Search for R-parity violating supersymmetry with displaced vertices in proton-proton collisions at sqrt(s) = 8 TeV

Results are reported from a search for R-parity violating supersymmetry in proton-proton collision events collected by the CMS experiment at a center-of-mass energy of sqrt(s) = 8 TeV. The data sample corresponds to an integrated luminosity of 17.6 inverse femtobarns. This search assumes a minimal flavor violating model in which the lightest supersymmetric particle is a long-lived neutralino or gluino, leading to a signal with jets emanating from displaced vertices. In a sample of events with two displaced vertices, no excess yield above the expectation from standard model processes is observed, and limits are placed on the pair production cross section as a function of mass and lifetime of the neutralino or gluino. At 95% confidence level, the analysis excludes cross sections above approximately 1 fb for neutralinos or gluinos with mass between 400 and 1500 GeV and mean proper decay length between 1 and 30 mm. Gluino masses are excluded below 1 and 1.3 TeV for mean proper decay lengths of 300 micrometers and 1 mm, respectively, and below 1.4 TeV for the range 2-30 mm. The results are also applicable to other models in which long-lived particles decay into multijet final states.


Introduction
In spite of extensive efforts by the ATLAS and CMS Collaborations at the CERN LHC, the superpartners of standard model (SM) particles predicted by supersymmetry (SUSY) [1,2] have not yet been observed. If superpartners are produced and R-parity [3] is conserved, the lightest supersymmetric particle (LSP) passes through the detector unobserved, except for a potentially large amount of missing transverse energy. The assumption of R-parity conservation is motivated by experimental observations such as limits on the proton lifetime [4]. This assumption is not strictly required as long as either lepton or baryon number is conserved, or the associated R-parity violating (RPV) [5] terms in the Lagrangian are extremely small. Searches for a variety of signatures have not yet found any evidence for RPV SUSY [6-10].
In minimal flavor violating (MFV) models of RPV SUSY [11,12], the Yukawa couplings between superpartners and SM particles are the sole source of flavor symmetry violation, and the amplitudes for lepton-and baryon-number changing interactions are correspondingly small. At the LHC, the LSP typically decays within the detector volume, so there is no large missing transverse energy. The production processes of the superpartners are similar to those in the minimal supersymmetric standard model in that superpartners are produced in pairs, but the phenomenology depends on the identity of the LSP.
This analysis uses a benchmark signal model described in Ref. [12], in which the LSP is assumed to be either a neutralino or a gluino that is sufficiently heavy to decay into a top antiquark and a virtual top squark. The virtual top squark then decays via a baryon-number violating process to strange and bottom antiquarks, as shown in Fig. 1. Although this decay is heavily suppressed by the Yukawa coupling, it still dominates the top squark rate, with other partial widths being suppressed by a factor of 100 or more. As a consequence, the LSP is long-lived, with a lifetime that depends on the model parameters. For large parts of the parameter space, pair-produced LSPs lead to interesting signatures. Observable effects include increased top quark production rates; events with many jets, especially b quark jets; and events with displaced vertices. The decay of the LSP results in multiple jets emerging from a displaced vertex, often with wide opening angles. To identify the displaced vertices, we use a custom vertex reconstruction algorithm optimized for these distinctive features. This algorithm differs from standard methods used to identify b quark jets [13], which assume a single jet whose momentum is aligned with the vertex displacement from the primary vertex. Our signature consists of two vertices, well separated in space. Studies based on event samples from Monte Carlo (MC) simulation show that SM background events rarely contain even one such reconstructed displaced vertex. In the even rarer events with two displaced vertices, the vertices are usually not well separated from times τ (0.1 ≤ cτ ≤ 30 mm) are produced. In these samples, neutralinos are produced in pairs; each neutralino is forced to undergo a three-body decay into top, bottom, and strange (anti-)quarks. Backgrounds arising from SM processes are dominated by multijet and top quark pair (tt) events. The multijet processes include b quark pair events. Smaller contributions come from single top quark production (single t), vector boson production in association with additional jets (V+jets), diboson production (VV), and top quark pairs with a radiated vector boson (tt +V). Processes with a single vector boson include virtual photons, W bosons, or Z bosons, while the diboson processes include WW, WZ, and ZZ. Single top events are simulated with POWHEG 1.0 [21][22][23][24][25]; diboson events are simulated with PYTHIA 6.426 [26]; all other backgrounds are simulated using MADGRAPH 5.1 [27]. For all samples, hadronization and showering are done using PYTHIA 6.426 with tune Z2*. The Z2* tune is derived from the Z1 tune [28], which uses the CTEQ5L parton distribution set, whereas Z2* adopts CTEQ6L [29]. The detector response for all simulated samples is modeled using a GEANT4-based simulation [30] of the CMS detector. The effects of additional pp interactions per bunch crossing ("pileup") are included by overlaying additional simulated minimum-bias events, such that the resulting distribution of the number of interactions matches that observed in the experiment.

