Search for long-lived particles decaying to final states with a pair of muons in proton-proton collisions at $\sqrt{s}$ = 13.6 TeV

An inclusive search for long-lived exotic particles (LLPs) decaying to final states with a pair of muons is presented. The search uses data corresponding to an integrated luminosity of 36.6 fb$^{-1}$ collected by the CMS experiment from the proton-proton collisions at $\sqrt{s}$ = 13.6 TeV in 2022, the first year of Run 3 of the CERN LHC. The experimental signature is a pair of oppositely charged muons originating from a common vertex spatially separated from the proton-proton interaction point by distances ranging from several hundred $\mu$m to several meters. The sensitivity of the search benefits from new triggers for displaced dimuons developed for Run 3. The results are interpreted in the framework of the hidden Abelian Higgs model, in which the Higgs boson decays to a pair of long-lived dark photons, and of an $R$-parity violating supersymmetry model, in which long-lived neutralinos decay to a pair of muons and a neutrino. The limits set on these models are the most stringent to date in wide regions of lifetimes for LLPs with masses larger than 10 GeV.


Introduction
Long-lived particles (LLPs) that are unobserved as yet are predicted by many extensions of the standard model (SM), in particular by various supersymmetry (SUSY) scenarios [1,2] and "hidden-sector" models [3,4].Such particles could manifest themselves through decays to SM particles at macroscopic distances from the proton-proton (pp) interaction point (IP).This paper describes an inclusive search for an exotic massive LLP decaying to a pair of oppositely charged muons, referred to as a "displaced dimuon", originating from a secondary vertex spatially separated from the IP.The analysis is based on a data set of pp collisions corresponding to an integrated luminosity of 36.6 fb −1 collected with the CMS detector at √ s = 13.6 TeV during 2022, the first year of Run 3 of the CERN LHC.It is a continuation and extension of the CMS analysis [5] performed using data collected at √ s = 13 TeV during Run 2 (2016-2018) and corresponding to an integrated luminosity of 97.6 fb −1 (referred to below as the CMS Run 2 analysis).A minimal set of requirements and loose event selection criteria allow the search to be sensitive to a wide range of models predicting LLPs that decay to final states that include a pair of oppositely charged muons.Improvements in the triggers result in a significantly higher efficiency for displaced dimuons in Run 3, particularly at dimuon masses of a few tens of GeV.The present search explores the LLP mass range above 10 GeV and is sensitive to vertex displacements ranging from several hundred µm to several meters.
We interpret the results of the search in the frameworks of two benchmark models: the hidden Abelian Higgs model (HAHM), in which displaced dimuons arise from decays of hypothetical dark photons [6], and a simplified SUSY model, in which long-lived neutralinos decay to a pair of muons and a neutrino as a result of R-parity violation (RPV) [2].The results for the HAHM model from Run 3 are statistically combined with the results of the Run 2 analysis [5].The Run 2 search [5] and the present search are complementary to a CMS search [7], which uses data collected in Run 2 with a dedicated high-rate data stream in order to explore otherwise inaccessible parameter space at low dimuon masses.A search for LLPs decaying to displaced dimuons has also been performed by CMS in Run 1, using data taken at √ s = 8 TeV and corresponding to an integrated luminosity of 20.5 fb −1 [8,9], and by the ATLAS Collaboration in Run 2, using data corresponding to an integrated luminosity of 32.9 fb −1 [10,11].This paper is organized as follows.Section 2 describes the CMS detector.Section 3 presents the signal models, as well as the simulated signal and background event samples.Section 4 describes the analysis strategy, the triggers, and the offline event selection.Estimation of backgrounds and the associated systematic uncertainties are described in Section 5. Section 6 summarizes the systematic uncertainties affecting signal efficiencies.Section 7 describes the results of this analysis and their combination with the results of the CMS Run 2 analysis.The summary of the paper is given in Section 8. Tabulated results and supplementary material for reinterpreting the results in the framework of models not explicitly considered in this paper are provided in the HEPData record for this analysis [12].

The CMS detector
The central feature of the CMS detector is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker extending outwards to a radius of 1.1 m, a lead tungstate crystal electromagnetic calorimeter, and a brass and scintillator hadron calorimeter, each composed of a barrel and two endcap sections.Forward calorimeters extend the coverage in pseudorapidity η provided by the barrel and endcap detectors.Muons are detected in gas-ionization chambers covering the range |η| < 2.4 and embedded in the steel flux-return yoke outside the solenoid.The muon system is composed of four types of chambers: drift tubes (DTs) in the barrel (|η| < 1.2), cathode strip chambers (CSCs) in the endcaps (0.9 < |η| < 2.4), resistive-plate chambers in both the barrel and the endcaps, and gas electron multipliers in the forward regions of the endcaps.The chambers are assembled into four "stations" at increasing distance from the IP.The stations in the barrel are located approximately 4, 5, 6, and 7 m away from the IP radially, while the stations in the endcap are located approximately 7.0, 8.0, 9.5, and 10.5 m away from the IP along the beam line axis on both ends of the detector.Each station provides reconstructed hits in several detection planes, which are combined into track segments, forming the basis of muon reconstruction in the muon system [13].A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematical variables, can be found in Refs.[14,15].
Events of interest are selected using a two-tiered trigger system.The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of approximately 100 kHz within a fixed latency of 4 µs [16].At the next stage, a farm of processors running a version of the full event reconstruction software optimized for fast processing, known as the high-level trigger (HLT), reduces the event rate to about 1 kHz before data storage [17].At the HLT, muon candidates are reconstructed in two steps.In the first step, referred to as Level 2 (L2), muons are reconstructed using only the information from the muon detectors, whereas at the stage referred to as Level 3 (L3), tracker information is also used.

Signal models and simulated samples
Two signal models with different final-state topologies and event kinematics are used in the optimization of event selection criteria and in the interpretation of results.The first belongs to a class of models featuring a "hidden" or "dark" sector of matter that does not interact directly with the SM particles, but can manifest itself through mixing effects.This HAHM benchmark [6,18] contains an extra dark gauge field U(1) D , which mixes kinetically with the hypercharge SM gauge field ("vector portal") and gives rise to a spin-1 mediator known as the dark photon Z D .The symmetry of U(1) D is broken by a new dark Higgs field H D , which mixes with the SM Higgs boson H ("Higgs portal") and gives mass m(Z D ) to the dark photon.If there are no hidden-sector states with masses smaller than m(Z D ), the mixing through the vector portal with the SM photon and Z boson causes the dark photon to decay exclusively to SM particles, with a sizable branching fraction to leptons.Pair production of the Z D via the Higgs portal with subsequent decays of dark photons via the vector portal is shown in Fig. 1 (left).
The present search probes the regime of m(Z D ) > 10 GeV with small values of the Z-Z D kinetic mixing parameter ϵ [6].In this regime, the dark photon is long-lived, since its mean proper lifetime τ(Z D ) is proportional to ϵ −2 .In particular, the dark photon with 10 GeV ≲ m(Z D ) < m(H)/2 is expected to have macroscopically large mean proper decay lengths, for example, cτ(Z D ) ≳ O(100 µm) for ϵ < O(10 −6 ).The Z D production rate is governed by the branching fraction B(H → Z D Z D ), which does not depend on ϵ but is proportional to the square of κm 2 (H)/|m 2 (H) − m 2 (H D )|, where κ is the H-H D mixing parameter.Since κ and m(H D ) affect only the overall dark photon production rate, sampling of m(Z D ) and ϵ is sufficient to explore different kinematical and topological scenarios of the model.We generated a set of 24 simulated HAHM event samples with m(Z D ) between 10 and 60 GeV and ϵ between 10 −7 and 2 × 10 −9 .In this mass range, the model's prediction for B( Feynman diagrams for (left) the HAHM model, showing the production of longlived dark photons Z D via the Higgs portal, through H-H D mixing with the parameter κ, with subsequent decays to pairs of muons or other fermions via the vector portal; and (right) pair production of squarks followed by q → q χ 0 1 decays, where the RPV neutralino is assumed to be a long-lived particle that decays into a neutrino and two charged leptons.
10 GeV and 10.7% at m(Z D ) = 60 GeV.The dark Higgs boson is assumed to be heavy enough so that H → H D H D decays are kinematically forbidden.(In the sample generation, we use m(H D ) = 400 GeV and κ = 0.01.)The production of dark photons is modeled at leading order by MADGRAPH5 aMC@NLO [19] version 2.9.9.The samples are generated only for the dominant gluon-fusion production mechanism, but the Higgs boson production cross section is normalized to the most recent theoretical prediction for the sum of all production modes for m(H) = 125 GeV at √ s = 13.6 TeV, 59.8 pb [20,21].The decays of the dark photons are modeled by PYTHIA 8.306 [22].
We also consider a simplified benchmark model inspired by RPV SUSY and featuring displaced µ + µ − ν vertices.Unlike the HAHM, where the two-body LLP decay leads to displaced µ + µ − vertices that are reconstructed with the dimuon invariant mass m µµ corresponding to the LLP mass, the presence of a neutrino at the decay vertex leads to a nonpeaking m µµ distribution with a broad spectrum below the endpoint at the LLP mass.In this model, which was used by CMS in the Run 1 searches for displaced dimuons [8,9] and by ATLAS in the Run 2 search for pairs of displaced charged leptons [11], the LLP is assumed to be an RPV neutralino χ 0 1 that results from decays of mass-degenerate squarks, q → q χ 0 1 , which are pair produced in pp collisions.Nonzero values of RPV couplings λ 122 and λ 232 enable displaced χ 0 1 decays into a pair of oppositely charged muons and a neutrino, χ 0 1 → µ + µ − ν [23,24].The Feynman diagram for this process is shown in Fig. 1

