CMS logoCMS event Hgg
Compact Muon Solenoid
LHC, CERN

CMS-EXO-22-020 ; CERN-EP-2024-031
Search for long-lived particles using displaced vertices and missing transverse momentum in proton-proton collisions at $ \sqrt{s}= $ 13 TeV
Phys. Rev. D 109 (2024) 112005
Abstract: A search for the production of long-lived particles in proton-proton collisions at a center-of-mass energy of 13 TeV at the CERN LHC is presented. The search is based on data collected by the CMS experiment in 2016-2018, corresponding to a total integrated luminosity of 137 fb$ ^{-1} $. This search is designed to be sensitive to long-lived particles with mean proper decay lengths between 0.1 and 1000 mm, whose decay products produce a final state with at least one displaced vertex and missing transverse momentum. A machine learning algorithm, which improves the background rejection power by more than an order of magnitude, is applied to improve the sensitivity. The observation is consistent with the standard model background prediction, and the results are used to constrain split supersymmetry (SUSY) and gauge-mediated SUSY breaking models with different gluino mean proper decay lengths and masses. This search is the first CMS search that shows sensitivity to hadronically decaying long-lived particles from signals with mass differences between the gluino and neutralino below 100 GeV. It sets the most stringent limits to date for split-SUSY models and gauge-mediated SUSY breaking models with gluino proper decay length less than 6 mm.
Figures & Tables Summary References CMS Publications
Figures

png pdf
Figure 1:
Diagrams of the split-SUSY model (left) and GMSB SUSY model (right). In the split-SUSY model, a pair of long-lived gluinos is produced, and each decays to two quarks and one neutralino. In the GMSB SUSY model, a pair of long-lived gluinos is produced, and each decays to a gluon and a gravitino.

png pdf
Figure 1-a:
Diagrams of the split-SUSY model (left) and GMSB SUSY model (right). In the split-SUSY model, a pair of long-lived gluinos is produced, and each decays to two quarks and one neutralino. In the GMSB SUSY model, a pair of long-lived gluinos is produced, and each decays to a gluon and a gravitino.

png pdf
Figure 1-b:
Diagrams of the split-SUSY model (left) and GMSB SUSY model (right). In the split-SUSY model, a pair of long-lived gluinos is produced, and each decays to two quarks and one neutralino. In the GMSB SUSY model, a pair of long-lived gluinos is produced, and each decays to a gluon and a gravitino.

png pdf
Figure 2:
An illustration of the architecture of the IN, where the flow of data is indicated by arrows. Rectangular boxes represent data matrices, while diamonds represent multilayer perceptrons (MLPs). The original input information ($ O $) is integrated with relation matrices ($ R_{\text{r}} $ and $ R_{\text{s}} $) to form a graph that captures interactions between tracks. This graph is subsequently processed by an MLP ($ \phi_{R} $) to compute the effect ($ E $) of the interactions. The effect is then combined with $ R_{\text{r}} $ and merged with the original input $ O $. To assess the influence ($ P $) of the effect on the original information, it undergoes further processing via another MLP ($ \phi_{O} $). Finally, the influence is passed through an MLP ($ \phi_{\text{output}} $) and a sigmoid function to produce the final output.

png pdf
Figure 3:
Distributions of $ S_{\text{ML}} $ for data, simulated background, and signal. Events with $ n_{\text{track}} $ of 3 (upper), 4 (middle), and $ \geq $5 (lower) are shown individually. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and neutralino mass of 1900 GeV (left) and 1800 GeV (right). Different gluino proper decay lengths and mass difference between the gluino and neutralino, are shown as $ c\tau $ and $ \Delta m $ in the legend. All distributions are normalized to unity.

png pdf
Figure 3-a:
Distributions of $ S_{\text{ML}} $ for data, simulated background, and signal. Events with $ n_{\text{track}} $ of 3 (upper), 4 (middle), and $ \geq $5 (lower) are shown individually. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and neutralino mass of 1900 GeV (left) and 1800 GeV (right). Different gluino proper decay lengths and mass difference between the gluino and neutralino, are shown as $ c\tau $ and $ \Delta m $ in the legend. All distributions are normalized to unity.