Event preselection
To ensure that the four-jet trigger efficiency is high and well understood, more stringent criteria are applied offline, requiring at least four jets in the calorimeter with p T > 60 GeV. These jets are reconstructed from calorimeter energy deposits, which are clustered by the anti-k T algorithm [31,32] with a distance parameter of 0.5. The trigger efficiency determined using events satisfying a single-muon trigger is (96.2 ± 0.2)% for events with four offline jets with p T > 60 GeV. The simulation overestimates this efficiency by a factor of 1.022 ± 0.002, so, where used, its normalization is corrected by this amount.
Jets considered in the rest of the analysis are those obtained in the full event reconstruction performed using a particle-flow (PF) algorithm [33,34]. The PF algorithm reconstructs and identifies photons, electrons, muons, and charged and neutral hadrons with an optimized combination of information from the various elements of the CMS detector. Before clustering the PF candidates into jets, charged PF candidates are excluded if they originate from a pp interaction vertex other than the primary vertex, which is the one with the largest scalar Σ|p T | 2 . The resulting particles are clustered into jets, again by the anti-k T algorithm with a distance parameter of 0.5. Jets used in the analysis must satisfy p T > 20 GeV and |η| < 2.5.
For an event to be selected for further analysis, the scalar sum of the p T of jets in the event H T is required to be at least 500 GeV. This requirement has little impact on signal events but is useful for suppressing SM background.

Vertex reconstruction
Displaced vertices are reconstructed from tracks in the CMS silicon tracker. These tracks are required to have p T > 1 GeV, at least eight measurements in the tracker including one in the pixel detector, and a transverse impact parameter with respect to the beam axis of at least 100 µm. The impact parameter requirement favors vertices that are displaced from the primary vertex. The vertex reconstruction algorithm starts by forming seed vertices from all pairs of tracks that satisfy these requirements. Each vertex is fitted with the Kalman filter approach [35], and a fit is considered successful if it has a χ 2 per degree of freedom (χ 2 /dof) that is less than 5. The vertices are then merged iteratively until no pair of vertices shares tracks. Specifically, for each pair of vertices that shares one or more tracks, if the three-dimensional (3D) distance between the vertices is less than 4 times the uncertainty in that distance, a vertex is fit to the tracks from both, and they are replaced by the merged vertex if the fit has χ 2 /dof < 5. Otherwise, each track is assigned to one vertex or the other depending on its 3D impact parameter significance with respect to each of the vertices, as follows: • if the track is consistent with both vertices (both impact parameters less than 1.5 standard deviations), assign it to the vertex that has more tracks already; • if the track's impact parameter is greater than 5 standard deviations from either vertex, drop it from that vertex; • otherwise, assign the track to the vertex to which it has a smaller impact parameter significance.
Each remaining vertex is then refit, and if the fit satisfies the requirement of χ 2 /dof < 5, the old vertex is replaced with the new one; otherwise it is dropped entirely.
This algorithm is similar in many regards to those used to identify ("tag") b quark jets [13]. Typical b tagging algorithms, however, are optimized for identifying the decay in flight of a particle into a single jet and consequently make requirements that degrade sensitivity to the multijet final states sought here. For example, b tagging algorithms generally require that the tracks assigned to a vertex are approximately aligned with the flight direction from the primary vertex to the decay point, which is inefficient when there are multiple jets in the final state, including some that may be directed at large angles with respect to the flight path. The b tagging algorithms also discard tracks with impact parameters beyond those typical for b quark daughters (>2 mm), thereby significantly reducing the efficiency for finding vertices with large displacements.

