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CMS-PAS-JME-24-001
DeepMET: Improving missing transverse momentum estimation with a deep neural network
Abstract: At hadron colliders, the net transverse momentum of particles that do not interact with the detector (missing transverse momentum) is a crucial observable in many analyses. In the standard model, missing transverse momentum originates from neutrinos. Many beyond-the-standard-model particles such as dark matter candidates are also expected to leave the experimental apparatus undetected. This note presents a novel missing transverse momentum estimator DeepMET, developed for the CMS experiment at the LHC, that is based on deep neural networks. DeepMET produces a weight for each reconstructed particle based on its properties. The estimator is the negative vector sum over all reconstructed particles of their weighted transverse momenta. Compared with other estimators currently employed by CMS, DeepMET improves the missing transverse momentum resolution by 10-20%, shows improvement for a wide range of final states, is easier to train, and is more resilient against the effects of additional proton-proton interactions accompanying the collision of interest. A version of DeepMET that is less dependent on correct reconstruction of the hard scattering vertex position is also presented.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
DeepMET DNN architecture. For each event, all particles in the event are considered as input. Since the number of particles varies event by event, the exact dimension is unknown and is indicated by a question mark.

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Figure 2:
Recoil responses of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data (solid) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 3:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ q_{\mathrm{T}} $ of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 3-a:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ q_{\mathrm{T}} $ of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 3-b:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ q_{\mathrm{T}} $ of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 4:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data (solid) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections. The systematic uncertainties for PUPPI $ p_{\mathrm{T}}^\text{miss} $ due to the JES, the JER, and variations in the EU are added in quadrature and displayed with a band.

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Figure 4-a:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data (solid) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections. The systematic uncertainties for PUPPI $ p_{\mathrm{T}}^\text{miss} $ due to the JES, the JER, and variations in the EU are added in quadrature and displayed with a band.

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Figure 4-b:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data (solid) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections. The systematic uncertainties for PUPPI $ p_{\mathrm{T}}^\text{miss} $ due to the JES, the JER, and variations in the EU are added in quadrature and displayed with a band.

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Figure 5:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} < $ 50 GeV.

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Figure 5-a:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} < $ 50 GeV.

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Figure 5-b:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} < $ 50 GeV.

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Figure 6:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} > $ 50 GeV.

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Figure 6-a:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} > $ 50 GeV.

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Figure 6-b:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. number of reconstructed PVs of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} > $ 50 GeV.

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Figure 7:
Response (top), response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in $ \mathrm{W}+ $jets MC simulations. Solid (dashed) lines are from events where the LV is (in)correctly identified

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Figure 7-a:
Response (top), response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in $ \mathrm{W}+ $jets MC simulations. Solid (dashed) lines are from events where the LV is (in)correctly identified

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Figure 7-b:
Response (top), response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in $ \mathrm{W}+ $jets MC simulations. Solid (dashed) lines are from events where the LV is (in)correctly identified

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Figure 7-c:
Response (top), response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in $ \mathrm{W}+ $jets MC simulations. Solid (dashed) lines are from events where the LV is (in)correctly identified

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Figure 8:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_\mathrm{T} $ (right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in $ \mathrm{W}+ $jets MC simulations.

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Figure 8-a:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_\mathrm{T} $ (right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in $ \mathrm{W}+ $jets MC simulations.

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Figure 8-b:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_\mathrm{T} $ (right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in $ \mathrm{W}+ $jets MC simulations.

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Figure 9:
Comparison of $ p_{\mathrm{T}}^\text{miss} $ resolution for various physics processes in simulated events. The considered processes are HH production via gluon fusion with $ \mathrm{H}\mathrm{H}\to\mathrm{b}\mathrm{b}\tau\tau $ (top right), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (top right), $ \mathrm{t}\mathrm{t}\mathrm{H} $ production with either $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ (middle left) or $ \mathrm{H}\to\mu\mu $ (middle right), the SMS T2b-4bd process (bottom left), and the SMS TChiZZ process (bottom right).

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Figure 9-a:
Comparison of $ p_{\mathrm{T}}^\text{miss} $ resolution for various physics processes in simulated events. The considered processes are HH production via gluon fusion with $ \mathrm{H}\mathrm{H}\to\mathrm{b}\mathrm{b}\tau\tau $ (top right), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (top right), $ \mathrm{t}\mathrm{t}\mathrm{H} $ production with either $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ (middle left) or $ \mathrm{H}\to\mu\mu $ (middle right), the SMS T2b-4bd process (bottom left), and the SMS TChiZZ process (bottom right).

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Figure 9-b:
Comparison of $ p_{\mathrm{T}}^\text{miss} $ resolution for various physics processes in simulated events. The considered processes are HH production via gluon fusion with $ \mathrm{H}\mathrm{H}\to\mathrm{b}\mathrm{b}\tau\tau $ (top right), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (top right), $ \mathrm{t}\mathrm{t}\mathrm{H} $ production with either $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ (middle left) or $ \mathrm{H}\to\mu\mu $ (middle right), the SMS T2b-4bd process (bottom left), and the SMS TChiZZ process (bottom right).