png pdf
Figure 3-b:
Distributions of $ S_{\text{ML}} $ for data, simulated background, and signal. Events with $ n_{\text{track}} $ of 3 (upper), 4 (middle), and $ \geq $5 (lower) are shown individually. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and neutralino mass of 1900 GeV (left) and 1800 GeV (right). Different gluino proper decay lengths and mass difference between the gluino and neutralino, are shown as $ c\tau $ and $ \Delta m $ in the legend. All distributions are normalized to unity.

png pdf
Figure 3-c:
Distributions of $ S_{\text{ML}} $ for data, simulated background, and signal. Events with $ n_{\text{track}} $ of 3 (upper), 4 (middle), and $ \geq $5 (lower) are shown individually. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and neutralino mass of 1900 GeV (left) and 1800 GeV (right). Different gluino proper decay lengths and mass difference between the gluino and neutralino, are shown as $ c\tau $ and $ \Delta m $ in the legend. All distributions are normalized to unity.

png pdf
Figure 3-d:
Distributions of $ S_{\text{ML}} $ for data, simulated background, and signal. Events with $ n_{\text{track}} $ of 3 (upper), 4 (middle), and $ \geq $5 (lower) are shown individually. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and neutralino mass of 1900 GeV (left) and 1800 GeV (right). Different gluino proper decay lengths and mass difference between the gluino and neutralino, are shown as $ c\tau $ and $ \Delta m $ in the legend. All distributions are normalized to unity.

png pdf
Figure 3-e:
Distributions of $ S_{\text{ML}} $ for data, simulated background, and signal. Events with $ n_{\text{track}} $ of 3 (upper), 4 (middle), and $ \geq $5 (lower) are shown individually. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and neutralino mass of 1900 GeV (left) and 1800 GeV (right). Different gluino proper decay lengths and mass difference between the gluino and neutralino, are shown as $ c\tau $ and $ \Delta m $ in the legend. All distributions are normalized to unity.

png pdf
Figure 3-f:
Distributions of $ S_{\text{ML}} $ for data, simulated background, and signal. Events with $ n_{\text{track}} $ of 3 (upper), 4 (middle), and $ \geq $5 (lower) are shown individually. The distributions are shown for split-SUSY signals with a gluino mass of 2000 GeV and neutralino mass of 1900 GeV (left) and 1800 GeV (right). Different gluino proper decay lengths and mass difference between the gluino and neutralino, are shown as $ c\tau $ and $ \Delta m $ in the legend. All distributions are normalized to unity.

png pdf
Figure 4:
The distribution of $ n_{\text{track}} $ in different $ S_{\text{ML}} $ regions for simulated background events. Events with 0 $ < S_{\text{ML}} < $ 0.2 (blue), 0.2 $ < S_{\text{ML}} < $ 0.6 (red), and 0.6 $ < S_{\text{ML}} < $ 1.0 (green) are compared. All distributions are normalized to unity. The similar $ n_{\text{track}} $ distributions demonstrate that $ n_{\text{track}} $ and $ S_{\text{ML}} $ are decorrelated.

png pdf
Figure 5:
The distribution of $ d_{\mathrm{BV}} $ in $ \mathrm{K^0_S} $ vertices in data (black) and simulation (purple). The lower panel shows the ratio between data and simulation.

png pdf
Figure 6:
The vertex reconstruction efficiency (left) and ML tagging efficiency (right) for artificially displaced vertices in data (black) and simulation (red). In this example, the artificially displaced vertices are corrected to mimic split-SUSY signal events with gluino mass of 2000 GeV and neutralino mass of 1800 GeV. The uncertainties are too small to be visible in the plot.

png pdf
Figure 6-a:
The vertex reconstruction efficiency (left) and ML tagging efficiency (right) for artificially displaced vertices in data (black) and simulation (red). In this example, the artificially displaced vertices are corrected to mimic split-SUSY signal events with gluino mass of 2000 GeV and neutralino mass of 1800 GeV. The uncertainties are too small to be visible in the plot.