Vertex variables and selection
The vertexing procedure produces multiple vertices per event, only some of which are consistent with the signal. In order to select quality vertices, we impose additional requirements on the vertex and its associated tracks and jets. The requirements for each vertex are: • at least five tracks; • at least three tracks with p T > 3 GeV; • at least one pair of tracks with separation ∆R < 0.4, where ∆R = √ (∆η) 2 + (∆φ) 2 , to favor vertices that include multiple tracks from a single jet; • at least one pair of tracks with ∆R > 1.2 to favor vertices involving multiple jets; • ∆R < 4 for all pairs of tracks, to suppress wide-angle track coincidences; • at least one jet that shares one or more tracks with the vertex; • displacement in x-y of the vertex from the detector origin of less than 25 mm, to suppress vertices from interactions in the beam pipe or detector material; • uncertainty in the x-y distance of the vertex from the beam axis of less than 25 µm.
In the data, 181 076 events have one vertex satisfying the above requirements, 251 have two of them, and no events have more than two. The candidate sample is composed of two-vertex events.

Signal discrimination in two-vertex events
The signal is extracted from the two-vertex events using the spatial separation between the vertices. In signal events, the two LSPs are emitted approximately back-to-back, leading to large separations. We define the distance between the two vertices in the x-y plane as d VV , and fit this distribution to extract the signal. The fit to the observed d VV distribution is described in Sec. 8.
The signal d VV templates are taken directly from simulation, with a distinct template for each LSP mass M and lifetime τ. In signal simulation, fewer than 10% of events in the candidate sample have more than two selected vertices. For these events, the two vertices with the highest number of tracks are selected for the d VV calculation, and in the case where two vertices have the same number of tracks, the vertex with decay products that have the higher invariant mass is chosen. The mass is reconstructed using the momenta of the associated tracks, assuming that the particles associated with the tracks have the charged pion mass. Figure 2 shows the d VV distribution of an example simulated signal with cτ = 1 mm, M = 400 GeV, and production cross section 1 fb, overlaid on the simulated background. The bins in d VV are chosen to be sensitive to the peaking nature of the background at low d VV ; five 200 µm bins are used from 0 to 1 mm, then one bin from 1 to 50 mm where the contribution from the long-lived signal dominates. Figure 3 shows the signal efficiency as a function of LSP mass and lifetime in the region d VV > 600 µm, where the background is low. The signal efficiency generally increases as lifetime increases, until the lifetime is so long that decays more often occur beyond our fiducial limit at the beam pipe. The efficiency also generally increases as mass increases, up to approximately 800 GeV where it begins to decrease because of the event selection criteria, particularly the limit on the opening angle between track pairs in a vertex.

