Search for long-lived particles decaying into displaced jets in proton-proton collisions at $\sqrt{s} =$ 13 TeV

TL;DR

This paper reports a search for long-lived particles decaying into displaced jets using CMS data at 13 TeV, setting new limits on particle masses and decay lengths, and constraining various supersymmetry models.

Contribution

First search to set limits on long-lived particles decaying into displaced jets at 13 TeV with CMS, improving constraints on supersymmetry models.

Findings

Excluded cross sections above 0.2 fb for particles over 1000 GeV

Gluino masses up to 2400 GeV excluded for decay lengths 10-100 mm

Most restrictive limits to date on these long-lived particle models

Abstract

A search for long-lived particles decaying into jets is presented. Data were collected with the CMS detector at the LHC from proton-proton collisions at a center-of-mass energy of 13 TeV in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The search examines the distinctive topology of displaced tracks and secondary vertices. The selected events are found to be consistent with standard model predictions. For a simplified model in which long-lived neutral particles are pair produced and decay to two jets, pair production cross sections larger than 0.2 fb are excluded at 95% confidence level for a long-lived particle mass larger than 1000 GeV and proper decay lengths between 3 and 130 mm. Several supersymmetry models with gauge-mediated supersymmetry breaking or $R$-parity violation, where pair-produced long-lived gluinos or top squarks decay to several final-state topologies containing displaced jets, are also tested. For these models, in the mass ranges above 200 GeV, gluino masses up to 2300-2400 GeV and top squark masses up to 1350-1600 GeV are excluded for proper decay lengths approximately between 10 and 100 mm. These are the most restrictive limits to date on these models.

Tables

Table 1. Figure 1: The distributions of vertex track multiplicity (upper left), vertex L xy subscript 𝐿 xy L_{\mathrm{xy}} significance (upper right), cluster RMS (lower left), and likelihood discriminant (lower right), for data, simulated QCD multijet events, and simulated signal events. The lower panel of each plot shows the ratio between the data and the simulated QCD multijet events. Data and simulated events are selected with the displaced-jet trigger. The offline \HT \HT \HT is required to be larger than 400 \GeV , and the jets are required to have \pt > 50 ​ \GeV \pt 50 \GeV \pt>50\GeV and \abs ​ η < 2.0 \abs 𝜂 2.0 \abs{\eta}<2.0 . The error bars and bands represent the statistical uncertainties of each distribution. Three benchmark signal distributions are shown (dashed lines) for the jet-jet model with m X = 300 ​ \GeV subscript 𝑚 𝑋 300 \GeV m_{X}=300\GeV and varying lifetimes. For visualization each signal process is given a cross section, σ 𝜎 \sigma , such that σ ​ 35.9 ​ \fbinv = 1 × 10 6 𝜎 35.9 \fbinv 1 superscript 10 6 \sigma\ 35.9\fbinv=1\times 10^{6} .

${\mathrm{RMS}}_{\mathrm{cluster}}=\sqrt{\frac{1}{N_{\mathrm{tracks}}}\sum _{i=1}^{N_{\mathrm{tracks}}}\frac{{\left(L_{xy}^{\exp }\left(i\right)-L_{xy}\right)}^2}{L_{xy}^2}}.$

(2)

Table 2. Figure 2: Numbers of predicted and observed background events for the nominal background method and the three cross-checks in the control region. Shown are the comparisons for likelihood discriminant thresholds of 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 (left); and for thresholds of 0.95, 0.96, 0.97, 0.98, 0.99, and 0.9993 (right). The error bars represent the statistical uncertainties of the predictions and the observations. The data points at different likelihood discriminant thresholds are correlated, since the events passing higher likelihood discriminant thresholds also pass lower likelihood discriminant thresholds.

