade147, K. Kawagoe87, T. Kawaguchi114, T. Kawamoto142, G. Kawamura53, E.F. Kay172, F.I. Kaya166, S. Kazakos13, V.F. Kazanin119b,119a, Y. Ke152, J.M. Keaveney33a, R. Keeler172, G.V. Kehris59, J.S. Keller34, A.S. Kelly94, D. Kelsey153, J.J. Kempster20, J. Kendrick20, K.E. Kennedy39, O. Kepka138, S. Kersten178, B.P. Kerševan91, S. Ketabchi Haghighat163, M. Khandoga133, A. Khanov127, A.G. Kharlamov119b,119a, T. Kharlamova119b,119a, E.E. Khoda145, T.J. Khoo18, G. Khoriauli173, E. Khramov79, J. Khubua 156b , M. Kiehn 36 , A. Kilgallon 129 , E. Kim 161 , Y.K. Kim 37 , N. Kimura 94 , A. Kirchhoff 53 , D. Kirchmeier48, C. Kirfel24, J. Kirk141, A.E. Kiryunin113, T. Kishimoto160, D.P. Kisliuk163, C. Kitsaki10, O. Kivernyk24, M. Klassen61a, C. Klein34, L. Klein173, M.H. Klein104, M. Klein90, U. Klein90, P. Klimek36, A. Klimentov29, F. Klimpel113, T. Klingl24, T. Klioutchnikova36, F.F. Klitzner112, P. Kluit117, S. Kluth113, E. Kneringer76, T.M. Knight163, A. Knue52, D. Kobayashi87, R. Kobayashi85, M. Kocian150, T. Kodama160, P. Kodys140, D.M. Koeck153, P.T. Koenig 24 , T. Koffas 34 , N.M. Köhler 36 , M. Kolb 142 , I. Koletsou 4 , T. Komarek 128 , K. Köneke 52 , A.X.Y. Kong1, T. Kono124, N. Konstantinidis94, B. Konya96, R. Kopeliansky65, S. Koperny83a, K. Korcyl84, K. Kordas159, G. Koren158, A. Korn94, S. Korn53, I. Korolkov13, N. Korotkova111, B. Kortman117, O. Kortner113, S. Kortner113, W.H. Kostecka118, V.V. Kostyukhin148,162, A. Kotsokechagia64, A. Kotwal49, A. Koulouris36, A. Kourkoumeli-Charalampidi70a,70b, C. Kourkoumelis9, E. Kourlitis6, O. Kovanda153, R. Kowalewski172, W. Kozanecki142, A.S. Kozhin120, V.A. Kramarenko111, G. Kramberger91, P. Kramer98, M.W. Krasny133, A. Krasznahorkay36, J.A. Kremer98, J. Kretzschmar90, K. Kreul18, P. Krieger163, F. Krieter112, S. Krishnamurthy101, A. Krishnan61b, M. Krivos140, K. Krizka17, K. Kroeninger47, H. Kroha113, J. Kroll138, J. Kroll134, K.S. Krowpman105, U. Kruchonak79, H. Krüger24, N. Krumnack78, M.C. Kruse49, J.A. Krzysiak84, A. Kubota161, O. Kuchinskaia162, S. Kuday3a, D. Kuechler46, J.T. Kuechler46, S. Kuehn36, T. Kuhl46, V. Kukhtin79, Y. Kulchitsky106,z, S. Kuleshov144d,144b, M. Kumar33g, N. Kumari100, M. Kuna58, A. Kupco138, T. Kupfer47, O. Kuprash52, H. Kurashige82, L.L. Kurchaninov164a, Y.A. Kurochkin106, A. Kurova110, E.S. Kuwertz36, – 37 – JHEP06(2022)005 M. Kuze161, A.K. Kvam145, J. Kvita128, T. Kwan102, K.W. Kwok62a, C. Lacasta170, F. Lacava72a,72b, H. Lacker18, D. Lacour133, N.N. Lad94, E. Ladygin79, B. Laforge133, T. Lagouri144e, S. Lai53, I.K. Lakomiec83a, N. Lalloue58, J.E. Lambert126, S. Lammers65, W. Lampl7, C. Lampoudis159, E. Lançon29, U. Landgraf52, M.P.J. Landon92, V.S. Lang52, J.C. Lange53, R.J. Langenberg101, A.J. Lankford167, F. Lanni29, K. Lantzsch24, A. Lanza70a, A. Lapertosa55b,55a, J.F. Laporte142, T. Lari68a, F. Lasagni