Background template
Background vertices arise from poorly measured tracks. These tracks can arise from the same jet, or from several jets in multijet events. Because it is an effect of misreconstruction, twovertex background events are the coincidence of single background vertices.
Multijet events and tt production contribute 85% and 15% of the background in the two-vertex sample, respectively. Other sources of background, such as V+jets and single t events, are negligible. Approximately half of the background events include one or more b quark jets, whose displaced decay daughters combine with misreconstructed tracks to form vertices.
Instead of relying on simulation to reproduce the background, we construct a background template, denoted by d C VV , from data. Taking advantage of the fact that two-vertex background events can be modeled using the one-vertex events, we define a control sample that consists of the 181 076 events with exactly one vertex. Each value entering the d C VV template is the distance in the x-y plane between two toy vertices, each determined by a value of the x-y distance from the beam axis to the vertex, denoted by d BV , and a value of the azimuthal angle of the vertex, denoted by φ BV .
The two values of d BV are sampled from the distribution of d BV for the one-vertex sample, which is shown in Fig. 4. The observed distribution is in good agreement with the sum of the background contributions from simulation.
The two values of φ BV are chosen using information about the jet directions in a one-vertex event. Since background vertices come from misreconstructed tracks, they tend to be located perpendicular to jet momenta. Therefore, we select a jet at random, preferring those with larger p T because of their higher track multiplicity, and sample a value of φ BV from a Gaussian distribution with width 0.4 radians, centered on a direction perpendicular to the jet in the transverse plane. To obtain the second value of φ BV , we repeat this procedure using the same one-vertex event, allowing the same jet to be chosen twice.
The vertex reconstruction algorithm merges neighboring vertices. To emulate this behavior in our background template construction procedure, we discard pairs of vertices that are not  The agreement is well within the statistical uncertainty. When normalized to the observed number of two-vertex events, the difference in their yields in the region d VV > 600 µm is 0.6 ± 2.6 events.

Systematic uncertainties
The signal is extracted from a fit of a weighted sum of the signal and background templates to the observed d VV distribution. For the signal, the simulation provides both the d VV distribution and its normalization, and systematic uncertainties arise from sources such as vertex reconstruction efficiency, track reconstruction, track multiplicity, pileup conditions, the detector alignment, and the jet energies. For the background, for which the template is derived from a control sample, the systematic uncertainties come from effects that could cause a discrepancy between the constructed d C VV distribution and the nominal d VV distribution.

Systematic uncertainties related to signal distribution and efficiency
The dominant systematic uncertainty in the signal normalization arises from the difference between the vertexing efficiencies in the simulation and data. This effect is evaluated in an independent study in which artificial signal-like vertices are produced in background events by displacing tracks associated with jets by a known displacement vector, and then applying the vertex reconstruction algorithm. The magnitude of the displacement vector is sampled from an exponential distribution with scale parameter 1 mm, restricted to values between 0.3 and 25 mm, similar to the expected distribution of signal vertices. The direction is calculated from the momentum of the jets in the event, but is smeared to emulate the difference between the flight and momentum directions in simulated signal events due to track inefficiency and unaccounted neutral particles. Events are required to satisfy the preselection requirements described in Sec. 4, and the displaced jets satisfy p T > 50 GeV and ∆R < 4 for all pairs. To estimate the vertexing efficiency, we evaluate the fraction of events in which a vertex satisfying the requirements described in Sec. 5.2 is reconstructed within 50 µm of the artificial vertex. This fraction is evaluated for different numbers of displaced light parton or b quark jets, with the ratio of efficiencies between data and simulation approaching unity for larger numbers of jets, independent of the size of the displacement. The largest disagreement between data and simulation occurs for the case where tracks from two light parton jets are displaced, where the fraction is 70% in simulation and 64% in data, with negligible statistical uncertainty. The ratio of efficiencies between data and simulation gives an 8.6% uncertainty per vertex. For two-vertex events, the uncertainty is 17%.
Additional studies explore the sensitivity of other effects that could alter the signal template. The vertex clustering depends on the number of charged particles in the event, which can vary based on the model of the underlying event used in PYTHIA [36]. The signal templates resulting from the choice of the underlying event model differ by no more than 1% in any bin and the overall efficiency changes by no more than 3%. This 3% is taken as a systematic uncertainty.
To test the sensitivity to a possible misalignment, the signal samples have been reconstructed using several tracker misalignment scenarios corresponding to various "weak modes": coherent distortions of the tracker geometry left over by the alignment procedure that lead to a systematic bias in the track parameters for no penalty in χ 2 of the overall alignment fit [37]. These misalignments change the overall efficiency by no more than 2%, which is taken as a systematic uncertainty.
To study sensitivity to the pileup distribution, we vary the inelastic pp cross section used in the pileup weighting by ±5% [38]. This variation is found to have an effect of less than 1% on the signal efficiency.
The uncertainty in the jet energy scale affects the total energy measured, and could change whether an event passes the jet p T or H T selections. This effect is studied by varying the jet energy scale and resolution [18], and is found to change the signal efficiency by less than 1%. A 2.6% uncertainty [39] is associated with the integrated luminosity for the 2012 data set and the derived signal cross section. The uncertainty in the trigger efficiency is less than 1%. Table 1 summarizes the systematic uncertainties in the signal efficiency. We assume there are no correlations among them, so we add them in quadrature to obtain the overall uncertainty.