$Z=\sqrt{2}{\text{erf}}^{-1}\left[2p-1\right],$

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Equations

$$\zeta =\frac{{\sum }_{\mathrm{track}\in \mathrm{P}{\mathrm{V}}_1}{E}_{\mathrm{track}}^{\mathrm{Je}{\mathrm{t}}_1}+{\sum }_{\mathrm{track}\in \mathrm{P}{\mathrm{V}}_2}{E}_{\mathrm{track}}^{\mathrm{Je}{\mathrm{t}}_2}}{E_{\mathrm{Je}{\mathrm{t}}_1}+E_{\mathrm{Je}{\mathrm{t}}_2}},$$

$$\mathcal{L}=\frac{p_{\mathrm{S}}}{p_{\mathrm{S}}+p_{\mathrm{B}}}=\frac{1}{1+p_{\mathrm{B}}/p_{\mathrm{S}}}=\frac{1}{1+{\prod }_i{p}_{\mathrm{Bi}}/p_{\mathrm{Si}}},$$

Full text

0.1 Introduction

A large number of extensions to the standard model (SM) predict the production of long-lived particles at the CERN LHC that can further decay into final states containing jets. The theoretical motivations are extremely rich [1]; examples include split supersymmetry (SUSY) [2, 3, 4, 5, 6, 7], SUSY with weak $R$-parity violation (RPV) [8, 9, 10, 11], SUSY with gauge-mediated supersymmetry breaking (GMSB) [12, 13, 14], “stealth SUSY” [15, 16], “Hidden Valley” models [17, 18, 19], baryogenesis triggered by weakly interacting massive particles (WIMPs) [20, 21, 22] and twin Higgs models [23, 24, 25].

In this paper, we search for long-lived particles decaying into jets, with each long-lived particle having a decay vertex displaced from the production vertex by up to $55\cm$ in the transverse plane. Events used in this analysis were collected with the CMS detector [26] at the LHC from proton-proton ($\Pp\Pp$) collisions at a center-of-mass energy of $13\TeV$ in 2016, corresponding to an integrated luminosity of 35.9\fbinv. The analysis examines dijets formed by jets clustered from energy deposits in the calorimeters. For the displaced-jet signal, the tracks left by charged particles originating from the decay of a long-lived particle will usually exhibit large displacements with respect to the primary vertex, allowing the reconstruction of a secondary vertex within the associated dijet. The properties of the secondary vertex can be utilized to discriminate between the long-lived signatures and the SM backgrounds. Although the objects studied here are dijets, two separate displaced single jets can pass the selection criteria, even when each displaced vertex contains only one jet. A variety of models predict long-lived particles decaying into displaced jets and we test several of them, including SUSY models with GMSB or RPV, as will be discussed in detail in Section 0.3.

Results of searches for similar long-lived particle signatures at $\sqrt{s}=8$\TeVhave been reported by ATLAS [27, 28], CMS [29, 30, 31], and LHCb [32, 33]. The ATLAS Collaboration has reported on a search at $\sqrt{s}=13$\TeV, which includes a missing transverse momentum requirement [34]. The CMS Collaboration has reported several long-lived particle searches at $\sqrt{s}=13\TeV$; one doesn’t utilize secondary vertex information [35], and another searches for a pair of displaced vertices within the beam pipe [36]. The search presented in this paper is designed to be sensitive to multiple final-state topologies containing displaced jets, and is therefore sensitive to a wide range of long-lived particle signatures.

0.2 The CMS detector

The central feature of the CMS apparatus is a superconducting solenoid of 6\unitm internal diameter, providing a magnetic field of 3.8\unitT. Within the solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap detectors. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid.

The silicon tracker measures charged particles in the pseudorapidity range $\abs{\eta}<2.5$. It consists of 1440 silicon pixel and 15 148 silicon strip detector modules. For nonisolated particles of $1<\pt<10\GeV$ and $\abs{\eta}<1.4$, the track resolutions are typically 1.5$\%$ in $\pt$, and 25–90 (45–150)$\mum$ in the transverse (longitudinal) impact parameter [37].