Manghi23b, M. Lassnig36, V. Latonova138, T.S. Lau62a, A. Laudrain98, A. Laurier34, M. Lavorgna69a,69b, S.D. Lawlor93, Z. Lawrence99, M. Lazzaroni68a,68b, B. Le99, B. Leban91, A. Lebedev78, M. LeBlanc36, T. LeCompte150, F. Ledroit-Guillon58, A.C.A. Lee94, G.R. Lee16, L. Lee59, S.C. Lee155, L.L. Leeuw33c, B. Lefebvre164a, H.P. Lefebvre93, M. Lefebvre172, C. Leggett17, K. Lehmann149, G. Lehmann Miotto36, W.A. Leight101, A. Leisos159,s, M.A.L. Leite80c, C.E. Leitgeb46, R. Leitner140, K.J.C. Leney42, T. Lenz24, S. Leone71a, C. Leonidopoulos50, A. Leopold151, C. Leroy108, R. Les105, C.G. Lester32, M. Levchenko135, J. Levêque4, D. Levin104, L.J. Levinson176, D.J. Lewis20, B. Li14b, B. Li60b, C. Li60a, C-Q. Li60c,60d, H. Li60a, H. Li60b, H. Li60b, J. Li60c, K. Li145, L. Li60c, M. Li14a,14d, Q.Y. Li60a, S. Li60d,60c,c, T. Li60b, X. Li46, Z. Li60b, Z. Li132, Z. Li102, Z. Li90, Z. Liang14a, M. Liberatore46, B. Liberti73a, K. Lie62c, J. Lieber Marin 80b , K. Lin 105 , R.A. Linck 65 , R.E. Lindley 7 , J.H. Lindon 2 , A. Linss 46 , E. Lipeles 134 , A. Lipniacka16, T.M. Liss169,ae, A. Lister171, J.D. Little4, B. Liu14a, B.X. Liu149, D. Liu60d,60c, J.B. Liu60a, J.K.K. Liu32, K. Liu60d,60c, M. Liu60a, M.Y. Liu60a, P. Liu14a, Q. Liu60d,145,60c, X. Liu60a, Y. Liu46, Y. Liu14c,14d, Y.L. Liu104, Y.W. Liu60a, M. Livan70a,70b, J. Llorente Merino 149 , S.L. Lloyd 92 , E.M. Lobodzinska 46 , P. Loch 7 , S. Loffredo 73a,73b , T. Lohse 18 , K. Lohwasser 146 , M. Lokajicek 138 , J.D. Long 169 , I. Longarini 72a,72b , L. Longo 67a,67b , R. Longo 169 , I. Lopez Paz36, A. Lopez Solis46, J. Lorenz112, N. Lorenzo Martinez4, A.M. Lory112, A. Lösle52, X. Lou45a,45b, X. Lou14a, A. Lounis64, J. Love6, P.A. Love89, J.J. Lozano Bahilo170, G. Lu14a, M. Lu77, S. Lu134, Y.J. Lu63, H.J. Lubatti145, C. Luci72a,72b, F.L. Lucio Alves14c, A. Lucotte58, F. Luehring65, I. Luise152, O. Lundberg151, B. Lund-Jensen151, N.A. Luongo129, M.S. Lutz158, D. Lynn 29 , H. Lyons 90 , R. Lysak 138 , E. Lytken 96 , F. Lyu 14a , V. Lyubushkin 79 , T. Lyubushkina 79 , H. Ma29, L.L. Ma60b, Y. Ma94, D.M. Mac Donell172, G. Maccarrone51, J.C. MacDonald146, R. Madar 38 , W.F. Mader 48 , J. Maeda 82 , T. Maeno 29 , M. Maerker 48 , V. Magerl 52 , J. Magro 66a,66c , D.J. Mahon39, C. Maidantchik80b, A. Maio137a,137b,137d, K. Maj83a, O. Majersky28a, S. Majewski129, N. Makovec64, V. Maksimovic15, B. Malaescu133, Pa. Malecki84, V.P. Maleev135, F. Malek58, D. Malito41b,41a, U. Mallik77, C. Malone32, S. Maltezos10, S. Malyukov79, J. Mamuzic170, G. Mancini51, J.P. Mandalia92, I. Mandić91, L. Manhaes de Andrade Filho80a, I.M. Maniatis159, M. Manisha142, J. Manjarres Ramos48, D.C. Mankad176, K.H. Mankinen96, A. Mann112, A. Manousos76, B. Mansoulie142, S. Manzoni36, A. Marantis159,s, G. Marchiori5, M. Marcisovsky138, L. Marcoccia73a,73b, C. Marcon96, M. Marinescu20, M. Marjanovic126, Z. Marshall17, S. Marti-Garcia170, T.A. Martin174, V.J. Martin50, B. Martin