Systematic uncertainties related to background estimate
The d C VV background template is constructed from a large sample of events with a single vertex. Systematic uncertainties in the d C VV template are estimated by varying the d C VV construction method and taking the difference between the d C VV distributions using the default and alternate methods. The method for constructing d C VV involves drawing two values of d BV and two values of φ BV , with an angle between vertices ∆φ VV , so the main uncertainties come from effects related to the d BV and ∆φ VV distributions.
The production of b quarks in pairs introduces a correlation between the vertex distances in two-vertex events that is not accounted for when single vertices are paired at random. In simulation, events without b quarks have a mean d BV of ∼160 µm, while events with b quarks, which account for 15% of one-vertex events, have a mean d BV of ∼190 µm, without significant dependence on b quark momentum. We quantify this effect by sorting the simulated background events into those with and without b quarks, constructing the d C VV distributions for each, and then combining them in the proportions 45:55, which is the ratio of b-quark to non-b-quark events in two-vertex background events determined from simulation. The systematic uncertainty is taken to be the difference between the simulated yields obtained with this procedure and the standard one, scaled to the observed two-vertex yield.
The d C VV construction method discards pairs of vertices that would overlap, consistently leading to a two-vertex angular distribution that peaks at ±π radians. To assess the systematic uncertainty related to assumptions about the angular distribution between vertices, we draw ∆φ VV from the angular distribution between vertices in simulated two-vertex background events. This leads to a d C VV distribution with a more strongly peaked ∆φ VV distribution, and provides a conservative estimate of the uncertainty.
The statistical uncertainty from the limited number of one-vertex events that are used to construct the two-vertex distribution is studied using a resampling method. Using the d BV distribution as the parent, we randomly sample ten new d BV pseudodata distributions, and use each to construct a d C VV distribution. The root-mean-square variation in bin-by-bin yields in the set of distributions gives the statistical uncertainty.
There is a small contribution to the uncertainty in the prediction of d C VV due to the binning of the d BV parent distribution; moving the d BV tail bin edges around by an amount compatible with the vertex position resolution, 20 µm, varies the prediction in d C VV only in the last two bins: by 0.06 events in the 0.8-1.0 mm bin, and by 0.09 events in the 1.0-50 mm bin.
The results of these four studies are summarized in Table 2. In assessing the overall systematic uncertainty in the background template, we add in quadrature the values and their uncertainties, assuming no correlations.
In principle, there can also be uncertainties in the background template due to the effects described in Sec. 7.1. To assess the impact of the underlying event and possible tracker misalignment, we generate five million all-hadronic tt events for each scenario, but observe no change in d C VV larger than 1%. In addition, we vary the inelastic pp cross section used in pileup weighting by ±5%, the number of pileup interactions, and the jet energy scale and resolution, and observe effects at the percent-level or less in each case. Since the normalization of the template is a free parameter of the fit, uncertainties such as those in the integrated luminosity, trigger efficiency, and vertex reconstruction efficiency do not enter.

Fitting, signal extraction, and statistical interpretation
The distribution of d VV , the separation between vertices in the x-y plane for two-vertex events, is used to discriminate between signal and background, with the signal templates taken directly from the MC simulation and the background template constructed from the observed onevertex event sample. In the following sections, we describe the fitting and statistical procedures used for the search.

