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| CMS-EXO-19-011 ; CERN-EP-2019-281 | ||
| A deep neural network to search for new long-lived particles decaying to jets | ||
| CMS Collaboration | ||
| 27 December 2019 | ||
| Mach. Learn.: Sci. Technol. 1 (2020) 035012 | ||
| Abstract: A tagging algorithm to identify jets that are significantly displaced from the proton-proton (pp) collision region in the CMS detector at the LHC is presented. Displaced jets can arise from the decays of long-lived particles (LLPs), which are predicted by several theoretical extensions of the standard model. The tagger is a multiclass classifier based on a deep neural network, which is parameterised according to the proper decay length $c\tau_0$ of the LLP. A novel scheme is defined to reliably label jets from LLP decays for supervised learning. Samples of pp collision data, recorded by the CMS detector at a centre-of-mass energy of 13 TeV, and simulated events are used to train the neural network. Domain adaptation by backward propagation is performed to improve the simulation modelling of the jet class probability distributions observed in pp collision data. The potential performance of the tagger is demonstrated with a search for long-lived gluinos, a manifestation of split supersymmetric models. The tagger provides a rejection factor of 10 000 for jets from standard model processes, while maintaining an LLP jet tagging efficiency of 30-80% for gluinos with 1 mm $\leq c\tau_0 \leq$ 10 m. The expected coverage of the parameter space for split supersymmetry is presented. | ||
| Links: e-print arXiv:1912.12238 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Two example ${\mathrm{\widetilde{g}}} \to \mathrm{q} \mathrm{\bar{q}} \tilde{\chi}^0_1 $ decay chains, constructed from information provided by the MadGraph 5_aMC@NLO [55] and PYTHIA [56] programs. The positions of various particles in the $\eta $-$\phi $ plane are shown: the LLP (${{\mathrm{\widetilde{g}}}}$) and its daughter particles ($\mathrm{q} \mathrm{\bar{q}} \tilde{\chi}^0_1 $) are shown in the lower and middle planes, respectively; the upper plane depicts the location of the stable particles after hadronisation, with shaded ellipses overlaid to indicate the reconstructed jets. Each quark and its decay is assigned a unique colour. The dotted lines indicate the links between parent and daughter particles. |
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Figure 1-a:
An example ${\mathrm{\widetilde{g}}} \to \mathrm{q} \mathrm{\bar{q}} \tilde{\chi}^0_1 $ decay chain, constructed from information provided by the MadGraph 5_aMC@NLO [55] and PYTHIA [56] programs. The positions of various particles in the $\eta $-$\phi $ plane are shown: the LLP (${{\mathrm{\widetilde{g}}}}$) and its daughter particles ($\mathrm{q} \mathrm{\bar{q}} \tilde{\chi}^0_1 $) are shown in the lower and middle planes, respectively; the upper plane depicts the location of the stable particles after hadronisation, with shaded ellipses overlaid to indicate the reconstructed jets. Each quark and its decay is assigned a unique colour. The dotted lines indicate the links between parent and daughter particles. |
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Figure 1-b:
An example ${\mathrm{\widetilde{g}}} \to \mathrm{q} \mathrm{\bar{q}} \tilde{\chi}^0_1 $ decay chain, constructed from information provided by the MadGraph 5_aMC@NLO [55] and PYTHIA [56] programs. The positions of various particles in the $\eta $-$\phi $ plane are shown: the LLP (${{\mathrm{\widetilde{g}}}}$) and its daughter particles ($\mathrm{q} \mathrm{\bar{q}} \tilde{\chi}^0_1 $) are shown in the lower and middle planes, respectively; the upper plane depicts the location of the stable particles after hadronisation, with shaded ellipses overlaid to indicate the reconstructed jets. Each quark and its decay is assigned a unique colour. The dotted lines indicate the links between parent and daughter particles. |
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Figure 2:
An overview of the DNN architecture, which comprises convolutional and dense layers; the numbers of filters and nodes are indicated. Dropout layers and activation functions are not shown. The input features are grouped by object type and ($m \times n$) indicates the maximum number of objects ($m$) and the number of features per object ($n$). The gradients of the class $(L_\text {class})$ and domain $(L_\text {domain})$ losses with respect to the weights $\vec{w}$, used during backward propagation, are shown. |
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Figure 3:
A schematic of the input pipeline for training the DNN, which uses the TensorFlow (TF) queue system with custom operation kernels for reading root trees from disk, (${p_{\mathrm {T}}}$, $\eta $) resampling for SM jets, and generating random ${c\tau _{0}}$ values for jets from SM backgrounds and data. |