dit Latour16, L. Martinelli72a,72b, M. Martinez13,t, P. Martinez Agullo170, V.I. Martinez Outschoorn101, P. Martinez Suarez13, S. Martin-Haugh141, V.S. Martoiu27b, A.C. Martyniuk94, A. Marzin36, S.R. Maschek113, L. Masetti98, T. Mashimo160, J. Masik99, A.L. Maslennikov119b,119a, L. Massa23b, P. Massarotti69a,69b, P. Mastrandrea71a,71b, A. Mastroberardino41b,41a, T. Masubuchi160, T. Mathisen168, A. Matic112, N. Matsuzawa160, J. Maurer27b, B. Maček91, D.A. Maximov119b,119a, R. Mazini155, I. Maznas159, M. Mazza105, S.M. Mazza143, C. Mc Ginn29, J.P. Mc Gowan102, S.P. Mc Kee104, T.G. McCarthy113, W.P. McCormack17, E.F. McDonald103, A.E. McDougall117, J.A. Mcfayden153, G. Mchedlidze156b, M.A. McKay42, R.P. Mckenzie33g, D.J. Mclaughlin 94 , K.D. McLean 172 , S.J. McMahon 141 , P.C. McNamara 103 , R.A. McPherson 172,v , J.E. Mdhluli 33g , S. Meehan 36 , T. Megy 38 , S. Mehlhase 112 , A. Mehta 90 , B. Meirose 43 , D. Melini 157 , B.R. Mellado Garcia33g, A.H. Melo53, F. Meloni46, A. Melzer24, E.D. Mendes Gouveia137a, – 38 – JHEP06(2022)005 A.M. Mendes Jacques Da Costa20, H.Y. Meng163, L. Meng89, S. Menke113, M. Mentink36, E. Meoni 41b,41a , C. Merlassino 132 , L. Merola 69a,69b , C. Meroni 68a , G. Merz 104 , O. Meshkov 109,111 , J.K.R. Meshreki148, J. Metcalfe6, A.S. Mete6, C. Meyer65, J-P. Meyer142, M. Michetti18, R.P. Middleton 141 , L. Mijović 50 , G. Mikenberg 176 , M. Mikestikova 138 , M. Mikuž 91 , H. Mildner 146 , A. Milic163, C.D. Milke42, D.W. Miller37, L.S. Miller34, A. Milov176, D.A. Milstead45a,45b, T. Min14c, A.A. Minaenko120, I.A. Minashvili156b, L. Mince57, A.I. Mincer123, B. Mindur83a, M. Mineev79, Y. Minegishi160, Y. Mino85, L.M. Mir13, M. Miralles Lopez170, M. Mironova132, T. Mitani175, A. Mitra174, V.A. Mitsou170, O. Miu163, P.S. Miyagawa92, Y. Miyazaki87, A. Mizukami81, J.U. Mjörnmark96, T. Mkrtchyan61a, M. Mlynarikova118, T. Moa45a,45b, S. Mobius53, K. Mochizuki108, P. Moder46, P. Mogg112, A.F. Mohammed14a, S. Mohapatra39, G. Mokgatitswane33g, B. Mondal148, S. Mondal139, K. Mönig46, E. Monnier100, L. Monsonis Romero170, J. Montejo Berlingen36, M. Montella125, F. Monticelli88, N. Morange64, A.L. Moreira De Carvalho137a, M. Moreno Llácer170, C. Moreno Martinez13, P. Morettini55b, S. Morgenstern174, D. Mori149, M. Morii59, M. Morinaga160, V. Morisbak131, A.K. Morley36, L. Morvaj36, P. Moschovakos36, B. Moser117, M. Mosidze156b, T. Moskalets52, P. Moskvitina116, J. Moss31,m, E.J.W. Moyse101, S. Muanza100, J. Mueller136, R. Mueller19, D. Muenstermann89, G.A. Mullier 96 , J.J. Mullin 134 , D.P. Mungo 68a,68b , J.L. Munoz Martinez 13 , F.J. Munoz Sanchez 99 , M. Murin99, W.J. Murray174,141, A. Murrone68a,68b, J.M. Muse126, M. Muškinja17, C. Mwewa29, A.G. Myagkov120,aa, A.J. Myers8, A.A. Myers136, G. Myers65, M. Myska139, B.P. Nachman17, O. Nackenhorst47, A.Nag