(right).
The search uses benchmark signal samples that are generated assuming B( 1 → e + e − ν) = 0.5, which gives rise to events with up to two displaced dimuon vertices.To explore a wide range of kinematic variables and event topologies, we chose six m( q ) values in the range between 125 GeV and 1.6 TeV, and for each chosen m( q ), generated sets of samples with ∆m = m( q ) − m( χ 0 1 ) of 25, 200, and 650 GeV, and sets with constant m( χ 0 1 ) values of 50 and 500 GeV such that m( χ 0 1 ) < m( q ).To study a wide range of signal displacements, each set contains three samples with the generated cτ( χ 0 1 ) values corresponding to mean transverse decay lengths of approximately 3, 30, and 250 cm in the laboratory frame.All other SUSY particles (e.g., gluinos and sleptons) are assumed to be too heavy to be produced.(Their masses are set to 10 TeV.)The samples are generated with PYTHIA 8.306.The squark-antisquark production cross sections are calculated with NNLL-fast version 2.0 to approximate next-to-nextto-leading order (NNLO) in the strong coupling constant, including the resummation of soft gluon emission at next-to-next-to-leading logarithmic accuracy [25].The computation uses the NNLO PDF4LHC21 parton distributions functions (PDFs) [26].
Since the optimization of the event selection criteria and the evaluation of the residual backgrounds are performed using data, the simulated background samples are used primarily to gain a better understanding of the nature and composition of background events passing the event selection.Simulated background samples used in the analysis include Drell-Yan (DY) dilepton production; tt, tW, and tW events; W and Z boson pair production (dibosons); samples of J/ψ mesons produced in b hadron cascade decays; W+jets; and events comprised of jets produced through the strong interaction that are enriched in muons from semileptonic decays of hadrons containing b or c quarks.
The simulated signal and background samples are produced with PDFs NNPDF3.1 [27] at NNLO, using the CP5 tune [28], which is optimized for these PDFs, to model the underlying event.The passage of particles through the detector is simulated by GEANT4 [29].Simulated minimum bias events are superimposed on a hard interaction in simulated events to describe the effect of additional inelastic pp interactions within the same or neighboring bunch crossings, known as pileup.All simulated events are then reconstructed with the same algorithms as used for data.A reweighting procedure that combines events in all simulated signal samples at a given signal mass [30] is employed to calculate the efficiencies for lifetimes different from those of the available samples.

Analysis strategy
An LLP produced in the hard interaction of the colliding protons may travel a significant distance in the detector before decaying into muons.While trajectories of the muons produced well within the silicon tracker can be reconstructed by both the tracker and the muon system, tracks of muons produced in the outer tracker layers or beyond can only be reconstructed by the muon system.Since the dimuon vertex resolution and the background composition differ dramatically depending on whether the muon is reconstructed in the tracker, we classify all reconstructed dimuon events into three mutually exclusive categories: a) both muons are reconstructed using both the tracker and the muon system (TMS-TMS category); b) both muons are reconstructed using only the muon system, as "standalone" muons (STA-STA category); and c) one muon is reconstructed only in the muon system, whereas the other muon is reconstructed using both the tracker and the muon system (STA-TMS category).These three categories of events are analyzed separately, with each benefiting from dedicated event selection criteria and background evaluation.The STA-TMS category, which had the lowest sensitivity among the three categories in the Run 2 analysis [5], is not used for the results presented in this paper; the results in the other two categories are statistically combined.
The beam spot is identified with the mean position of the pp interaction vertices.The primary vertex (PV) is taken to be the vertex corresponding to the hardest scattering in the event, evaluated using tracking information alone, as described in Section 9.4.1 of Ref. [31].A pair of reconstructed muon tracks is fitted to a common secondary vertex (SV), which is expected to be displaced with respect to the PV.The transverse decay vector ⃗ L xy is defined from the PV to the SV in the plane transverse to the beam direction, while the transverse decay length L xy is the magnitude of this vector.The transverse impact parameter d 0 is defined as the distance of closest approach of the muon track in the transverse plane with respect to the PV.