In the region $\abs{\eta}<1.74$, the HCAL cells have widths of $0.087$ in pseudorapidity and $0.087$ in azimuth. In the $\eta$-$\phi$ plane, and for $\abs{\eta}<1.48$, the HCAL cells map on to $5{\times}5$ arrays of ECAL crystals to form calorimeter towers projecting radially outward from the nominal interaction point. For $\abs{\eta}>1.74$, the coverage of the towers increases progressively to a maximum of $0.174$ in $\Delta\eta$ and $\Delta\phi$. Within each tower, the energy deposits in ECAL and HCAL cells are summed to define the calorimeter tower energies, and are subsequently used to provide the energies and directions of hadronic jets.

Events of interest are selected using a two-tiered trigger system [38]. The first level (L1), composed of custom hardware processors, uses information from the calorimeters and muon detectors to select events at a rate of around $100\unit{kHz}$ within a time interval of less than 4$\mus$. The second level, known as the high-level trigger (HLT), consists of a farm of processors running a version of the full event reconstruction software optimized for fast processing, and reduces the event rate to around $1\unit{kHz}$ before data storage.

A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [26].

0.3 Data sets and simulated samples

Data were collected with a dedicated HLT displaced-jet trigger. At the trigger level, jets are reconstructed from the energy deposits in the calorimeter towers, clustered using the anti-$\kt$ algorithm [39, 40] with a distance parameter of 0.4. In this process, the contribution from each calorimeter tower is assigned a momentum, the absolute value and the direction of which are given by the energy measured in the tower and the coordinates of the tower. The raw jet energy is obtained from the sum of the tower energies, and the raw jet momentum from the vector sum of the tower momenta, which results in a nonzero jet mass. The raw jet energies are then corrected [41] to establish a relative uniform response of the calorimeter in $\eta$ and a calibrated absolute response in transverse momentum $\pt$.

Events may contain multiple primary vertices, corresponding to multiple $\Pp\Pp$ collisions occurring in the same bunch crossing. The reconstructed vertex with the largest value of summed physics-object $\pt^{2}$ is taken to be the primary $\Pp\Pp$ interaction vertex, referred to as the leading primary vertex. The physics objects are the “jets,” clustered using the jet finding algorithm [39, 40] with the tracks assigned to the vertex as inputs, and the associated missing transverse momentum, taken as the negative vector sum of the $\pt$ of those jets. More details are given in Section 9.4.1 of Ref. [42].

The displaced-jet trigger requires an $\HT$ larger than 350$\GeV$, where $\HT$ is defined as the scalar sum of the transverse momenta of all jets satisfying $\pt>40\GeV$ and $\abs{\eta}<2.5$ in the event. The trigger also requires the presence of at least two jets, each of them satisfying the following requirements:

• •

$\pt>40\GeV$ and $\abs{\eta}<2.0$;

• •

at most two associated prompt tracks, which are tracks having a transverse impact parameter (with respect to the leading primary vertex) smaller than 1.0$\unit{mm}$; and

• •

at least one associated displaced track, defined as a track with a transverse impact parameter (with respect to the leading primary vertex) larger than 0.5\mm, and an impact parameter significance larger than 5.0, where the significance is the ratio of the impact parameter to its uncertainty.

The main background of this analysis arises from the SM events comprised uniquely of jets produced through the strong interaction, referred to as quantum chromodynamics (QCD) multijet events. The QCD multijet sample is simulated with $\MGvATNLO$ 2.2.2 [43] at leading order, which is interfaced with $\PYTHIA$ 8.212 [44] for parton showering, hadronization, and fragmentation. Jets from the matrix element calculations are matched to parton shower jets using the MLM algorithm [45]. The CUETP8M1 tune [46] is used for modeling the underlying event. For parton distribution function (PDF) modeling, the NNPDF3.0 PDF set [47] is used.