Nag48, K. Nagai132, K. Nagano81, J.L. Nagle29, E. Nagy100, A.M. Nairz36, Y. Nakahama81, K. Nakamura81, H. Nanjo130, R. Narayan42, E.A. Narayanan115, I. Naryshkin135, M. Naseri34, C. Nass24, G. Navarro22a, J. Navarro-Gonzalez170, R. Nayak158, P.Y. Nechaeva109, F. Nechansky46, T.J. Neep20, A. Negri70a,70b, M. Negrini23b, C. Nellist116, C. Nelson102, K. Nelson104, S. Nemecek138, M. Nessi36,f, M.S. Neubauer169, F. Neuhaus98, J. Neundorf46, R. Newhouse171, P.R. Newman20, C.W. Ng136, Y.S. Ng18, Y.W.Y. Ng167, B. Ngair 35e , H.D.N. Nguyen 108 , R.B. Nickerson 132 , R. Nicolaidou 142 , D.S. Nielsen 40 , J. Nielsen 143 , M. Niemeyer53, N. Nikiforou11, V. Nikolaenko120,aa, I. Nikolic-Audit133, K. Nikolopoulos20, P. Nilsson29, H.R. Nindhito54, A. Nisati72a, N. Nishu2, R. Nisius113, S.J. Noacco Rosende88, T. Nobe160, D.L. Noel32, Y. Noguchi85, I. Nomidis133, M.A. Nomura29, M.B. Norfolk146, R.R.B. Norisam94, J. Novak91, T. Novak46, O. Novgorodova48, L. Novotny139, R. Novotny115, L. Nozka128, K. Ntekas167, E. Nurse94, F.G. Oakham34,af, J. Ocariz133, A. Ochi82, I. Ochoa137a, J.P. Ochoa-Ricoux144a, S. Oda87, S. Oerdek168, A. Ogrodnik83a, A. Oh99, C.C. Ohm151, H. Oide161, R. Oishi160, M.L. Ojeda46, Y. Okazaki85, M.W. O’Keefe90, Y. Okumura160, A. Olariu27b, L.F. Oleiro Seabra137a, S.A. Olivares Pino144e, D. Oliveira Damazio29, D. Oliveira Goncalves80a, J.L. Oliver167, M.J.R. Olsson167, A. Olszewski84, J. Olszowska84, Ö.O. Öncel52, D.C. O’Neil149, A.P. O’neill19, A. Onofre137a,137e, P.U.E. Onyisi11, R.G. Oreamuno Madriz118, M.J. Oreglia37, G.E. Orellana88, D. Orestano74a,74b, N. Orlando13, R.S. Orr163, V. O’Shea57, R. Ospanov60a, G. Otero y Garzon30, H. Otono87, P.S. Ott61a, G.J. Ottino17, M. Ouchrif35d, J. Ouellette29, F. Ould-Saada131, M. Owen57, R.E. Owen141, K.Y. Oyulmaz21a, V.E. Ozcan21a, N. Ozturk8, S. Ozturk21d, J. Pacalt128, H.A. Pacey32, K. Pachal49, A. Pacheco Pages13, C. Padilla Aranda13, S. Pagan Griso17, G. Palacino65, S. Palazzo50, S. Palestini36, M. Palka83b, J. Pan179, D.K. Panchal11, C.E. Pandini117, J.G. Panduro Vazquez93, P. Pani46, G. Panizzo66a,66c, L. Paolozzi54, C. Papadatos108, S. Parajuli42, A. Paramonov6, C. Paraskevopoulos10, D. Paredes Hernandez62b, B. Parida176, T.H. Park163, A.J. Parker31, M.A. Parker32, F. Parodi55b,55a, E.W. Parrish118, V.A. Parrish50, J.A. Parsons39, U. Parzefall52, B. Pascual Dias108, L. Pascual Dominguez158, V.R. Pascuzzi17, F. Pasquali117, E. Pasqualucci72a, S. Passaggio55b, F. Pastore93, P. Pasuwan45a,45b, J.R. Pater99, A. Pathak177, J. Patton90, T. Pauly36, J. Pearkes150, M. Pedersen131, R. Pedro137a, – 39 – JHEP06(2022)005 S.V. Peleganchuk119b,119a, O. Penc138, C. Peng62b, H. Peng60a, M. Penzin162, B.S. Peralva80a, A.P. Pereira Peixoto58, L. Pereira Sanchez45a,45b, D.V. Perepelitsa29, E. Perez