png pdf
Figure 6-b:
The vertex reconstruction efficiency (left) and ML tagging efficiency (right) for artificially displaced vertices in data (black) and simulation (red). In this example, the artificially displaced vertices are corrected to mimic split-SUSY signal events with gluino mass of 2000 GeV and neutralino mass of 1800 GeV. The uncertainties are too small to be visible in the plot.

png pdf
Figure 7:
A schematic diagram of the signal (red), validation (yellow), and control (gray) regions. The letter in each box corresponds to the region label described in the text.

png pdf
Figure 8:
Left: the 95% $ \text{CL}_\text{s} $ upper limit on the product of the cross section and branching fraction squared for the split-SUSY signal model with a mass splitting of 100 GeV, shown as a function of gluino mass and $ c\tau $. Right: the 95% $ \text{CL}_\text{s} $ upper limit on the product of the cross section and branching fraction squared for the split-SUSY model with a $ c\tau $ of 10 mm, shown as a function of gluino mass and mass splitting. For both plots, the observed (solid black) and expected (dashed red) exclusion curves are shown.

png pdf
Figure 8-a:
Left: the 95% $ \text{CL}_\text{s} $ upper limit on the product of the cross section and branching fraction squared for the split-SUSY signal model with a mass splitting of 100 GeV, shown as a function of gluino mass and $ c\tau $. Right: the 95% $ \text{CL}_\text{s} $ upper limit on the product of the cross section and branching fraction squared for the split-SUSY model with a $ c\tau $ of 10 mm, shown as a function of gluino mass and mass splitting. For both plots, the observed (solid black) and expected (dashed red) exclusion curves are shown.

png pdf
Figure 8-b:
Left: the 95% $ \text{CL}_\text{s} $ upper limit on the product of the cross section and branching fraction squared for the split-SUSY signal model with a mass splitting of 100 GeV, shown as a function of gluino mass and $ c\tau $. Right: the 95% $ \text{CL}_\text{s} $ upper limit on the product of the cross section and branching fraction squared for the split-SUSY model with a $ c\tau $ of 10 mm, shown as a function of gluino mass and mass splitting. For both plots, the observed (solid black) and expected (dashed red) exclusion curves are shown.

png pdf
Figure 9:
The 95% $ \text{CL}_\text{s} $ upper limit on the product of the cross section and branching fraction squared for the GMSB SUSY signal model, shown as a function of gluino mass and $ c\tau $. The observed (solid black) and expected (dashed red) exclusion curves are shown.
Tables

png pdf
Table 1:
Summary of systematic uncertainties that affect the signal yield. The magnitude of each systematic varies by data-taking period and signal parameters, so a range of values is given in each case.