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Figure 9-c:
Comparison of $ p_{\mathrm{T}}^\text{miss} $ resolution for various physics processes in simulated events. The considered processes are HH production via gluon fusion with $ \mathrm{H}\mathrm{H}\to\mathrm{b}\mathrm{b}\tau\tau $ (top right), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (top right), $ \mathrm{t}\mathrm{t}\mathrm{H} $ production with either $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ (middle left) or $ \mathrm{H}\to\mu\mu $ (middle right), the SMS T2b-4bd process (bottom left), and the SMS TChiZZ process (bottom right).

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Figure 9-d:
Comparison of $ p_{\mathrm{T}}^\text{miss} $ resolution for various physics processes in simulated events. The considered processes are HH production via gluon fusion with $ \mathrm{H}\mathrm{H}\to\mathrm{b}\mathrm{b}\tau\tau $ (top right), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (top right), $ \mathrm{t}\mathrm{t}\mathrm{H} $ production with either $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ (middle left) or $ \mathrm{H}\to\mu\mu $ (middle right), the SMS T2b-4bd process (bottom left), and the SMS TChiZZ process (bottom right).

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Figure 9-e:
Comparison of $ p_{\mathrm{T}}^\text{miss} $ resolution for various physics processes in simulated events. The considered processes are HH production via gluon fusion with $ \mathrm{H}\mathrm{H}\to\mathrm{b}\mathrm{b}\tau\tau $ (top right), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (top right), $ \mathrm{t}\mathrm{t}\mathrm{H} $ production with either $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ (middle left) or $ \mathrm{H}\to\mu\mu $ (middle right), the SMS T2b-4bd process (bottom left), and the SMS TChiZZ process (bottom right).

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Figure 9-f:
Comparison of $ p_{\mathrm{T}}^\text{miss} $ resolution for various physics processes in simulated events. The considered processes are HH production via gluon fusion with $ \mathrm{H}\mathrm{H}\to\mathrm{b}\mathrm{b}\tau\tau $ (top right), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (top right), $ \mathrm{t}\mathrm{t}\mathrm{H} $ production with either $ \mathrm{H}\to\mathrm{b}\mathrm{b} $ (middle left) or $ \mathrm{H}\to\mu\mu $ (middle right), the SMS T2b-4bd process (bottom left), and the SMS TChiZZ process (bottom right).

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Figure 10:
The $ \phi $ distribution of different $ p_{\mathrm{T}}^\text{miss} $ estimators before (left) and after (right) $ xy $ corrections, in data (markers) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 10-a:
The $ \phi $ distribution of different $ p_{\mathrm{T}}^\text{miss} $ estimators before (left) and after (right) $ xy $ corrections, in data (markers) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 10-b:
The $ \phi $ distribution of different $ p_{\mathrm{T}}^\text{miss} $ estimators before (left) and after (right) $ xy $ corrections, in data (markers) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 11:
Data-MC comparisons of DeepMET $ p_{\mathrm{T}}^\text{miss} $ (top left), recoil $ p_{\mathrm{T}} $ (top right), $ u_{\parallel} $ (bottom left), and $ u_{\perp} $ (bottom right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin.

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Figure 11-a:
Data-MC comparisons of DeepMET $ p_{\mathrm{T}}^\text{miss} $ (top left), recoil $ p_{\mathrm{T}} $ (top right), $ u_{\parallel} $ (bottom left), and $ u_{\perp} $ (bottom right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin.

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Figure 11-b:
Data-MC comparisons of DeepMET $ p_{\mathrm{T}}^\text{miss} $ (top left), recoil $ p_{\mathrm{T}} $ (top right), $ u_{\parallel} $ (bottom left), and $ u_{\perp} $ (bottom right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin.

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Figure 11-c:
Data-MC comparisons of DeepMET $ p_{\mathrm{T}}^\text{miss} $ (top left), recoil $ p_{\mathrm{T}} $ (top right), $ u_{\parallel} $ (bottom left), and $ u_{\perp} $ (bottom right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin.

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Figure 11-d:
Data-MC comparisons of DeepMET $ p_{\mathrm{T}}^\text{miss} $ (top left), recoil $ p_{\mathrm{T}} $ (top right), $ u_{\parallel} $ (bottom left), and $ u_{\perp} $ (bottom right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin.

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Figure 12:
Response (top) and response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 12-a:
Response (top) and response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 12-b:
Response (top) and response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections.

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Figure 12-c:
Response (top) and response-corrected resolutions of $ u_{\parallel} $ (bottom left) and $ u_{\perp} $ (bottom right) of different $ p_{\mathrm{T}}^\text{miss} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections.
Tables

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Table 1:
Overview of the simulated event samples used for performance studies.
Summary
This paper presents a new $ p_{\mathrm{T}}^\text{miss} $ estimator, DeepMET, which is based on a deep neural network. DeepMET utilizes each individual particle reconstructed by the CMS particle-flow algorithm as input and assigns a weight $ w_i $ and two bias terms $ b_{i,x}, b_{i,y} $ to each candidate. The estimated $ p_{\mathrm{T}}^\text{miss} $ is the negative of the vector sum of the weighted transverse momenta of all candidates plus their bias contributions. With only 4541 trainable parameters, DeepMET manages to achieve 10-20% better resolution compared with the current PF and PUPPI $ p_{\mathrm{T}}^\text{miss} $ estimators. In addition, the DeepMET algorithm shows a larger resilience to pileup. DeepMET demonstrates the potential to improve the precision of SM measurements and to achieve a higher sensitivity in BSM searches.
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Compact Muon Solenoid
LHC, CERN