Codina164a, M. Perganti10, L. Perini68a,68b, H. Pernegger36, S. Perrella36, A. Perrevoort116, O. Perrin38, K. Peters46, R.F.Y. Peters99, B.A. Petersen36, T.C. Petersen40, E. Petit100, V. Petousis139, C. Petridou159, A. Petrukhin148, M. Pettee17, N.E. Pettersson36, K. Petukhova140, A. Peyaud142, R. Pezoa144f, L. Pezzotti36, G. Pezzullo179, T. Pham103, P.W. Phillips141, M.W. Phipps169, G. Piacquadio 152 , E. Pianori 17 , F. Piazza 68a,68b , R. Piegaia 30 , D. Pietreanu 27b , A.D. Pilkington 99 , M. Pinamonti66a,66c, J.L. Pinfold2, C. Pitman Donaldson94, D.A. Pizzi34, L. Pizzimento73a,73b, A. Pizzini117, M.-A. Pleier29, V. Plesanovs52, V. Pleskot140, E. Plotnikova79, G. Poddar4, R. Poettgen 96 , R. Poggi 54 , L. Poggioli 133 , I. Pogrebnyak 105 , D. Pohl 24 , I. Pokharel 53 , S. Polacek 140 , G. Polesello70a, A. Poley149,164a, R. Polifka139, A. Polini23b, C.S. Pollard132, Z.B. Pollock125, V. Polychronakos29, D. Ponomarenko110, L. Pontecorvo36, S. Popa27a, G.A. Popeneciu27d, D.M. Portillo Quintero164a, S. Pospisil139, P. Postolache27c, K. Potamianos132, I.N. Potrap79, C.J. Potter32, H. Potti1, T. Poulsen46, J. Poveda170, G. Pownall46, M.E. Pozo Astigarraga36, A. Prades Ibanez170, P. Pralavorio100, M.M. Prapa44, D. Price99, M. Primavera67a, M.A. Principe Martin97, M.L. Proffitt145, N. Proklova110, K. Prokofiev62c, F. Prokoshin79, G. Proto73a,73b, S. Protopopescu29, J. Proudfoot6, M. Przybycien83a, D. Pudzha135, P. Puzo64, D. Pyatiizbyantseva110, J. Qian104, Y. Qin99, T. Qiu92, A. Quadt53, M. Queitsch-Maitland24, G. Rabanal Bolanos59, D. Rafanoharana52, F. Ragusa68a,68b, J.A. Raine54, S. Rajagopalan29, K. Ran14a,14d, V. Raskina133, D.F. Rassloff61a, S. Rave98, B. Ravina57, I. Ravinovich176, M. Raymond 36 , A.L. Read 131 , N.P. Readioff 146 , D.M. Rebuzzi 70a,70b , G. Redlinger 29 , K. Reeves 43 , D. Reikher158, A. Reiss98, A. Rej148, C. Rembser36, A. Renardi46, M. Renda27b, M.B. Rendel113, A.G. Rennie57, S. Resconi68a, M. Ressegotti55b,55a, E.D. Resseguie17, S. Rettie94, B. Reynolds125, E. Reynolds17, M. Rezaei Estabragh178, O.L. Rezanova119b,119a, P. Reznicek140, E. Ricci75a,75b, R. Richter113, S. Richter45a,45b, E. Richter-Was83b, M. Ridel133, P. Rieck123, P. Riedler36, M. Rijssenbeek152, A. Rimoldi70a,70b, M. Rimoldi46, L. Rinaldi23b,23a, T.T. Rinn169, M.P. Rinnagel112, G. Ripellino151, I. Riu13, P. Rivadeneira46, J.C. Rivera Vergara172, F. Rizatdinova127, E. Rizvi92, C. Rizzi54, B.A. Roberts174, B.R. Roberts17, S.H. Robertson102,v, M. Robin46, D. Robinson32, C.M. Robles Gajardo144f, M. Robles Manzano98, A. Robson57, A. Rocchi73a,73b, C. Roda71a,71b, S. Rodriguez Bosca61a, Y. Rodriguez Garcia22a, A. Rodriguez Rodriguez52, A.M. Rodríguez Vera164b, S. Roe36, J.T. Roemer167, A.R. Roepe126, J. Roggel178, O. Røhne131, R.A. Rojas172, B. Roland52, C.P.A. Roland65, J. Roloff29, A. Romaniouk110, M. Romano23b, A.C. Romero