png pdf
Table 2:
Number of predicted and observed events in the control, validation, and search regions. Predictions are calculated using Eqs. (2) and (3) and fitting the data under the background-only hypothesis. Regions are organized by $ S_{\text{ML}} $ and $ n_{\text{track}} $ values, and region names corresponding to Fig. 7 are given in parentheses. The predicted number of events that pass the $ S_{\text{ML}} $ selection and the observed number of events that pass or fail the $ S_{\text{ML}} $ selection are shown in separate rows.
Summary
A search for the production of long-lived particles that decay to at least one displaced vertex with missing transverse momentum in proton-proton collisions at a center-of-mass energy of 13 TeV collected by the CMS detector has been presented. The analysis extends the previous CMS search [24] by improving the sensitivity to events with low total jet energy, targeting events with as few as one displaced vertex, and introducing a dedicated machine learning algorithm that reduces the number of background events in the signal region by 94%. Split supersymmetry (SUSY) and gauge-mediated SUSY breaking are used as benchmark signal models for statistical interpretations in this search. At 95% confidence level, the search excludes long-lived gluinos predicted by the split-SUSY model with masses below 1800 GeV and mean proper decay lengths in the range of 1 to 100 mm, when the mass splitting is 100 GeV. For mass splittings above 50 GeV, gluinos with masses below 1600 GeV and mean proper decay lengths between 1 and 30 mm are excluded. For the gauge-mediated SUSY breaking model, gluinos with masses below 2200 GeV and mean proper decay lengths between 0.3 and 100 mm are excluded. This search is the first CMS search that shows sensitivity to hadronically decaying long-lived particles from signals with mass differences between the gluino and neutralino below 100 GeV. It sets the most stringent limits to date for split-SUSY models and for GMSB gluinos with proper decay length less than 6 mm.
References
1 G. F. Giudice and A. Romanino Split supersymmetry NPB 699 (2004) 65 hep-ph/0406088
2 J. L. Hewett, B. Lillie, M. Masip, and T. G. Rizzo Signatures of long-lived gluinos in split supersymmetry JHEP 09 (2004) 070 hep-ph/0408248
3 N. Arkani-Hamed, S. Dimopoulos, G. F. Giudice, and A. Romanino Aspects of split supersymmetry NPB 709 (2005) 3 hep-ph/0409232
4 P. Gambino, G. F. Giudice, and P. Slavich Gluino decays in split supersymmetry NPB 726 (2005) 35 hep-ph/0506214
5 A. Arvanitaki, N. Craig, S. Dimopoulos, and G. Villadoro Mini-split JHEP 02 (2013) 126 1210.0555
6 N. Arkani-Hamed et al. Simply unnatural supersymmetry 1212.6971
7 P. Fayet Supergauge invariant extension of the Higgs mechanism and a model for the electron and its neutrino NPB 90 (1975) 104
8 G. R. Farrar and P. Fayet Phenomenology of the production, decay, and detection of new hadronic states associated with supersymmetry PLB 76 (1978) 575
9 S. Weinberg Supersymmetry at ordinary energies. Masses and conservation laws PRD 26 (1982) 287
10 R. Barbier et al. $ R $-parity violating supersymmetry Phys. Rept. 420 (2005) 1 hep-ph/0406039
11 G. F. Giudice and R. Rattazzi Theories with gauge mediated supersymmetry breaking Phys. Rept. 322 (1999) 419 hep-ph/9801271
12 P. Meade, N. Seiberg, and D. Shih General gauge mediation Prog. Theor. Phys. Suppl. 177 (2009) 143 0801.3278
13 M. Buican, P. Meade, N. Seiberg, and D. Shih Exploring general gauge mediation JHEP 03 (2009) 016 0812.3668
14 J. Fan, M. Reece, and J. T. Ruderman Stealth supersymmetry JHEP 11 (2011) 012 1105.5135
15 J. Fan, M. Reece, and J. T. Ruderman A stealth supersymmetry sampler JHEP 07 (2012) 196 1201.4875
16 M. J. Strassler and K. M. Zurek Echoes of a hidden valley at hadron colliders PLB 651 (2007) 374 hep-ph/0604261
17 M. J. Strassler and K. M. Zurek Discovering the Higgs through highly-displaced vertices PLB 661 (2008) 263 hep-ph/0605193
18 T. Han, Z. Si, K. M. Zurek, and M. J. Strassler Phenomenology of hidden valleys at hadron colliders JHEP 07 (2008) 008 0712.2041