Trigger algorithms
Events were collected with dedicated triggers aimed at recording dimuons produced both within and outside of the tracker.In Run 2, these triggers required two muons reconstructed in the muon system alone, without using any information from the tracker [32].They were deployed in 2016 and 2018 and included a beam spot constraint in the muon track fits at L1 but not at the HLT.The values of the L1 p T thresholds varied from 11 and 4 GeV (for the leading and subleading L1 muons, respectively) during most of 2016 to 15 and 7 GeV at the end of Run 2. Each HLT muon was required to be within the region |η| < 2.0 and to have transverse momentum p T > 28 (23) GeV for 2016 (2018) data taking.
The primary goal of the trigger optimization performed for Run 3 data taking was to increase the signal efficiency by lowering as much as possible the p T thresholds and by removing the beam spot constraint at L1, without increasing considerably the resulting trigger rate.Two additional sets of L1 triggers were introduced.One set comprises double-muon triggers with either no or a very low (4.5 GeV) muon-p T threshold, which were made possible by requiring that the L1 muon candidates have opposite signs, segments in at least three different muon stations, angular separation ∆R µµ = √ (∆η µµ ) 2 + (∆ϕ µµ ) 2 that does not exceed a threshold that varies between 1.2 and 1.4, and |η| < 1.5 in the trigger with no explicit p T requirement.The other set takes advantage of a new track-finding procedure in the barrel section of the L1 muon trigger.This procedure enables the reconstruction of L1 muon candidates and the determination of their p T without using the beam spot constraint [15].These triggers require this p T be larger than 15 and 7 GeV for the leading and subleading L1 muon, respectively.The p T thresholds are lowered to 6 and 4 GeV when d 0 of both L1 muons is larger than 25 cm.The new L1 triggers mitigate the efficiency loss that was present in Run 2 for displaced muons not pointing to the beamspot [5], thereby improving the trigger efficiency for LLPs with cτ ≳ 10 cm.The relative efficiency gain evaluated using the simulated HAHM signal events increases as cτ increases, reaching a plateau at 20 to 50% (depending on m(Z D )) at cτ(Z D ) ≈ 10 m.
The events selected by the aforementioned L1 triggers were then required to be selected by a logical OR of the 2018 L2 trigger paths used in the Run 2 analysis [5] and the newly designed HLT paths.The new paths use two complementary algorithms described below, and are characterized by p T thresholds that depend on the muon d 0 , as illustrated in Fig. 2. The first algorithm, labeled Run 3 (2022, L2) in Fig. 2, imports some of the elements of the offline analysis into the online selection, in order to take advantage of the superior tracker resolution in determining muon d 0 .Instead of stopping the online reconstruction at the L2 stage (muon system alone) as it was done in the Run 2 trigger, the algorithm attempts to reconstruct the muon candidates at the L3 stage as well (similar to offline TMS muons).If either of the two L2 muon candidates is reconstructed at L3 as a muon with d 0 < 1 cm, the event is discarded, since such an L2 muon candidate is likely to originate from the background processes.The resulting trigger operates with muon p T thresholds of 10 GeV and improves significantly the signal efficiency in the STA-STA category, while contributing only about 1% additional HLT rate.
The second new HLT algorithm, labeled Run 3 (2022, L3) in Fig. 2, introduces new paths relying entirely on the online L3 muon reconstruction.A moderate threshold on the impact parameter of each muon, d 0 > 0.01 cm, allows the p T thresholds to be fairly low: 16 GeV on the leading muon µ 1 and 10 GeV on the subleading muon µ 2 .The resulting trigger greatly improves the signal efficiency in the TMS-TMS category, while adding only another ≈1% of HLT rate.An increase in the number of background events selected by the trigger led to the refinements in the offline event selection described in Section 4.3.
The combined L1-HLT efficiency of the various displaced dimuon trigger paths and their com- bination as a function of cτ is shown in Fig. 3 for the simulated HAHM signal events with m(Z D ) = 20 GeV.Because the Run 2 triggers (dashed black) have no restrictions on d 0 , they continue to have the highest efficiency (15%) at cτ < 0.02 cm.The addition of the Run 3 (2022, L3) paths (blue) increases the overall efficiency (black) by more than a factor of 2 for cτ = 0.1-1 cm.The efficiency of this trigger starts to drop at cτ ≳ 5 cm, when dimuons are produced beyond the innermost tracker layers and the L3 muon reconstruction efficiency decreases.At larger cτ values, the addition of the Run 3 (2022, L2) paths (red) strongly contributes to the improvement of the signal efficiency, e.g., by more than a factor of 3 at cτ = 1 m.The decline of the efficiencies at the largest cτ is driven by the increased fraction of dimuons produced outside the CMS detector.Overall, the addition of new L1 and HLT paths improves the trigger efficiency for Z D with m(Z D ) > 10 GeV and cτ ≳ 0.1 cm by a factor of 2 to 4, depending on cτ and mass.The performance of the trigger was validated using data as described in Section 6.