Hernandez169, N. Rompotis90, M. Ronzani123, L. Roos133, S. Rosati72a, B.J. Rosser134, E. Rossi4, E. Rossi69a,69b, L.P. Rossi55b, L. Rossini46, R. Rosten125, M. Rotaru27b, B. Rottler52, D. Rousseau64, D. Rousso32, G. Rovelli70a,70b, A. Roy169, A. Rozanov100, Y. Rozen157, X. Ruan33g, A.J. Ruby90, T.A. Ruggeri1, F. Rühr52, A. Ruiz-Martinez170, A. Rummler36, Z. Rurikova52, N.A. Rusakovich79, H.L. Russell172, L. Rustige38, J.P. Rutherfoord7, E.M. Rüttinger146, K. Rybacki89, M. Rybar140, E.B. Rye131, A. Ryzhov120, J.A. Sabater Iglesias54, P. Sabatini170, L. Sabetta72a,72b, H.F-W. Sadrozinski143, R. Sadykov79, F. Safai Tehrani72a, B. Safarzadeh Samani153, M. Safdari150, S. Saha102, M. Sahinsoy113, A. Sahu178, M. Saimpert142, M. Saito160, T. Saito160, D. Salamani36, G. Salamanna74a,74b, A. Salnikov150, J. Salt170, A. Salvador Salas13, D. Salvatore41b,41a, F. Salvatore153, A. Salzburger36, D. Sammel52, D. Sampsonidis159, D. Sampsonidou60d,60c, J. Sánchez170, A. Sanchez Pineda4, V. Sanchez Sebastian170, H. Sandaker131, C.O. Sander46, I.G. Sanderswood89, J.A. Sandesara101, M. Sandhoff178, C. Sandoval22b, D.P.C. Sankey141, A. Sansoni51, C. Santoni38, H. Santos137a,137b, S.N. Santpur17, A. Santra176, K.A. Saoucha146, A. Sapronov79, J.G. Saraiva137a,137d, J. Sardain100, O. Sasaki81, K. Sato165, C. Sauer61b, F. Sauerburger52, E. Sauvan4, P. Savard163,af, R. Sawada160, C. Sawyer141, L. Sawyer95, – 40 – JHEP06(2022)005 136 Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh PA; United States of America 137 (a)Laboratório de Instrumentação e Física Experimental de Partículas — LIP, Lisboa;(b)Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Lisboa; (c) Departamento de Física, Universidade de Coimbra, Coimbra; (d) Centro de Física Nuclear da Universidade de Lisboa, Lisboa;(e)Departamento de Física, Universidade do Minho, Braga;(f)Departamento de Física Teórica y del Cosmos, Universidad de Granada, Granada (Spain);(g)Instituto Superior Técnico, Universidade de Lisboa, Lisboa; Portugal 138 Institute of Physics of the Czech Academy of Sciences, Prague; Czech Republic 139 Czech Technical University in Prague, Prague; Czech Republic 140 Charles University, Faculty of Mathematics and Physics, Prague; Czech Republic 141 Particle Physics Department, Rutherford Appleton Laboratory, Didcot; United Kingdom 142 IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette; France 143 Santa Cruz Institute for Particle Physics, University of California Santa Cruz, Santa Cruz CA; United States of America 144 (a)Departamento de Física, Pontificia Universidad Católica de Chile, Santiago;(b)Millennium Institute for Subatomic physics at high energy frontier (SAPHIR), Santiago;(c)Instituto de Investigación Multidisciplinario en Ciencia y Tecnología, y Departamento de Física, Universidad de La Serena;(d)Universidad Andres Bello, Department of Physics, Santiago;(e)Instituto de Alta Investigación, Universidad de Tarapacá, Arica;(f)Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso; Chile 145 