19 Z. Chacko, H.-S. Goh, and R. Harnik Natural electroweak breaking from a mirror symmetry PRL 96 (2006) 231802 hep-ph/0506256
20 D. Curtin and C. B. Verhaaren Discovering uncolored naturalness in exotic Higgs decays JHEP 12 (2015) 072 1506.06141
21 H.-C. Cheng, S. Jung, E. Salvioni, and Y. Tsai Exotic quarks in twin Higgs models JHEP 03 (2016) 074 1512.02647
22 ATLAS Collaboration Search for long-lived, massive particles in events with displaced vertices and missing transverse momentum in $ \sqrt{s} $ = 13 TeV $ pp $ collisions with the ATLAS detector PRD 97 (2018) 052012 1710.04901
23 ATLAS Collaboration Search for long-lived, massive particles in events with a displaced vertex and a muon with large impact parameter in $ pp $ collisions at $ \sqrt{s} = $ 13 TeV with the ATLAS detector PRD 102 (2020) 032006 2003.11956
24 CMS Collaboration Search for long-lived particles decaying to jets with displaced vertices in proton-proton collisions at $ \sqrt{s}= $ 13 TeV PRD 104 (2021) 052011 CMS-EXO-19-013
2104.13474
25 CMS Collaboration Search for long-lived particles using displaced jets in proton-proton collisions at $ \sqrt{s} = $ 13 TeV PRD 104 (2021) 012015 CMS-EXO-19-021
2012.01581
26 ATLAS Collaboration Search for long-lived, massive particles in events with displaced vertices and multiple jets in pp collisions at $ \sqrt{s} $ = 13 TeV with the ATLAS detector JHEP 06 (2023) 200 2301.13866
27 E. A. Moreno et al. JEDI-net: a jet identification algorithm based on interaction networks EPJC 80 (2020) 58 1908.05318
28 E. A. Moreno et al. Interaction networks for the identification of boosted $ {H} \rightarrow b\overline{b} $ decays PRD 102 (2020) 012010 1909.12285
29 CMS Collaboration Search for natural and split supersymmetry in proton-proton collisions at $ \sqrt{s}= $ 13 TeV in final states with jets and missing transverse momentum JHEP 05 (2018) 025 CMS-SUS-16-038
1802.02110
30 CMS Collaboration HEPData record for this analysis link
31 CMS Collaboration The CMS experiment at the CERN LHC JINST 3 (2008) S08004
32 CMS Collaboration Description and performance of track and primary-vertex reconstruction with the CMS tracker JINST 9 (2014) P10009 CMS-TRK-11-001
1405.6569
33 Tracker Group of the CMS Collaboration The CMS Phase-1 pixel detector upgrade JINST 16 (2021) P02027 2012.14304
34 CMS Collaboration Track impact parameter resolution for the full pseudo rapidity coverage in the 2017 dataset with the CMS Phase-1 pixel detector CMS Detector Performance Summary CMS-DP-2020-049, 2020
CDS
35 CMS Collaboration Particle-flow reconstruction and global event description with the CMS detector JINST 12 (2017) P10003 CMS-PRF-14-001
1706.04965
36 CMS Collaboration Technical proposal for the Phase-II upgrade of the Compact Muon Solenoid CMS Technical Proposal CERN-LHCC-2015-010, CMS-TDR-15-02, 2015
link
37 M. Cacciari, G. P. Salam, and G. Soyez The anti-$ k_{\mathrm{T}} $ jet clustering algorithm JHEP 04 (2008) 063 0802.1189
38 M. Cacciari, G. P. Salam, and G. Soyez FastJet user manual EPJC 72 (2012) 1896 1111.6097
39 CMS Collaboration Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV JINST 12 (2017) P02014 CMS-JME-13-004
1607.03663
40 CMS Collaboration CMS jet algorithms performance in 13 TeV data CMS Physics Analysis Summary, 2016
CMS-PAS-JME-16-003
CMS-PAS-JME-16-003
41 CMS Collaboration Performance of missing transverse momentum reconstruction in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using the CMS detector JINST 14 (2019) P07004 CMS-JME-17-001
1903.06078
42 CMS Collaboration Performance of the CMS Level-1 trigger in proton-proton collisions at $ \sqrt{s} = $ 13 TeV JINST 15 (2020) P10017 CMS-TRG-17-001
2006.10165
43 CMS Collaboration The CMS trigger system JINST 12 (2017) P01020 CMS-TRG-12-001
1609.02366
44 T. Sjöstrand et al. An introduction to PYTHIA 8.2 Comput. Phys. Commun. 191 (2015) 159 1410.3012
45 CMS Collaboration Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements EPJC 80 (2020) 4 CMS-GEN-17-001