Muon reconstruction and event selection
Optimal performance for the wide range of displacements of secondary vertices considered in the analysis cannot be achieved by a single muon reconstruction algorithm.To accurately reconstruct muons produced near the IP, commonly used algorithms developed for prompt muons are employed.These algorithms combine measurements from both the tracker and the muon system.Two such TMS algorithms are the global muon and tracker muon reconstruction algorithms [13,33].The global muon algorithm reconstructs muons by fitting hits in the tracker and segments in the muon system into a common track.The tracker muon algorithm, on the other hand, builds muons by extrapolating tracks in the inner tracker to the muon system and requiring loose geometric matching to DT or CSC segments.However, the efficiency of these algorithms decreases rapidly as the distance between the IP and the muon origin increases.In contrast, algorithms that rely solely on information from the muon system can still efficiently reconstruct muons produced in the outer tracker layers and beyond.These STA algorithms [13,33] can reconstruct muons with displacements of up to a few meters.However, they exhibit poorer spatial and momentum resolution compared to muons reconstructed using the more precise information from the silicon tracker.
To benefit from the advantages offered by both types of algorithms, we begin the muon selection with the muons reconstructed by a specific STA algorithm that eliminates the beam spot constraints from all stages of the muon reconstruction procedure.This approach yields the highest efficiency and the finest resolution for highly displaced muons, surpassing all other available STA algorithms.Subsequently, we attempt to match each STA muon with muons reconstructed using global muon and tracker muon algorithms, and replace the STA muon with an associated TMS muon if a match is found.As in the Run 2 analysis [5], we reject events in which no HLT muon pair that triggered the event matches two STA muons.Due to the need to reduce large backgrounds as much as possible, careful optimization of the event, muon, and dimuon selection was done for the Run 2 analysis, as described in Section 4 of Ref. [5].A summary of the selection criteria used in the Run 2 analysis is given in Table 1 of Ref. [5].Most of the selection criteria are unchanged, as is the association between STA and TMS muons for those tracks originating within the tracker volume.The rest of this section of the paper describes only the changes and refinements to the muon and dimuon selection for this Run 3 search, while also introducing analysis variables that are used in the background estimation.
Because of the increase in the background as a result of the lower p T trigger thresholds, an iso-lation requirement is useful when applied to the STA muons.Both STA muons in the STA-STA category are required to have relative tracker isolation I STA rel, trk < 0.15, where I STA rel, trk is defined as the sum of the p T of tracks within a cone of ∆R = √ (∆η) 2 + (∆ϕ) 2 < 0.3 around the trajectory of the muon extrapolated to the point of closest approach to the PV divided by the muon track p T .When evaluated using events that pass all other selection criteria, this isolation requirement is more than 90% efficient for signal and suppresses background from events with jets that are produced through the strong interaction, collectively referred to as quantum chromodynamics (QCD) events, by about a factor of 2. The TMS muon isolation criterion, I TMS rel, trk < 0.075, remained unchanged with respect to the Run 2 analysis [5].
The Run 2 analysis required that the dimuons be displaced with respect to the PV by imposing requirements on the L xy significance L xy /σ L xy , where σ L xy is the uncertainty in L xy [5].A significant fraction of remaining events in the STA-STA category suffer from unreliable SV reconstruction; we thus require in addition that σ L xy < 20 cm.
In the TMS-TMS category, the sensitivity of the search is further improved by binning events in min(d 0 /σ d 0 ), which is the minimum value of the ratio of d 0 to its uncertainty for the two muons forming a dimuon.Unlike signal events with macroscopic cτ values, the expected background has a steeply falling min(d 0 /σ d 0 ) distribution, which motivates the splitting of the signal region (SR) into three bins of min(d 0 /σ d 0 ) ranges.The bin ranges are the same as those in the Run 2 analysis, namely 6-10, 10-20, and >20.
A quantity that is useful for suppressing and evaluating the SM background that satisfies all other selection requirements is the azimuthal angle ∆Φ between ⃗ L xy and the transverse mo- mentum vector ⃗ p T,µµ of the dimuon system.A major source of SM background events is from prompt high-mass dimuons that are reconstructed as displaced due to instrumental or reconstruction failures.Such dimuons mostly arise from DY dimuon production.Events from DY τ + τ − production with both τ leptons decaying to muons lead to a background with characteristics similar to those of the mismeasured DY µ + µ − events; contributions from processes such as tt and diboson production are relatively small.Dimuons originating in these events, collectively referred to as DY events, are expected to have a distribution of |∆Φ| symmetric about π/2, because the dimuon momentum vector is uncorrelated with the ⃗ L xy vector.On the other hand, when a pair of muons is produced in the decay of an LLP originating at the PV, the resulting ⃗ p T,µµ and ⃗ L xy are collinear, and the distribution of |∆Φ| peaks at zero.This can be seen in Fig. 4, which compares the |∆Φ| distributions of TMS-TMS and STA-STA dimuons in data samples obtained by inverting some of the selection criteria and enriched in DY events with the |∆Φ| distributions for events passing the full selection except for the |∆Φ| requirement in all HAHM and RPV SUSY signal samples combined.There is a small asymmetry in the |∆Φ| distribution for DY events in the STA-STA category, which is caused by the event selection criteria.
To address the different |∆Φ| distributions in the two types of signal models, we define different critical values |∆Φ| C for requiring |∆Φ| < |∆Φ| C .To define the SR for the HAHM model, where |∆Φ| strongly peaks at zero and the tail is driven by the resolution, we use |∆Φ| C = π/10 in the STA-STA category and π/30 in the TMS-TMS category.The tighter requirement in the TMS-TMS category takes advantage of the better tracker resolution.For the RPV SUSY model, where the distribution is broader due to the undetected neutrino among the decay products, we use a looser requirement of the Run 2 analysis, |∆Φ| C = π/4, in both dimuon categories.For the chosen |∆Φ| C values, the signal efficiency is 90-99% in the HAHM and 60-99% in the RPV SUSY models, depending on the Lorentz boost of the LLP; the corresponding DY background rejection factors are, respectively, 15-20 and 4-6, depending on the dimuon category.We use the   In addition to defining |∆Φ| SR and CRs, we classify selected dimuons as opposite-sign (OS) or same-sign (SS), based on the observed muon charges.The signal selection requires that dimuons be OS, while SS dimuons constitute a CR used to evaluate backgrounds arising from QCD events.
The last important source of SM backgrounds consists of QCD events in which there are dimuons produced in decays of J/ψ mesons and other low-mass SM resonances, or formed from the products of the b hadron cascade decays (b → cµ 1 X followed by c → µ 2 X).These events are suppressed by requiring that m µµ > 10 GeV.However, it was observed that low-p T muons can appear as muons with higher p T , with straighter tracks, when reconstructed from a small number of measurements.This gives rise to dimuons with an overestimated m µµ (above the 10 GeV threshold) and a mistakenly formed displaced vertex.These dimuons typically have small |∆Φ| (either due to the collinearity of the ⃗ p T,µµ and ⃗ L xy vectors or overestimated muon p T ) and may exhibit large values of L xy /σ L xy and d 0 /σ d 0 that resemble signal-like characteristics.To suppress such events, which are particularly abundant in the STA-STA category due to its low resolution, we reject STA-STA dimuons whose separation in η is small (|∆η µµ | < 0.1) if one of the muons is reconstructed in the barrel from fewer than 25 DT hits or if the sum of the segments belonging to both muons in the dimuon is fewer than 6.These requirements are identical to those used in the Run 2 analysis.
Finally, to test for the existence of an LLP with a given mass, dimuons satisfying the selection criteria are required to have m µµ within a specified interval containing the probed LLP mass.The width of each interval is chosen according to the mass resolution and the expected background.For the interpretation in the framework of the HAHM model, where the LLP decay products do not contain any undetected particles, the full widths of the chosen m µµ intervals are approximately equal to 6-8 times the mass resolution at this mass.This choice typically yields intervals containing a large fraction (90-99%) of putative signal with the probed mass.Since the mass resolution in the TMS-TMS category is far superior to that in the STA-STA category (1-3% compared to 10-25%, for LLP masses between 20 and 350 GeV), the minimum width of m µµ intervals varies from 3 GeV in the TMS-TMS category to ≈20 GeV in the STA-STA category.
In the RPV SUSY model, the presence of a neutrino in the χ 0 1 → µ + µ − ν decay vertex leads to a nonpeaking dimuon invariant mass distribution with an endpoint at m( χ 0 1 ).To improve the mass resolution and the signal-to-background discrimination in signals featuring an LLP decay vertex formed by a dimuon plus neutral or unobserved particles, we use the quantity referred to as the corrected SV mass, defined as where p µµ is the magnitude of the dimuon momentum vector ⃗ p µµ , and θ is the angle between ⃗ p µµ and the vector connecting the PV with the SV.The motivation behind this variable, which was used at LEP and the SLC and recently by LHCb [34] and CMS [35], is to rely on the conservation of momentum and correct for the missing mass of the vertex due to unaccounted particles.In the case where only the dimuon belongs to the LLP decay vertex (and before measurement error), θ = 0 and m corr µµ = m µµ .If, however, the decay vertex includes other particles, then θ > 0, m corr µµ > m µµ , and the corrected mass is the minimum mass that the LLP, in this case the χ 0 1 , can have in order to be consistent with the measured direction of flight.The m corr µµ distributions of simulated RPV SUSY events show a clear peak at m( χ 0 1 ) in both dimuon categories.We profit from the improvement in mass resolution offered by m corr µµ and use m corr µµ intervals to probe different m( χ 0 1 ).As with m µµ intervals for the HAHM model, the width of the intervals is chosen to contain a large fraction of the RPV SUSY signal (typically 80-90%).In the STA-STA category, we additionally require m µµ > 15 GeV to avoid the leakage of background events from small m µµ to large m corr µµ .Figure 5 shows, as an example, the full event selection efficiency for the HAHM signal with m(Z D ) = 20 GeV as a function of cτ, and illustrates relative improvements in the efficiencies from the new trigger algorithms.A large increase in the overall efficiency, shown in the lower panel, is apparent; most of the efficiency gain from the improvements in the trigger algorithms and shown in Fig. 3 is retained after the full offline event selection.Similar efficiency increases are seen at other probed Z D masses.

Background estimates and their systematic uncertainties
Background events that meet the event selection criteria cannot be reliably simulated since they consist of misreconstructed prompt muons and muons in jets.Therefore, we rely on analyzing events in the recorded data to estimate the expected background.To achieve this, we employ CRs where one or more selection criteria are inverted, creating a region predominantly populated by a specific type of background while having an insignificant contribution from the signal processes.The specific definitions of these CRs and the procedure for evaluating the background differ across dimuon categories and are elaborated on in the rest of this section.The background evaluation methods are nearly all identical to those employed in the Run 2 analysis [5].The only exception is the evaluation of QCD backgrounds in the STA-STA category, which can now benefit from events rejected by the new STA muon isolation requirement.In order to prevent potential bias in the event selection, the events that satisfy the full set of selection criteria (i.e., those in the SR) were kept concealed ("blinded") until the final stages of the analysis.
One particular type of background events arises from cosmic ray muons crossing the detector within the acceptance of the muon system.Such muons are often reconstructed as two back-to- back muons, one in the upper half and one in the lower half of the detector.For each dimuon category, the contribution from cosmic ray muons is assessed independently by examining the number of dimuons that meet all the selection criteria except for angular requirements designed to reject putative dimuons that are formed from back-to-back muons [5].To evaluate this contribution, we use the rejection factors of these requirements, which are determined from a sample of cosmic ray muons recorded during periods without any beam activity.In both dimuon categories, the remaining background originating from cosmic ray muons is estimated to be less than 0.1 events in all mass intervals combined.