Department of Physics, University of Washington, Seattle WA; United States of America 146 Department of Physics and Astronomy, University of Sheffield, Sheffield; United Kingdom 147 Department of Physics, Shinshu University, Nagano; Japan 148 Department Physik, Universität Siegen, Siegen; Germany 149 Department of Physics, Simon Fraser University, Burnaby BC; Canada 150 SLAC National Accelerator Laboratory, Stanford CA; United States of America 151 Department of Physics, Royal Institute of Technology, Stockholm; Sweden 152 Departments of Physics and Astronomy, Stony Brook University, Stony Brook NY; United States of America 153 Department of Physics and Astronomy, University of Sussex, Brighton; United Kingdom 154 School of Physics, University of Sydney, Sydney; Australia 155 Institute of Physics, Academia Sinica, Taipei; Taiwan 156 (a)E. Andronikashvili Institute of Physics, Iv. Javakhishvili Tbilisi State University, Tbilisi;(b)High Energy Physics Institute, Tbilisi State University, Tbilisi; Georgia 157 Department of Physics, Technion, Israel Institute of Technology, Haifa; Israel 158 Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv; Israel 159 Department of Physics, Aristotle University of Thessaloniki, Thessaloniki; Greece 160 International Center for Elementary Particle Physics and Department of Physics, University of Tokyo, Tokyo; Japan 161 Department of Physics, Tokyo Institute of Technology, Tokyo; Japan 162 Tomsk State University, Tomsk; Russia 163 Department of Physics, University of Toronto, Toronto ON; Canada 164 (a) TRIUMF, Vancouver BC; (b) Department of Physics and Astronomy, York University, Toronto ON; Canada 165 Division of Physics and Tomonaga Center for the History of the Universe, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba; Japan 166 Department of Physics and Astronomy, Tufts University, Medford MA; United States of America 167 Department of Physics and Astronomy, University of California Irvine, Irvine CA; United States of America 168 Department of Physics and Astronomy, University of Uppsala, Uppsala; Sweden 169 Department of Physics, University of Illinois, Urbana IL; United States of America – 47 – JHEP06(2022)005 170 Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia — CSIC, Valencia; Spain 171 Department of Physics, University of British Columbia, Vancouver BC; Canada 172 Department of Physics and Astronomy, University of Victoria, Victoria BC; Canada 173 Fakultät für Physik und Astronomie, Julius-Maximilians-Universität Würzburg, Würzburg; Germany 174 Department of Physics, University of Warwick, Coventry; United Kingdom 175 Waseda University, Tokyo; Japan 176 Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot; Israel 177 Department of Physics, University of Wisconsin, Madison WI; United States of America 178 Fakultät für Mathematik und Naturwissenschaften, Fachgruppe