Fitting procedure
To estimate the signal and background event yields, a binned shape fit is performed using an extended maximum likelihood method. Initially neglecting terms arising from uncertainty in the templates, the log-likelihood function is given by s, b, ν)] . (1) Here n i is the number of observed events in bin i; s and b are the normalizations of the signal and background templates corresponding to the yields; ν denotes the shape parameters µ clear and σ clear used in the background template construction procedure, as described in Sec. 6; and is the weighted sum of the signal and background frequencies a i in bin i. The only assumed shape uncertainty in the signal templates is that due to the finite MC statistics; the uncertainty is as high as 20% for the lowest lifetime and mass samples, but is generally no more than 1% in any bin for the majority of the templates. For the background templates, a Gaussian uncertainty is assumed in the value of the template in each bin, truncated at zero. To incorporate these uncertainties in the signal and background templates, a procedure similar to that of Barlow and Beeston [40] is followed, modified to allow a bin-by-bin Gaussian uncertainty in the background shape [41]. The final log-likelihood function is then given by replace the a i that maximize log L given (s, b, ν); the difference here is that the A The likelihood function is only weakly dependent on the background shape parameters ν, and when signal is injected, the best fit valuesν agree well with the background-only values. The fit is well behaved: for most signal templates, in pseudo-experiments where the true signal and background strengths are known, the distribution of the fitted yields for s and b have means consistent with those input, and the widths of the distributions as measured by their root-mean-square are consistent with the uncertainties in the fits. For the signal templates with low lifetimes, however, the signal yield is biased downward when an injected signal is present. This is due to the background shape being allowed to vary upward at high d VV within the uncertainties assigned. When no injected signal is present, there is a bias toward obtaining s > 0 when fitting using templates with cτ < 300 µm. Therefore, we only consider signals with cτ ≥ 300 µm in the fit and the search.

Statistical analysis
The test statistic q used to quantify any excess of signal events over the expected background is given by a profile likelihood ratio [42]: where for each value of s and b the nuisance parametersÂ i , andν are found that maximize the relevant likelihood. The probability under the background-only hypothesis, p 0 , to obtain a value of the test statistic at least as large as that observed, q obs , is estimated as the fraction of 10 000 pseudo-experiments with q ≥ q obs . This is referred to as the p-value for a particular signal hypothesis. The pseudo-experiments are generated using the background d C VV distribution corresponding to the background-onlyν, and background count b drawn from a Poisson distribution with mean equal to n, the number of events in the data. The nuisance parameters ν, A We obtain limits on the signal yield, which can be converted into limits on the product of the cross section for neutralino or gluino pair production and the square of the branching fraction for decay via the channel under study, denoted by σB 2 . To obtain limits on σB 2 , for a given number of signal events s 0 , we calculate the probability for the null hypothesis of s = s 0 versus the alternative that s < s 0 denoted by p s 0 . We do this in practice by generating 10 000 pseudo-experiments with s drawn from a Poisson distribution with mean s 0 , and b drawn from a Poisson distribution with mean n − s 0 . The background shape d C VV is taken from the ν from the original fit and signal shape corresponding to the signal hypothesis in question, with A (b) i from their Gaussian distributions. The null hypothesis probability p s 0 is then the fraction of pseudo-experiments where q ≥ q(s 0 ). We protect against downward fluctuations in the data by using the CL s criterion [43,44], defining the statistic as The 95% confidence level (CL) upper limit on s is then the biggest s 0 for which CL s is still greater than 0.05.
The limit on the signal yield is converted to a limit on σB 2 using the efficiencies calculated from simulation and the integrated luminosity of the data sample, 17.6 fb −1 . We include the effect of the estimated 18% signal efficiency uncertainty by varying the cross section in each pseudo-experiment by the value sampled from a log-normal density with location parameter 1 and scale parameter 0.18.