Estimation of Drell-Yan and other prompt backgrounds
The contribution from misreconstructed prompt high-mass dimuons, mainly originating from the DY process, to the total background is evaluated from events in the signal-free |∆Φ|symmetric CR as where ) are, respectively, the numbers of DY background events in the SR and its |∆Φ|-symmetric CR with |∆Φ| C representing the selection criterion applied; R i DY is the transfer factor accounting for the residual asymmetry in the population of events in the two |∆Φ| regions and obtained from auxiliary measurements; and the index i denotes the dimuon category (STA-STA or TMS-TMS).The number of DY dimuons in the CR is obtained from the total number of events in that region corrected by the expected contribution from QCD background events, estimated as discussed in Section 5.2.
To assess the symmetry of the |∆Φ| distributions in this class of background events, events in dedicated CRs are used.In the STA-STA category, we focus on events within data CRs that are obtained by reversing the STA-to-TMS association.Specifically, we select events where STA-STA dimuons satisfy all the selection criteria, except that each of the constituent STA muons is associated with a TMS muon.To ensure that these STA-STA dimuons are promptly produced (and not part of the signal), we require that the associated TMS-TMS dimuons, which offer superior spatial resolution, are prompt.This is achieved by imposing L xy /σ L xy < 1.0 for the associated TMS-TMS dimuon.To minimize contamination from muons originating from jets (which are discussed separately below), each TMS muon in the associated TMS-TMS dimuon is required to have

Estimation of QCD backgrounds
Many of the background processes yielding small-|∆Φ| OS dimuons also give rise to small-|∆Φ| SS dimuons, either because these processes are charge symmetric or via muon charge misassignment.Most of these dimuons are embedded in jets and are suppressed by the muon isolation requirements.Thus, we evaluate the contribution from the QCD backgrounds to the SR from events in CRs obtained by inverting two independent selection requirements: the isolation requirement (i.e., we select events where at least one of the muons fails to satisfy the isolation criteria used in the analysis) and the requirement of the OS dimuons (i.e., we select SS dimuons).
In the STA-STA category, we base our estimate of the QCD backgrounds on the number of events with OS nonisolated dimuons, using where N STA-STA QCD (OS; |∆Φ| < |∆Φ| C ) and N STA-STA noniso (OS; |∆Φ| < |∆Φ| C ) are, respectively, the numbers of OS isolated and nonisolated dimuons with small |∆Φ|, and R STA-STA QCD is the transfer factor between these numbers.The transfer factor is evaluated using SS dimuons in the same small-|∆Φ| region: with N STA-STA iso (SS; |∆Φ| < |∆Φ| C ) and N STA-STA noniso (SS; |∆Φ| < |∆Φ| C ) representing the numbers of, respectively, isolated and nonisolated SS STA-STA dimuons with |∆Φ| < |∆Φ| C .To improve the precision of the R STA-STA QCD measurement, we enlarge the sample of SS dimuons by removing tight requirements on the numbers of DT hits and muon segments applied to dimuons with |∆η µµ | < 0.1 (discussed in Section 4) as well as the generic requirement on the minimum number of DT hits [5].We obtain R STA-STA QCD values varying between 1.0 and 1.5 as a function of reconstructed dimuon mass and measured with an uncertainty of 20-40%.They are in good agreement with R STA-STA QCD values obtained from a sample of OS small-|∆Φ| events failing the criteria for dimuons with |∆η µµ | < 0.1.Systematic uncertainties arising from these two measurements are found to be much smaller than statistical uncertainties resulting from CR sample sizes.
Based on the Run 2 studies [5], we do not anticipate a significant contribution from |∆Φ|asymmetric low-mass dimuons in the TMS-TMS category.This is primarily due to the superior dimuon invariant mass resolution in this category.However, since there may still be a small contribution from |∆Φ|-asymmetric dimuons, we prefer not to rely solely on the symmetry of |∆Φ| in evaluating the background.Consequently, the method used is similar to that employed in the STA-STA category and bases our estimate of the QCD backgrounds on the number of SS dimuons, using ( The transfer factor R TMS-TMS QCD is obtained from the ratio of OS to SS dimuons in the CR with the muon isolation requirement reversed, which consists of dimuons passing the nominal event selection but with at least one muon with I TMS rel, trk > 0.075 and both with I TMS rel, trk < 0.5.We have verified that these events, as well as SS dimuons passing isolation requirements, contain negligible contributions from signal and DY events.As the SR is divided into several min(d 0 /σ d 0 ) bins, the evaluation of R TMS-TMS QCD is performed separately in each min(d 0 /σ d 0 ) bin.Since no significant dependence of the value of R TMS-TMS QCD on m µµ and m corr µµ is observed, R TMS-TMS QCD in each min(d 0 /σ d 0 ) bin is calculated by integrating events in the entire invariant mass spectrum.The measured values of R TMS-TMS QCD decrease from 2.0 to 1.3 as min(d 0 /σ d 0 ) increases, with the statistical uncertainties in the range 5-15%.A systematic uncertainty of 15% is assigned to account for variations of R TMS-TMS QCD as a function of the invariant mass and as the result of varying the definition and boundaries of the auxiliary CR.
To avoid potential overestimation of the DY backgrounds, we use the same QCD background evaluation technique for dimuons in the CR defined by |∆Φ| > π − |∆Φ| C .The obtained estimate of the QCD backgrounds is subtracted from the total to derive the estimate of DY dimuons in this |∆Φ| region, which is used for the evaluation of the DY backgrounds in the SR according to Eq. ( 2).This procedure is not applied in the STA-STA category, where the |∆Φ|-symmetric QCD background is negligible.The sum of the QCD and DY background estimates constitutes the total predicted background in the SR.According to the background evaluation method, the DY backgrounds are expected to dominate at small d 0 /σ d 0 and L xy /σ L xy values, whereas the relative QCD contribution becomes larger as d 0 /σ d 0 and L xy /σ L xy increase.The uncertainty in the background predictions is mainly driven by the statistical uncertainty arising from the limited number of events observed in the CRs.

Validation of background predictions
To ensure the reliability of the background evaluation method described in Sections 5.1 and 5.2, we examine the method's performance in various VRs, which are chosen to have minimal or no contribution from the signal being studied.Thus, we can verify that it accurately predicts the background and that any observed discrepancies are within acceptable limits.
The evaluation of DY backgrounds is examined in the VRs obtained by inverting the L xy /σ L xy and d 0 /σ d 0 requirements and thereby enriched in this class of events.An example is shown in Fig. 6, which compares the background predictions to the observed distributions in the  L xy /σ L xy < 6 VR for dimuons with m µµ > 15 GeV in the STA-STA category.To check how the validity of the method depends on |∆Φ| and the dimuon displacement, we perform the evaluation of the background in corresponding bins.The expected number of background events in the given VR is computed according to Eq. ( 2) separately in each |∆Φ| or L xy /σ L xy bin and compared to the observed data.The predictions of the method are consistent with the yields in data.
In the TMS-TMS category, we apply the background evaluation procedure to the TMS-TMS dimuons in the VR defined by 2 < min(d 0 /σ d 0 ) < 6.The comparison of the predicted background and data in bins of L xy /σ L xy for two |∆Φ| C requirements is shown in Fig. 7.The expected and observed numbers of events are in agreement in the entire probed L xy /σ L xy range.The evaluation of the |∆Φ|-asymmetric component of the background, which is particularly important in the STA-STA category, is tested in the low-mass (6 < m µµ < 10 GeV) VR where the QCD backgrounds dominate.Figure 8 shows a comparison of predicted and measured background in this VR as a function of |∆Φ| and m µµ for STA-STA dimuons.The yields in data are found to be consistent with the background predictions in all |∆Φ| and m µµ intervals.
Finally, to ensure the validity of the method at different values of the main discriminating variables in the TMS-TMS category, the validation checks are performed in bins of min(d 0 /σ d 0 ) and m µµ of TMS-TMS dimuons.Such checks include comparisons in the d 0 /σ d 0 sideband (2 < d 0 /σ d 0 < 6) in the |∆Φ| < π/4 SR, as well as those in the entire d 0 /σ d 0 range in the |∆Φ| sideband, π/4 < |∆Φ| < π/2.In the latter, the region with π/4 < |∆Φ| < π/2 is used as a signal-free proxy for the |∆Φ| < π/4 SR.The background evaluation procedure is applied to the OS and SS dimuons in the |∆Φ|-symmetric region, π/2 < |∆Φ| < 3π/4, as well as SS dimuons with π/4 < |∆Φ| < π/2.The comparisons of the predicted background and data as a function of min(d 0 /σ d 0 ) and m µµ for TMS-TMS dimuons in these VRs are shown in Fig. 9.The observed and expected numbers of events are consistent within statistical uncertainties.