Physik, Bergische Universität Wuppertal, Wuppertal; Germany 179 Department of Physics, Yale University, New Haven CT; United States of America aAlso at Borough of Manhattan Community College, City University of New York, New York NY; United States of America bAlso at Bruno Kessler Foundation, Trento; Italy cAlso at Center for High Energy Physics, Peking University; China dAlso at Centro Studi e Ricerche Enrico Fermi; Italy eAlso at CERN, Geneva; Switzerland fAlso at Département de Physique Nucléaire et Corpusculaire, Université de Genève, Genève; Switzerland gAlso at Departament de Fisica de la Universitat Autonoma de Barcelona, Barcelona; Spain hAlso at Department of Financial and Management Engineering, University of the Aegean, Chios; Greece i Also at Department of Physics and Astronomy, Michigan State University, East Lansing MI; United States of America jAlso at Department of Physics and Astronomy, University of Louisville, Louisville, KY; United States of America kAlso at Department of Physics, Ben Gurion University of the Negev, Beer Sheva; Israel lAlso at Department of Physics, California State University, East Bay; United States of America mAlso at Department of Physics, California State University, Sacramento; United States of America nAlso at Department of Physics, King’s College London, London; United Kingdom o Also at Department of Physics, St. Petersburg State Polytechnical University, St. Petersburg; Russia pAlso at Department of Physics, University of Fribourg, Fribourg; Switzerland qAlso at Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow; Russia rAlso at Graduate School of Science, Osaka University, Osaka; Japan sAlso at Hellenic Open University, Patras; Greece tAlso at Institucio Catalana de Recerca i Estudis Avancats, ICREA, Barcelona; Spain uAlso at Institut für Experimentalphysik, Universität Hamburg, Hamburg; Germany vAlso at Institute of Particle Physics (IPP); Canada wAlso at Institute of Physics, Azerbaijan Academy of Sciences, Baku; Azerbaijan xAlso at Institute of Theoretical Physics, Ilia State University, Tbilisi; Georgia yAlso at Instituto de Fisica Teorica, IFT-UAM/CSIC, Madrid; Spain zAlso at Joint Institute for Nuclear Research, Dubna; Russia aa Also at Moscow Institute of Physics and Technology State University, Dolgoprudny; Russia ab Also at National Research Nuclear University MEPhI, Moscow; Russia ac Also at Physics Department, An-Najah National University, Nablus; Palestine ad Also at Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg; Germany ae Also at The City College of New York, New York NY; United States of America af Also at TRIUMF, Vancouver BC; Canada ag Also at Università di Napoli Parthenope, Napoli; Italy ah Also at University of Chinese Academy of Sciences (UCAS), Beijing; China ai Also at Yeditepe University, Physics Department, Istanbul; Turkey ∗Deceased – 48 –