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Figure 4:
Distributions of the maximum probability for the LLP jet class obtained from all selected jets in a given event, ${P_\text {max}(\mathrm {LLP}| {c\tau _{0}})}$. The distributions from pp collision data (circular marker) and simulated events (histograms) are compared in the $\mu$+jets (upper row) and $\mu\mu$+jets (lower row) CRs, using a DNN trained without (left column) and with (right column) DA. All probabilities are evaluated with $ {c\tau _{0}} = $ 1 mm. The Jensen-Shannon divergence (JSD) is introduced in the text. The lower subpanels show the ratios of the binned yields obtained from data and Monte Carlo (MC) simulation. The statistical (hatched bands) and systematic (solid bands) uncertainties due to the finite-size simulation samples and the simulation mismodelling of the mistag rate, respectively, are also shown. |
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Figure 4-a:
Distribution of the maximum probability for the LLP jet class obtained from all selected jets in a given event, ${P_\text {max}(\mathrm {LLP}| {c\tau _{0}})}$. The distribution from pp collision data (circular marker) and simulated events (histograms) are compared in the $\mu$+jets CR, using a DNN trained without DA. All probabilities are evaluated with $ {c\tau _{0}} = $ 1 mm. The Jensen-Shannon divergence (JSD) is introduced in the text. The lower subpanel shows the ratios of the binned yields obtained from data and Monte Carlo (MC) simulation. The statistical (hatched bands) and systematic (solid bands) uncertainties due to the finite-size simulation samples and the simulation mismodelling of the mistag rate, respectively, are also shown. |
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Figure 4-b:
Distribution of the maximum probability for the LLP jet class obtained from all selected jets in a given event, ${P_\text {max}(\mathrm {LLP}| {c\tau _{0}})}$. The distribution from pp collision data (circular marker) and simulated events (histograms) are compared in the $\mu$+jets CR, using a DNN trained with DA. All probabilities are evaluated with $ {c\tau _{0}} = $ 1 mm. The Jensen-Shannon divergence (JSD) is introduced in the text. The lower subpanel shows the ratios of the binned yields obtained from data and Monte Carlo (MC) simulation. The statistical (hatched bands) and systematic (solid bands) uncertainties due to the finite-size simulation samples and the simulation mismodelling of the mistag rate, respectively, are also shown. |
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Figure 4-c:
Distribution of the maximum probability for the LLP jet class obtained from all selected jets in a given event, ${P_\text {max}(\mathrm {LLP}| {c\tau _{0}})}$. The distribution from pp collision data (circular marker) and simulated events (histograms) are compared in the $\mu\mu$+jets CR, using a DNN trained without DA. All probabilities are evaluated with $ {c\tau _{0}} = $ 1 mm. The Jensen-Shannon divergence (JSD) is introduced in the text. The lower subpanel shows the ratios of the binned yields obtained from data and Monte Carlo (MC) simulation. The statistical (hatched bands) and systematic (solid bands) uncertainties due to the finite-size simulation samples and the simulation mismodelling of the mistag rate, respectively, are also shown. |
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Figure 4-d:
Distribution of the maximum probability for the LLP jet class obtained from all selected jets in a given event, ${P_\text {max}(\mathrm {LLP}| {c\tau _{0}})}$. The distribution from pp collision data (circular marker) and simulated events (histograms) are compared in the $\mu\mu$+jets CR, using a DNN trained with DA. All probabilities are evaluated with $ {c\tau _{0}} = $ 1 mm. The Jensen-Shannon divergence (JSD) is introduced in the text. The lower subpanel shows the ratios of the binned yields obtained from data and Monte Carlo (MC) simulation. The statistical (hatched bands) and systematic (solid bands) uncertainties due to the finite-size simulation samples and the simulation mismodelling of the mistag rate, respectively, are also shown. |
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Figure 5:
The ROC curves illustrating the tagger performance for the split (solid line), GMSB (dashed line), and RPV (dot-dashed line) SUSY benchmark models, assuming ${c\tau _{0}}$ values of 1 mm (left) and 1 m (right). The thin line with hatched shading indicates the performance obtained with a DNN training using split SUSY samples but without the DA. The jet sample is defined in the text. |
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Figure 5-a:
The ROC curves illustrating the tagger performance for the split (solid line), GMSB (dashed line), and RPV (dot-dashed line) SUSY benchmark models, assuming ${c\tau _{0}}$ values of 1 mm. The thin line with hatched shading indicates the performance obtained with a DNN training using split SUSY samples but without the DA. The jet sample is defined in the text. |
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Figure 5-b:
The ROC curves illustrating the tagger performance for the split (solid line), GMSB (dashed line), and RPV (dot-dashed line) SUSY benchmark models, assuming ${c\tau _{0}}$ values of 1 m. The thin line with hatched shading indicates the performance obtained with a DNN training using split SUSY samples but without the DA. The jet sample is defined in the text. |
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Figure 6:
The LLP jet tagging efficiency as a function of the jet ${p_{\mathrm {T}}}$, $\eta $, and $N_{\mathrm {SV}}$ using a working point that yields a mistag rate of 0.01% for the udsg jet class, as obtained from an inclusive sample of simulated ${\mathrm{t} \mathrm{\bar{t}}}$ events. The efficiency curves are shown separately for the split (circular marker), GMSB (triangle marker), and RPV (square marker) SUSY benchmark models, assuming ${c\tau _{0}}$ values of 1 m (upper row) and 1 mm (lower row). |
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Figure 7:
The LLP jet tagging efficiency, using a working point that yields a mistag rate of 0.01% for the udsg jet class obtained from an inclusive sample of simulated ${\mathrm{t} \mathrm{\bar{t}}}$ events, when (left) the DNN is evaluated as a function of the model parameter value ${c\tau _{0}}$ for an uncompressed and a compressed split SUSY model, and (right) the DNN is evaluated over a range of ${c\tau _{0}}$ values for uncompressed split SUSY models generated with $ {c\tau _{0}} = $ 1 mm and 1 m; the dashed vertical lines indicate equality for the evaluated and generated values of ${c\tau _{0}}$ for each model. The fixed model parameters are defined in the legends. |
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Figure 7-a:
The LLP jet tagging efficiency, using a working point that yields a mistag rate of 0.01% for the udsg jet class obtained from an inclusive sample of simulated ${\mathrm{t} \mathrm{\bar{t}}}$ events, when the DNN is evaluated as a function of the model parameter value ${c\tau _{0}}$ for an uncompressed and a compressed split SUSY model. The fixed model parameters are defined in the legends. |
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Figure 7-b:
The LLP jet tagging efficiency, using a working point that yields a mistag rate of 0.01% for the udsg jet class obtained from an inclusive sample of simulated ${\mathrm{t} \mathrm{\bar{t}}}$ events, when the DNN is evaluated over a range of ${c\tau _{0}}$ values for uncompressed split SUSY models generated with $ {c\tau _{0}} = $ 1 mm and 1 m; the dashed vertical lines indicate equality for the evaluated and generated values of ${c\tau _{0}}$ for each model. |
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Figure 8:
The negative log-likelihood of a maximum likelihood fit to the Asimov data set as a function of the signal efficiency scale factor and $r/r_\text {UL}$ for a (left) uncompressed and (right) compressed scenario. The black solid (dashed) line indicate the 68 (95)% CL interval, while for $r = r_\text {UL}$ (white dotted line) the white solid and dashed lines indicate the SF constraints at 68% and 95% CL, respectively. The product of the LLP jet tagger efficiency and the SF is bound to $[0,1]$. |
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Figure 8-a:
The negative log-likelihood of a maximum likelihood fit to the Asimov data set as a function of the signal efficiency scale factor and $r/r_\text {UL}$ for an uncompressed scenario. The black solid (dashed) line indicate the 68 (95)% CL interval, while for $r = r_\text {UL}$ (white dotted line) the white solid and dashed lines indicate the SF constraints at 68% and 95% CL, respectively. The product of the LLP jet tagger efficiency and the SF is bound to $[0,1]$. |
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Figure 8-b:
The negative log-likelihood of a maximum likelihood fit to the Asimov data set as a function of the signal efficiency scale factor and $r/r_\text {UL}$ for a compressed scenario. The black solid (dashed) line indicate the 68 (95)% CL interval, while for $r = r_\text {UL}$ (white dotted line) the white solid and dashed lines indicate the SF constraints at 68% and 95% CL, respectively. The product of the LLP jet tagger efficiency and the SF is bound to $[0,1]$. |
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Figure 9:
Expected 95% CL lower limits on ${m_{{\mathrm{\widetilde{g}}}}}$ as a function of ${c\tau _{0}}$ for split SUSY models with an uncompressed (left) and a very compressed (right) mass spectrum. The shaded bands indicate the total uncertainty from both statistical and systematic sources. The model assumptions are indicated by the legends. The results are compared to the expected limits obtained in Ref. [27], indicated by the dashed lines. |
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Figure 9-a:
Expected 95% CL lower limits on ${m_{{\mathrm{\widetilde{g}}}}}$ as a function of ${c\tau _{0}}$ for split SUSY models with an uncompressed mass spectrum. The shaded band indicates the total uncertainty from both statistical and systematic sources. The model assumptions are indicated by the legends. The results are compared to the expected limits obtained in Ref. [27], indicated by the dashed line. |
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Figure 9-b:
Expected 95% CL lower limits on ${m_{{\mathrm{\widetilde{g}}}}}$ as a function of ${c\tau _{0}}$ for split SUSY models with a very compressed mass spectrum. The shaded band indicates the total uncertainty from both statistical and systematic sources. The model assumptions are indicated by the legends. The results are compared to the expected limits obtained in Ref. [27], indicated by the dashed line. |
| Tables | |
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Table 1:
The event counts and uncertainties for SM backgrounds and split SUSY models, as determined from simulation, in categories defined by ${H_{\mathrm {T}}}$ and (${N_\text {jet}}$, ${N_\text {tag}}$). The simulated samples are normalised to an integrated luminosity of 35.9 fb$^{-1}$. The uncompressed and compressed split SUSY models are defined in Section 4. The value of ${c\tau _{0}}$ is assumed to be 1 mm. The uncertainties include both statistical and systematic contributions. Expected counts for events that satisfy $ {N_\text {tag}} < 2$ are not shown. |
| Summary |
|
Many models of new physics beyond the standard model predict the production of long-lived particles (LLPs) in proton-proton (pp) collisions at the LHC. Jets arising from the decay of LLPs (LLP jets) can be appreciably displaced from the pp collisions. A novel tagger to identify LLP jets is presented. The tagger employs a deep neutral network (DNN) using an architecture inspired by the CMS DeepJet algorithm. Simplified models of split supersymmetry (SUSY), which yield neutralinos and LLP jets from the decay of long-lived gluinos, are used to train the DNN and demonstrate its performance. The application of various techniques related to the tagger are reported. A custom labelling scheme for LLP jets based on generator-level information from Monte Carlo programs is defined. The proper decay length ${c\tau_{0}}$ of the gluino is used as an external parameter to the DNN, which allows hypothesis testing over several orders of magnitude in ${c\tau_{0}}$ with a single DNN. The DNN is trained using samples of both simulated events and pp collision data. The application of domain adaptation by backward propagation significantly improves the agreement of the DNN output for simulation and data, by an order of magnitude according to the Jensen-Shannon divergence, when compared to training the DNN with simulation only. The method is validated using signal-depleted control samples of pp collisions at a centre-of-mass energy of 13 TeV. The samples were recorded by the CMS experiment and correspond to an integrated luminosity of 35.9 fb$^{-1}$. Training the DNN with collision data does not significantly degrade the tagger performance. The tagger rejects 99.99% of light-flavour jets from standard model processes, as measured in an inclusive $\mathrm{t\bar{t}}$ sample, while retaining approximately 30-80% of LLP jets for split SUSY models with 1 mm $\leq \text{c}\tau_0 \leq $ 10 m and a gluino-neutralino mass difference of at least 200 GeV. Finally, the potential performance of the tagger is demonstrated in the framework of a search for split SUSY in final states containing jets and significant missing transverse momentum. Simulated event samples provide the expected contributions from standard model background processes. Candidate signal events were categorised according to the scalar sum of jet momenta, the number of jets, and the number of tagged LLP jets. Expected lower limits on the gluino mass at 95% confidence level are determined with a binned likelihood fit as a function of ${c\tau_{0}}$ in the range from 10 $\mu$m to 10 m. A procedure to constrain a correction to the LLP jet tagger efficiency in the likelihood fit is introduced. Competitive limits are demonstrated: models with a long-lived gluino of mass ${\gtrsim}$ 2 TeV, a neutralino mass of 100 GeV, and a proper decay length in the range 1 mm $\leq {c\tau_{0}} \leq$ 1 m are expected to be excluded by this search. |
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