Systematic uncertainties affecting signal
The modeling of signal efficiencies in simulation was extensively studied in the Run 2 search [5].Since no changes affecting this analysis were made in the CMS detector or in the muon reconstruction algorithms between Run 2 and Run 3, many of the systematic uncertainties and datato-simulation corrections are taken directly from Ref. [5].New studies include modeling of signal efficiencies related to the new trigger algorithms and modified event selection criteria, such as the STA muon isolation.The studies are performed for each dimuon category separately, using dedicated data samples.Unless stated otherwise, we consider sources of uncertainties to be uncorrelated between different categories.
In both categories, the dominant systematic uncertainties and the largest data-to-simulation corrections arise from muon identification, muon reconstruction, and trigger efficiencies.At small displacements, the systematic effects related to these efficiencies are examined as a function of muon p T and η by applying the "tag-and-probe" method [33] to prompt muons from J/ψ meson and Z boson decays.The evolution of efficiencies as a function of displacement is studied using cosmic ray muons and muons from decays of nonprompt J/ψ mesons.These studies yield corrections to the simulated signal yields that range, depending on the signal sample, from 0.75 to unity for the STA-STA category and from 0.83 to unity for the TMS-TMS category.The overall uncertainty increases continuously with displacement, from ≈5% for prompt-like muons to ≈15% for muons with d 0 = 100 cm, reflecting the precision of studies using cosmic ray muons.Since a large part of this uncertainty stems from the evaluation of efficiencies of trigger algorithms common to both dimuon categories, it is taken as correlated between the categories.Dedicated studies were performed to examine the effect of the d 0 thresholds and looser muon p T requirements of the new displaced dimuon triggers.The efficiency of the Run 3 (2022, L3) triggers is evaluated using dimuons from decays of nonprompt J/ψ mesons selected by the triggers that use jets and event p T imbalance.As a result of these studies, the simulated yields of signal events selected by this set of triggers are scaled by a factor of 0.95, and an uncertainty of 5% is assigned.The efficiency of the Run 3 (2022, L2) triggers is studied using cosmic ray muons.While no systematic biases are observed, the largest data-simulation difference of 3% in bins of d 0 is assigned as a systematic uncertainty in the efficiency of these triggers.These corrections and uncertainties are included in the overall corrections and uncertainties discussed in the previous paragraph.
The accuracy of the modeling of the muon isolation requirements is assessed using muons from Z boson decays and, in the case of STA muons, cosmic ray muons selected in pp collision events.Based on the results of these studies, a systematic uncertainty of 6 (2)% is assigned to the efficiency of STA (TMS) muons.The uncertainty in the Higgs boson production cross section at 13.6 TeV amounts to +5% −7% [21].The remaining systematic uncertainties, e.g., those related to muon p T resolution and dimuon vertex reconstruction, are less than 5%.The uncertainty in the integrated luminosity is 2.3% [36].The uncertainty in the signal efficiency due to pileup modeling is 2%.Both luminosity and pileup uncertainties are correlated among the dimuon categories.

Results
The numbers of observed events and the predicted background yields in the STA-STA category are shown in Fig. 10 in representative m µµ and m corr µµ intervals.The width of the mass intervals and the |∆Φ| and m µµ requirements for events in Fig. 10 (left) and Fig. 10 (right) correspond to those chosen, respectively, for the study of the HAHM and of the RPV SUSY model.For illustrative purposes, signal distributions at the level of the median expected exclusion limits at 95% confidence level (CL) obtained from the ensemble of both dimuon categories in the background-only scenario are also shown.The numbers of observed events are consistent with background predictions.As expected for background events, most of the observed events have low m µµ .The numbers of observed events and the predicted background yields in the TMS-TMS category are shown in Figs.11-13.Figure 11 shows the distributions of min(d 0 /σ d 0 ) for TMS-TMS dimuons with (left) |∆Φ| < π/30 and (right) |∆Φ| < π/4, for events in all mass intervals combined.As expected for background events, the events in data are predominantly at low values of min(d 0 /σ d 0 ). Figure 12 shows the distributions of m corr µµ in three min(d 0 /σ d 0 ) bins, 6-10, 10-20, and >20, for dimuons with |∆Φ| < π/4, the looser |∆Φ| requirement used for the study of the RPV SUSY model.The numbers of events in the SR chosen for the study of the HAHM model, with the tighter requirement |∆Φ| < π/30, are smaller (with no more than one event per m µµ bin), as shown in Fig. 13.The numbers of observed events are consistent with background predictions in both SRs.The largest min(d 0 /σ d 0 ) bin, min(d 0 /σ d 0 ) > 20, contains the lowest experimental background and, except for the smallest lifetimes, most of the signal predicted by both models.
These results are used to set upper limits on B(H → Z D Z D ) in the HAHM model and on the product of the squark-antisquark production cross section σ(pp → q q ) and B( q → q χ 0 1 ) in the RPV SUSY model.The limit extraction is based on a modified frequentist approach [37,38] Comparison of observed and expected numbers of events in bins of m corr µµ in the TMS-TMS dimuon category, in the signal regions optimized for the RPV SUSY model.The number of observed events (black circles) is overlaid with the stacked filled histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of m corr µµ in three min(d 0 /σ d 0 ) bins: (left) 6-10, (center) 10-20, and (right) >20.Hatched histograms show statistical uncertainties in the total expected background.Contributions expected from signal events predicted by the RPV SUSY model with the parameters indicated in the legends are shown as red and blue histograms.Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility.The last bin includes events in the histogram overflow.Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility.The last bin includes events in the histogram overflow.uses the CMS statistical analysis tool COMBINE [39].The method yielding background predictions in the SR is implemented using a multibin likelihood, which is a product of Poisson distributions corresponding to the SR and CRs.The systematic uncertainties affecting the signal yield are incorporated as nuisance parameters using log-normal distributions.The expected and observed upper limits are evaluated through the use of simulated pseudo-experiments.For each signal model, the limits are first computed separately in each dimuon category.The individual likelihoods are then combined to obtain the limits in the ensemble of both categories.For the interpretation in the framework of the HAHM model, the results obtained in this analysis are also combined with the results of the Run 2 analysis [5] to achieve even stronger bounds on the model parameters.The combination of the two results takes into account the different cross sections of the Higgs boson production in collisions at 13.0 and 13.6 TeV [20,21].
The signal efficiencies used in the statistical interpretations of the results are obtained from simulation and further corrected by the data-to-simulation scale factors described in Section 6.They are computed separately for each dimuon category, mass interval, LLP lifetime, and signal model.Given the smallness of the expected background and taking into account the selection efficiencies discussed in Section 4, the introduction of a separate category for events with two dimuons would not increase the sensitivity of the analysis significantly even in the most favorable case for the 4µ signal events, namely B(LLP → µ + µ − X) = 1.The gain would be negligible for smaller B(Z D → µ + µ − ) values predicted by the HAHM model.Therefore, no distinction is made between events with one and two reconstructed dimuons of the same type.Events with two TMS-TMS dimuons are assigned to the min(d 0 /σ d 0 ) bin encompassing the larger of the two min(d 0 /σ d 0 ) values.
Figures 14 and 15 show the 95% CL upper limits obtained in the framework of the HAHM model under the assumption that m(H D ) > m(H)/2.The limits shown in these figures are set on B(H → Z D Z D ) as functions of the mean proper decay length of Z D for m(Z D ) in the range 10-60 GeV. Figure 14 shows the results obtained in this analysis, namely the expected limits in