One of the benchmark signal models is a simplified model, referred to as the jet-jet model, where long-lived scalar neutral particles X are pair-produced through a $2\to 2$ scattering process, mediated by an off-shell $\PZ$ boson propagator. Each X particle decays to a quark-antiquark pair, and is assumed to do so with equal branching fractions to $\cPqu$, $\cPqd$, $\cPqs$, $\cPqc$, and $\cPqb$ quark pairs. Although X could decay to top quark pairs, we chose a signature with a simple topology, such that the analysis strategy would be sensitive to a variety of models. Simulation shows that exclusion of the top quark pair decay mode leads to only small changes in the signal efficiency. The chosen signature has two displaced vertices, each of them the origin of one displaced jet pair. The samples are produced with different resonance masses ranging from 50 to 3000$\GeV$, and with different proper decay lengths ranging from $1\mm$ to 10\unitm.

Several SUSY models with long-lived particles are considered, where we mainly focus on testing SUSY particles with masses larger than $200\GeV$. The first is a GMSB SUSY model [1], in which the gluino is long lived and then decays to a gluon and a gravitino, referred to as the $\sGlu\to\Pg\sGra$ model. The gravitino is assumed to be the lightest supersymmetric particle (LSP) and manifests itself as missing transverse momentum. The signature is two displaced vertices, each of them the origin of a single displaced jet and missing transverse momentum. The samples are produced with gluino masses from 800 to 2500$\GeV$, and a proper decay length varying from 1$\mm$ to 10\unitm.

The second is an RPV SUSY model [48] with minimum flavor violation, where the gluino is long lived and decays to a top quark and a top squark, the top squark is assumed to be virtual and decays to a strange antiquark and a bottom antiquark through the RPV interaction with strength given by the coupling $\lambda^{\prime\prime}_{323}$ [11], effectively resulting in a three-body decay with a “multijet” final-state topology. This model is referred to as the $\sGlu\to\cPqt\cPqb\cPqs$ model. The samples are produced with gluino masses from 1200 to 3000$\GeV$, and a proper decay length varying from 1$\mm$ to 10\unitm.

Other signal models considered include an RPV SUSY model [49], in which the long-lived top squark decays to a bottom quark and a charged lepton via RPV interactions with strengths given by couplings $\Lamp_{331}$, $\lambda^{\prime}_{332}$, and $\lambda^{\prime}_{333}$ [11], assuming the decay rate to each of the three lepton flavors to be equal, referred to as the $\sTop\to\cPqb\ell$ model. The samples are produced with different top squark masses from 200 to 1600$\GeV$, and a proper decay length varying from 1$\mm$ to 1\unitm.

We also consider another SUSY model motivated by dynamical $R$-parity violation (dRPV) [50, 51], where the long-lived top squark decays to two down antiquarks via RPV interaction with strength given by a nonholomorphic RPV coupling $\eta^{\prime\prime}_{311}$ [52], referred to as the $\sTop\to\cPaqd\cPaqd$ model. The samples are produced with different top squark masses from 800 to 1800$\GeV$, and proper decay length varying from 1$\mm$ to 10\unitm.

All signal samples are produced with $\PYTHIA$ 8.212, and NNPDF2.3QED [53] is used for PDF modeling. When a gluino or top squark is long lived, it will have enough time to form a hadronic state, an $R$-hadron [9, 54, 55], which is simulated with $\PYTHIA$. For underlying event modeling the CUETP8M1 tune is utilized.

Both the background and the signal events are processed with a $\GEANTfour$-based [56] simulation for detailed CMS detector response. To take account of the effects of additional $\Pp\Pp$ interactions within the same or nearby bunch crossings (“pileup”), additional minimum bias events are overlaid on the simulated events to match the pileup distribution observed in the data.