Results of the fit
The result of the fit to data is shown in Fig. 6, for the LSP cτ = 1 mm, M = 400 GeV signal template. The observed counts in each bin, along with the predictions from the backgroundonly fit and the related uncertainties, are listed in Table 3. There is a small excess of events with 0.6 < d VV < 50 mm: 7 in the data, while the background-only fit predicts 4.1 ± 1.4, where the uncertainty is the overall systematic uncertainty discussed in Sec. 7. In the signal+background fits, a typical value for the signal yield is 1.7 ± 1.9, obtained with the cτ = 1 mm, M = 400 GeV signal hypothesis. The associated p-value obtained from pseudo-experiments is in the range   Figure 7 shows the observed 95% CL upper limits on σB 2 . As an example, for a neutralino with mass of 400 GeV and cτ of 10 mm, the observed 95% CL upper limit on σB 2 is 0.6 fb.

Upper limits on signal cross section
Exclusion curves are overlaid, assuming the gluino pair production cross section [45][46][47][48][49]. In the context of the MFV model that we are studying, either a neutralino or a gluino LSP can decay into the final state targeted in the search.
The scan in cτ is in steps of 100 µm from 300 µm to 1 mm, then in 1 mm steps up to 10 mm, and in 2 mm steps to 30 mm; the mass points are spaced by 100 GeV. The exclusion curves are produced by linear interpolation of the limit scan, which identifies the set of points for which the interpolated upper limit is less than the gluino pair production cross section (the neutralino pair production cross section is expected to be much smaller).

Extending the search to other signal models
The search for displaced vertices applies to other types of long-lived particles decaying to multiple jets. Here we present a generator-level selection that can be used to reinterpret the results of our analysis. For signal models in which there are two well-separated displaced vertices, this generator-level selection approximately replicates the reconstruction-level efficiency. The selection is based on the displacements of the long-lived particles, and the momenta and angular distributions of their daughter particles, which are taken to be u, d, s, c, and b quarks; electrons; and muons. The daughter particles are said to be "accepted" if they satisfy p T > 20 GeV and |η| < 2.5, and "displaced" if their transverse impact parameter with respect to the origin is at least 100 µm. The criteria of the generator-level selection are: • at least four accepted quarks with p T > 60 GeV; • H T of accepted quarks > 500 GeV; • for each vertex: • x-y distance from beam axis <25 mm; • at least one pair of accepted displaced daughter particles with ∆R > 1.2; • ∆R < 4 for all pairs of accepted displaced daughter particles; • at least one accepted displaced daughter quark; • ∑ p T of accepted displaced daughter particles > 200 GeV; • x-y distance between vertices > 600 µm.
In the region with d VV > 600 µm, the background level is well determined and is insensitive to fit parameters. Use of this generator-level selection replicates the reconstruction-level efficiency with an accuracy of 20% or better for a selection of models for which the signal efficiency is high (>10%). The selection may underestimate the trigger efficiency because it does not take into account effects such as initial-and final-state radiation, and may overestimate the efficiency for reconstructing vertices with b quark secondaries, since the b quark lifetime can impede the association of their decay products with the reconstructed vertices.

Summary
A search for R-parity violating SUSY in which long-lived neutralinos or gluinos decay into multijet final states was performed using proton-proton collision events collected with the CMS detector at √ s = 8 TeV in 2012. The data sample corresponded to an integrated luminosity of 17.6 fb −1 , and was collected requiring the presence of at least four jets. No excess above the prediction from standard model processes was observed, and at 95% confidence level, the data excluded cross section times branching fraction squared above approximately 1 fb for neutralinos or gluinos with mass between 400 and 1500 GeV and cτ between 1 and 30 mm. Assuming gluino pair production cross sections, gluino masses below 1 and 1.3 TeV were excluded for mean proper decay lengths of 300 µm and 1 mm, respectively, and below 1.4 TeV for the range 2-30 mm. While the search specifically addressed R-parity violating SUSY, the results were relevant to other massive particles that decay to two or more jets. These are the most restrictive bounds to date on the production and decay of pairs of such massive particles with intermediate lifetimes.