fb
Observed 68% quantile Expected 95% quantile Figure 16: The 95% CL upper limits on σ(pp → q q )B( q → q χ 0 1 ) as a function of cτ( χ 0 1 ) in the RPV SUSY model, for B( χ 0 1 → µ + µ − ν) = 0.5 and m( q ) ranging from (upper left) 125 GeV to (lower right) 1.6 TeV.The observed limits for various combinations of m( q ) and m( χ 0 1 ) indicated in the legends are shown as solid curves.The median expected limits and their 68 and 95% quantiles are shown, respectively, as dashed black curves and green and yellow bands for the case of m( χ 0 1 ) = 50 GeV and omitted for other neutralino masses for clarity.The gray horizontal lines indicate the theoretical values of the squark-antisquark production cross sections with the uncertainties shown as gray shaded bands.The predicted cross sections for m( q ) = 125, 200, and 350 GeV are, respectively, 7200, 840, and 50 pb, and fall outside the y-axis range.the individual dimuon categories as well as the expected and observed limits obtained in the ensemble of both categories.Figure 15 compares the observed limits obtained in this analysis with the corresponding Run 2 limits [5], and shows the expected and observed limits obtained in a combination of the two results.
Even though the size of the data sample used by this analysis is about a factor of 2.5 smaller than that in the Run 2 analysis, the constraints on the parameters of the HAHM model are comparable or tighter in a significant fraction of the parameter space, thanks mainly to improvements in the trigger algorithms.The combined limits on B(H → Z D Z D ) are approximately a factor of 2 more stringent than the limits obtained in the Run 2 analysis.They exclude B(H → Z D Z D ) of 1% in the range of cτ(Z D ) from a few tens of µm to 30 m (700 m) for m(Z D ) = 10 GeV (60 GeV) at 95% CL.In the m(Z D ) interval 20-60 GeV, B(H → Z D Z D ) as low as 0.01% is excluded at 95% CL in the cτ(Z D ) range of about 0.3 mm to 0.5 m, which corresponds to a wide range of ϵ values from ≈10 −8 to ≈10 −6 .These constraints on rare SM Higgs boson decays are tighter than those derived from searches for invisible Higgs boson decays [40,41] and from measurements of the SM Higgs boson couplings [42].At m(Z D ) > 20 GeV, the limits obtained are the most stringent limits to date for all cτ(Z D ) values except those between ≈0.1 and ≈10 cm (depending on m(Z D )), where a previous CMS search [7] using data collected with a dedicated high-rate data stream provides the best limits.
Figure 16 shows the observed and expected 95% CL upper limits obtained in the ensemble of both dimuon categories in the framework of the RPV SUSY model.The limits are set on the product σ(pp → q q )B( q → q χ 0 1 ) assuming B( χ 0 1 → µ + µ − ν) = 0.5.They are shown as functions of the mean proper decay length of χ 0 1 for the various combinations of m( q ) and m( χ 0 1 ) indicated in the legends, for m( q ) values ranging from 125 GeV to 1.6 TeV, and compared to the theoretical predictions.At a squark mass of 700 GeV, the data exclude the mean proper neutralino decay lengths between 30 µm and 350 m (at m( χ 0 1 ) = 50 GeV), and between 30 µm and 1.5 km (at m( χ 0 1 ) = 500 GeV).At a squark mass of 1.6 TeV, the excluded cτ( χ 0 1 ) range is between 0.07 and 4 cm for m( χ 0 1 ) = 50 GeV and between 70 µm and 2 m for m( χ 0 1 ) = 500 GeV.The limits obtained in this analysis are tighter than those derived by CMS in the Run 1 search [8,9] in all of the relevant (m( q ), m( χ 0 1 ), cτ( χ 0 1 )) parameter space and are more stringent at cτ( χ 0 1 ) ≲ 1 cm and cτ( χ 0 1 ) ≳ 1 m than the limits on the λ 122 RPV coupling set by the ATLAS Collaboration at m( q ) of 700 GeV and 1.6 TeV [11].

Summary
Data collected by the CMS experiment in proton-proton collisions at √ s = 13.6 TeV in 2022 and corresponding to an integrated luminosity of 36.6 fb −1 have been used to conduct an inclusive search for long-lived exotic neutral particles decaying to final states with a pair of oppositely charged muons.The search strategy is largely model independent and is sensitive to a broad range of lifetimes and masses.No significant excess of events above the standard model background is observed.The results are interpreted as limits on the parameters of the hidden Abelian Higgs model, in which the Higgs boson H decays to a pair of long-lived dark photons Z D , and of an R-parity violating supersymmetry model, in which long-lived neutralinos decay to a pair of muons and a neutrino.
Even though the size of the data sample used by this analysis is about a factor of 2.5 smaller than that used in the previous search for displaced dimuons by the CMS experiment in pp collisions at √ s = 13 TeV, the constraints on the parameters of the hidden Abelian Higgs model are comparable or tighter in a significant fraction of the parameter space, thanks mainly to improvements in the trigger algorithms.The combination of the results of this analysis with the results obtained at √ s = 13 TeV improves the constraints on the branching fraction of the Higgs boson to dark photons, B(H → Z D Z D ), by approximately a factor of 2. In the range 10-60 GeV of the Z D mass m(Z D ), B(H → Z D Z D ) = 1% is excluded at 95% confidence level in the range of proper decay length cτ(Z D ) from a few tens of µm to 30 m (700 m) for m(Z D ) = 10 GeV (60 GeV).For m(Z D ) greater than 20 GeV and less than m(H)/2, the combined limits provide the most stringent constraints to date on B(H → Z D Z D ) for cτ(Z D ) between 30 µm and ≈0.1 cm, and above ≈10 cm.When interpreted in the framework of the R-parity violating supersymmetry model at a squark mass of 1.6 TeV, the results exclude mean proper neutralino decay lengths between 0.07 and 4 cm for a 50 GeV neutralino and between 70 µm and 2 m for a 500 GeV neutralino.

1 Figure 2 :
Figure 2: The p T and d 0 coverage of the 2016 Run 2 triggers (light blue), 2018 Run 2 triggers (blue), and newly designed 2022 Run 3 triggers described in the text (red).The two values of the p T refer to the trigger thresholds for the muons.

Figure 3 :
Figure 3: Efficiencies of the various displaced dimuon trigger paths and their combination as a function of cτ for the HAHM signal events with m(Z D ) = 20 GeV.The efficiency is defined as the fraction of simulated events that satisfy the detector acceptance and the requirements of the following sets of trigger paths: the Run 2 (2018) triggers (dashed black); the Run 3 (2022, L3) triggers (blue); the Run 3 (2022, L2) triggers (red); and the OR of all these triggers (Run 3 (2022), black).The lower panel shows the ratio of the overall Run 3 (2022) efficiency to the Run 2 (2018) efficiency.

Figure 4 :
Figure 4: Distributions of |∆Φ| for (left) STA-STA and (right) TMS-TMS dimuons in data samples obtained by inverting some of the selection criteria and enriched in DY events (black circles) and for events passing all selection criteria except for a requirement on |∆Φ| in all HAHM (blue triangles) and RPV SUSY (orange squares) generated signal samples combined.All distributions are normalized to unit area.symmetric region, |∆Φ| > π − |∆Φ| C , as a control region (CR) for evaluating the contribution from DY and other prompt backgrounds, and the validation regions (VR) with π/4 < |∆Φ| < π/2 and π/2 < |∆Φ| < 3π/4 for validating background predictions, as discussed in Section 5.