1903.12179
46 NNPDF Collaboration Parton distributions from high-precision collider data EPJC 77 (2017) 663 1706.00428
47 W. Beenakker et al. NNLL-fast: predictions for coloured supersymmetric particle production at the LHC with threshold and Coulomb resummation JHEP 12 (2016) 133 1607.07741
48 J. Alwall et al. The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations JHEP 07 (2014) 079 1405.0301
49 J. Alwall et al. Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions EPJC 53 (2008) 473 0706.2569
50 R. Frederix and S. Frixione Merging meets matching in MC@NLO JHEP 12 (2012) 061 1209.6215
51 P. Nason A new method for combining NLO QCD with shower Monte Carlo algorithms JHEP 11 (2004) 040 hep-ph/0409146
52 S. Frixione, P. Nason, and C. Oleari Matching NLO QCD computations with parton shower simulations: the POWHEG method JHEP 11 (2007) 070 0709.2092
53 S. Alioli, P. Nason, C. Oleari, and E. Re A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX JHEP 06 (2010) 043 1002.2581
54 E. Re Single-top $ {\mathrm{W}}{\mathrm{t}} $-channel production matched with parton showers using the POWHEG method EPJC 71 (2011) 1547 1009.2450
55 S. Alioli, P. Nason, C. Oleari, and E. Re NLO single-top production matched with shower in POWHEG: $ s $- and $ t $-channel contributions JHEP 09 (2009) 111 0907.4076
56 NNPDF Collaboration Parton distributions for the LHC Run II JHEP 04 (2015) 040 1410.8849
57 GEANT4 Collaboration GEANT 4---a simulation toolkit NIM A 506 (2003) 250
58 R. Fr \"u hwirth Application of Kalman filtering to track and vertex fitting NIM A 262 (1987) 444
59 P. Billoir and S. Qian Simultaneous pattern recognition and track fitting by the Kalman filtering method NIM A 294 (1990) 219
60 P. Billoir and S. Qian Further test for the simultaneous pattern recognition and track fitting by the Kalman filtering method NIM A 295 (1990) 492
61 J. Zhou et al. Graph neural networks: A review of methods and applications AI Open 1 (2020) 57 1812.08434
62 F. Murtagh Multilayer perceptrons for classification and regression Neurocomputing 2 (1991) 183
63 T. Gneiting and A. E. Raftery Strictly proper scoring rules, prediction, and estimation Journal of the American Statistical Association 102 (2007) 359
64 A. Y. Ng Feature selection, L1 vs. L2 regularization, and rotational invariance in Proceedings of the Twenty-First International Conference on Machine Learning, 2004
link
65 G. Kasieczka and D. Shih Robust jet classifiers through distance correlation PRL 125 (2020) 122001 2001.05310
66 G. Kasieczka, B. Nachman, M. D. Schwartz, and D. Shih Automating the ABCD method with machine learning PRD 103 (2021) 035021 2007.14400
67 D. P. Kingma and J. Ba Adam: A method for stochastic optimization 1412.6980
68 E. Bols et al. Jet flavour classification using DeepJet JINST 15 (2020) P12012 2008.10519
69 J. Butterworth et al. PDF4LHC recommendations for LHC Run II JPG 43 (2016) 023001 1510.03865
70 CMS Collaboration Precision luminosity measurement in proton-proton collisions at $ \sqrt{s} = $ 13 TeV in 2015 and 2016 at CMS EPJC 81 (2021) 800 CMS-LUM-17-003
2104.01927
71 CMS Collaboration CMS luminosity measurement for the 2017 data-taking period at $ \sqrt{s} $ = 13 TeV CMS Physics Analysis Summary, 2018
link
CMS-PAS-LUM-17-004
72 CMS Collaboration CMS luminosity measurement for the 2018 data-taking period at $ \sqrt{s} $ = 13 TeV CMS Physics Analysis Summary, 2019
link
CMS-PAS-LUM-18-002
73 A. L. Read Presentation of search results: The CL$ _{\text{s}} $ technique JPG 28 (2002) 2693
74 T. Junk Confidence level computation for combining searches with small statistics NIM A 434 (1999) 435 hep-ex/9902006
75 ATLAS and CMS Collaborations, and LHC Higgs Combination Group Procedure for the LHC Higgs boson search combination in Summer 2011 Technical Report CMS-NOTE-2011-005, ATL-PHYS-PUB-2011-11, 2011
76 C. Borschensky et al. Squark and gluino production cross sections in pp collisions at $ \sqrt{s} $ = 13, 14, 33 and 100 TeV EPJC 74 (2014) 3174 1407.5066
Compact Muon Solenoid
LHC, CERN