0.4 Event reconstruction and preselection

The offline jet reconstruction and primary vertex selection follow the same procedures applied at the trigger level (as described in Section 0.3), except that the full offline information is used. After the trigger selection, events are selected offline requiring $\HT>400\GeV$; dijet candidates are formed from all possible pairs of jets in the event, where the jets are required to have transverse momenta $\pt>50\GeV$ and pseudorapidity $\abs{\eta}<2.0$. These selection criteria are chosen so that the online $\HT$ and jet $\pt$ requirements in the trigger are fully efficient. The track candidates used in this analysis are required to have “high purity” and to have transverse momenta $\pt>1\GeV$. The “high-purity” selection utilizes track information (including the normalized $\chi^{2}$ of the track fit, the impact parameters, and the hits in different layers) to reduce the fake rate and is optimized separately for each iteration of the track reconstruction, so that it is efficient for selecting tracks with different displacements. More details of the “high-purity” selection can be found in Section 4.4 of Ref. [37]. The $\eta$ and $\phi$ of the track are determined by the direction of the momentum vector at the closest point to the leading primary vertex. The tracks are then associated with the jets by requiring $\Delta R<0.5$, where $\Delta R=\sqrt{\smash[b]{(\Delta\eta)^{2}+(\Delta\phi)^{2}}}$ and $\Delta\eta$ ($\Delta\phi$) is the difference in $\eta$ ($\phi$) between the jet axis and the track direction. If a track satisfies $\Delta R<0.5$ for more than one jet, it is associated with the jet with smaller $\Delta R$.

To reconstruct secondary vertices, displaced tracks associated with each dijet candidate are selected by requiring transverse impact parameters (with respect to the leading primary vertex) larger than $0.5\mm$ and transverse impact parameter significances larger than 5. An adaptive vertex fitter algorithm [57] is then used for reconstructing a possible secondary vertex (containing at least 2 tracks) with the displaced tracks in each dijet. The adaptive vertex fitter utilizes an annealing algorithm in which the outlier tracks are down-weighted for each step, and thus exhibits robustness against outlier tracks. Only secondary vertices with a $\chi^{2}$ per degree-of-freedom ($\chi^{2}/\mathrm{n_{dof}}$) of less than 5.0 are selected. Also, the four-momentum of the vertex is reconstructed assuming the pion mass for all assigned tracks; the invariant mass of the vertex is required to be larger than $4\GeV$, and the transverse momentum of the vertex is required to be larger than $8\GeV$, in order to suppress long-lived SM mesons and baryons.

Each dijet candidate is required to have one reconstructed secondary vertex satisfying the above selection criteria. Furthermore, we select the track with the second-highest transverse (two-dimensional) impact parameter (IP) significance among the tracks that are assigned to the secondary vertex (the highest two-dimensional IP significance is usually more sensitive to the tail of impact parameter distribution in the background process, and is therefore less powerful). For displaced-jet signatures, where tracks tend to be more displaced, the two-dimensional IP significance of this selected track will be large. If it is smaller than 15, the dijet candidate is rejected. We also compute the ratio between the sum of energy for all the tracks assigned to the secondary vertex and the sum of the energy for all the tracks associated with the two jets. This ratio is expected to be large for displaced-jet signatures, therefore dijet candidates with a ratio smaller than 0.15 are rejected.

An additional variable, $\zeta$, is defined to characterize the contribution of prompt activity to the jets. For each track associated with a jet, the primary vertex (including the leading primary vertex and the pileup vertices) with the minimum three-dimensional impact parameter significance to the track is identified. If this minimum three-dimensional impact parameter significance is smaller than 5, we assign the track to this primary vertex. Then for each jet, we compute the track energy contribution from each primary vertex, and the primary vertex with the largest track energy contribution to the jet is chosen. Finally, we define $\zeta$ as

[TABLE]

which is the charged energy fraction of the dijet associated with the most compatible primary vertices. For displaced-jet signatures, $\zeta$ tends to be small since the jets are not compatible with primary vertices. Dijet candidates with $\zeta$ larger than 0.2 are rejected.

We do not require the secondary vertex to contain tracks from both jets in the dijet candidate. Two displaced single jets originating from two separate displaced vertices can be paired together and pass the selection, thus the search can be sensitive to long-lived particles decaying to a single jet (as in the $\sGlu\to\Glu\sGra$ model).

The preselection criteria of the analysis are summarized in Table 0.4. The variables used in the preselection are checked in data and QCD multijet MC events, and are found to be well-modeled in the MC events.