Figure 5 :
Figure5: Overall efficiencies in the STA-STA (green) and TMS-TMS (red) dimuon categories, as well as their combination (black) as a function of cτ for the HAHM signal events with m(Z D ) = 20 GeV.The solid curves show efficiencies achieved with the 2022 Run 3 triggers, whereas dashed curves show efficiencies for the subset of events selected by the triggers used in the 2018 Run 2 analysis.The efficiency is defined as the fraction of signal events that satisfy the criteria of the indicated trigger as well as the full set of offline selection criteria.The lower panel shows the relative improvement of the overall signal efficiency brought in by improvements in the trigger.
TMS rel, trk < 0.05.From this sample, we obtain R STA-STA DY = 0.75 ± 0.02 (stat.)for |∆Φ| C = π/10 and R STA-STA DY = 0.73 ± 0.02 (stat.)for |∆Φ| C = π/4.The value of R TMS-TMS DY is set to unity based on studies using simulation and data [5].In both STA-STA and TMS-TMS categories, no significant dependence of the transfer factor R i DY on reconstructed dimuon mass is observed, and a single value is used for all signal mass intervals.The systematic uncertainties in R STA-STA DY are assessed by comparing R STA-STA DY measured in individual mass intervals with the result of the inclusive measurement and by varying the boundaries and definitions of the auxiliary CRs.The latter includes repeating the measurements of R STA-STA DY in the region with only one STA-to-TMS association.Based on these studies, we assign a systematic uncertainty of 30% in R STA-STA DY .The systematic uncertainty in R TMS-TMS DY is assigned to be 15% based on the studies of the residual |∆Φ| asymmetry for events in the min(d 0 /σ d 0 ) and |∆Φ| side bins.

Figure 6 :
Figure 6: Example of background prediction checks in the STA-STA category: distributions of (left) |∆Φ| and (right) L xy /σ L xy for events with m µµ > 15 GeV in the L xy /σ L xy < 6 validation region in data (black circles) compared to the background predictions (histograms).The lower panels show the ratio of the observed to predicted number of events.Hatched histograms show the statistical uncertainty in the background prediction.

Figure 7 :
Figure 7: Example of background prediction checks in the TMS-TMS category: L xy /σ L xy distributions for events with (left) |∆Φ| < π/4 and (right) |∆Φ| < π/30 in the 2 < min(d 0 /σ d 0 ) < 6 validation regions compared to the background predictions.The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events.The last bin includes events in the histogram overflow.The lower panels show the ratio of the observed to predicted number of events.Hatched histograms show the statistical uncertainty in the background prediction.

Figure 8 :
Figure 8: Example of background prediction checks in the STA-STA category: distributions of (left) |∆Φ| and (right) m µµ for dimuons in the low-mass (6 < m µµ < 10 GeV) validation region in data (black circles) compared to the background predictions (histograms).The lower panels show the ratio of the observed to predicted number of events.Hatched histograms show the statistical uncertainty in the background prediction.

Figure 9 :
Figure 9: Example of background prediction checks in the TMS-TMS category: (left) distribution of min(d 0 /σ d 0 ) for events in the π/4 < |∆Φ| < π/2 validation region; (right) distribution of m µµ for events in the 2 < min(d 0 /σ d 0 ) < 6 validation region.The number of observed events (black circles) is overlaid with stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events.The last bin includes events in the histogram overflow.The lower panels show the ratios of the observed to predicted number of events.Hatched histograms show the statistical uncertainty in the background prediction.

Figure 10 :
Figure 10: Comparison of the observed (black points) and expected (histograms) numbers of events in nonoverlapping (left) m µµ and (right) m corr µµ intervals in the STA-STA dimuon category, in the signal regions optimized for the (left) HAHM and (right) RPV SUSY model.Yellow and green stacked filled histograms represent mean expected background contributions from QCD and DY, respectively, while statistical uncertainties in the total expected background are shown as hatched histograms.Signal contributions expected from simulated signals indicated in the legends are shown in red and blue.Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility.The last bin includes events in the histogram overflow. and

Figure 11 :
Figure 11: Distributions of min(d 0 /σ d 0 ) for TMS-TMS dimuons with (left) |∆Φ| < π/30 and (right) |∆Φ| < π/4, for events in all mass intervals combined, for both the validation (min(d 0 /σ d 0 ) < 6) and signal (min(d 0 /σ d 0 ) > 6) regions.The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events.Statistical uncertainties in the total expected background are shown as hatched histograms.Signal contributions expected from simulated signals indicated in the legends are shown in red and blue.Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility.Events are required to satisfy all nominal selection criteria with the exception of the d 0 /σ d 0 requirement.The last bin includes events in the histogram overflow.

Figure 13 :
Figure 13: Comparison of observed and expected numbers of events in bins of m µµ in the TMS-TMS dimuon category, in the signal regions optimized for the HAHM.The number of observed events (black circles) is overlaid with the stacked histograms showing the expected numbers of QCD (yellow) and DY (green) background events in bins of m µµ in three min(d 0 /σ d 0 ) bins: (left) 6-10, (center) 10-20, and (right) >20.Hatched histograms show statistical uncertainties in the total expected background.Signal contributions expected from simulated H → Z D Z D events with the parameters indicated in the legends are shown as red and blue histograms.Their yields are set to the corresponding median expected 95% CL exclusion limits obtained from the ensemble of both dimuon categories, scaled up as indicated in the legend to improve visibility.The last bin includes events in the histogram overflow.

Figure 14 :
Figure 14: The 95% CL upper limits on B(H → Z D Z D ) as a function of cτ(Z D ) in the HAHM model, for m(Z D ) ranging from (upper left) 10 GeV to (lower right) 60 GeV, in the STA-STA and TMS-TMS dimuon categories in 2022 data and their combination.The median expected limits obtained from the STA-STA and TMS-TMS dimuon categories are shown as dashed blue and red curves, respectively; the combined median expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves.The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.

Figure 15 :
Figure 15: The 95% CL upper limits on B(H → Z D Z D ) as a function of cτ(Z D ) in the HAHM model, for m(Z D ) ranging from (upper left) 10GeV to (lower right) 60 GeV, obtained in this analysis, the Run 2 analysis[5], and their combination.The observed limits in this analysis and in the Run 2 analysis[5] are shown as blue and red curves, respectively; the median combined expected limits are shown as dashed black curves; and the combined observed limits are shown as solid black curves.The green and yellow bands correspond, respectively, to the 68 and 95% quantiles for the combined expected limits.
the NKFIH research grants K 124845, K 124850, K 128713, K 128786, K 129058, K 131991, K 133046, K 138136, K 143460, K 143477, 2020-2.2.1-ED-2021-00181, and TKP2021-NKTA-64 (Hungary); the Council of Science and Industrial Research, India; ICSC -National Research Center for High Performance Computing, Big Data and Quantum Computing, funded by the NextGenerationEU program (Italy); the Latvian Council of Science; the Ministry of Education and Science, project no.2022/WK/14, and the National Science Center, contracts Opus 2021/41/B/ST2/01369 and 2021/43/B/ST2/01552 (Poland); the Fundac ¸ão para a Ciência e a Tecnologia, grant CEECIND/01334/2018 (Portugal); the National Priorities Research Program by Qatar National Research Fund; MCIN/AEI/10.13039/501100011033,ERDF "a way of making Europe", and the Programa Estatal de Fomento de la Investigaci ón Científica y Técnica de Excelencia María de Maeztu, grant MDM-2017-0765 and Programa Severo Ochoa del Principado de Asturias (Spain); the Chulalongkorn Academic into Its 2nd Century Project Advancement Project, and the National Science, Research and Innovation Fund via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation, grant B37G660013 (Thailand); the Kavli Foundation; the Nvidia Corporation; the SuperMicro Corporation; the Welch Foundation, contract C-1845; and the Weston Havens Foundation (USA).