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| CMS-JME-24-001 ; CERN-EP-2025-193 | ||
| Improving missing transverse momentum estimation with a deep neural network | ||
| CMS Collaboration | ||
| 15 September 2025 | ||
| Submitted to Phys. Rev. D | ||
| Abstract: At hadron colliders, the net transverse momentum of particles that do not interact with the detector (missing transverse momentum, $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $) is a crucial observable in many analyses. In the standard model, $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ originates from neutrinos. Many beyond-the-standard-model particles, such as dark matter candidates, are also expected to leave the experimental apparatus undetected. This paper presents a novel $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimator, DEEPMET, which is based on deep neural networks that were developed by the CMS Collaboration at the LHC. The DEEPMET algorithm produces a weight for each reconstructed particle based on its properties. The estimator is based on the negative vector sum of the weighted transverse momenta of all reconstructed particles in an event. Compared with other estimators currently employed by CMS, DEEPMET improves the $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ resolution by 10-30%, 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. | ||
| Links: e-print arXiv:2509.12012 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The DEEPMET DNN architecture. For each event, all PF candidates in the event are considered as input. $ N\times n $ represents the number of PF candidates in the event multiplied by the dimensionality of the per-particle feature space, where $ n $ can be 1, 2, 3, 8, 16, 32, and 64 in the architecture. |
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Figure 2:
Recoil responses of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data (markers) 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 $ {\vec 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 $ {\vec 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 $ {\vec 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 $ {\vec 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 $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ due to the JES, the JER, and $ E_U $ are added in quadrature and displayed with the gray 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 $ {\vec 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 $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ due to the JES, the JER, and $ E_U $ are added in quadrature and displayed with the gray 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 $ {\vec 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 $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ due to the JES, the JER, and $ E_U $ are added in quadrature and displayed with the gray 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 $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} $ smaller than 50 GeV. |
png pdf |
Figure 5-a:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ $ number of reconstructed PVs of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} $ smaller than 50 GeV. |
png pdf |
Figure 5-b:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ $ number of reconstructed PVs of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} $ smaller than 50 GeV. |
png pdf |
Figure 6:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ $ number of reconstructed PVs of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} $ larger than 50 GeV. |
png pdf |
Figure 6-a:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ $ number of reconstructed PVs of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} $ larger than 50 GeV. |
png pdf |
Figure 6-b:
Response-corrected resolutions of $ u_{\parallel} $ (left) and $ u_{\perp} $ (right) vs. $ $ number of reconstructed PVs of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections in the region with $ q_{\mathrm{T}} $ larger than 50 GeV. |
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Figure 7:
Response (upper), response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in W+jets MC simulations. Solid (dashed) lines are from events where the LPV is (in)correctly identified. |
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Figure 7-a:
Response (upper), response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in W+jets MC simulations. Solid (dashed) lines are from events where the LPV is (in)correctly identified. |
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Figure 7-b:
Response (upper), response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in W+jets MC simulations. Solid (dashed) lines are from events where the LPV is (in)correctly identified. |
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Figure 7-c:
Response (upper), response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in W+jets MC simulations. Solid (dashed) lines are from events where the LPV 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 $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after $ \mathrm{W}\to\mu\nu $ selections. |
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Figure 8-a:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_\mathrm{T} $ (right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after $ \mathrm{W}\to\mu\nu $ selections. |
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Figure 8-b:
Distributions of $ p_{\mathrm{T}}^\text{miss} $ (left) and $ m_\mathrm{T} $ (right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after $ \mathrm{W}\to\mu\nu $ selections. |
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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 $ (upper left), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (upper 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 (lower left), and the SMS TChiZZ process (lower 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 $ (upper left), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (upper 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 (lower left), and the SMS TChiZZ process (lower 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 $ (upper left), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (upper 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 (lower left), and the SMS TChiZZ process (lower 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 $ (upper left), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (upper 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 (lower left), and the SMS TChiZZ process (lower 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 $ (upper left), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (upper 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 (lower left), and the SMS TChiZZ process (lower right). |
png pdf |
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 $ (upper left), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (upper 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 (lower left), and the SMS TChiZZ process (lower right). |
png pdf |
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 $ (upper left), H production via vector boson fusion with $ \mathrm{H}\to\text{invisible} $ (upper 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 (lower left), and the SMS TChiZZ process (lower right). |
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Figure 10:
The $ \phi $ distribution of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators before (left) and after (right) the $ 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 $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators before (left) and after (right) the $ 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 $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators before (left) and after (right) the $ xy $ corrections, in data (markers) and MC simulations (dashed) after the $ \mathrm{Z}\to\mu\mu $ selections. |
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Figure 11:
Data-to-simulation comparisons of DEEPMET $ p_{\mathrm{T}}^\text{miss} $ (upper left), recoil $ p_{\mathrm{T}} $ (upper right), $ u_{\parallel} $ (lower left), and $ u_{\perp} $ (lower right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin. The gray band represents the systematic uncertainties discussed in Section 8.4. |
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Figure 11-a:
Data-to-simulation comparisons of DEEPMET $ p_{\mathrm{T}}^\text{miss} $ (upper left), recoil $ p_{\mathrm{T}} $ (upper right), $ u_{\parallel} $ (lower left), and $ u_{\perp} $ (lower right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin. The gray band represents the systematic uncertainties discussed in Section 8.4. |
png pdf |
Figure 11-b:
Data-to-simulation comparisons of DEEPMET $ p_{\mathrm{T}}^\text{miss} $ (upper left), recoil $ p_{\mathrm{T}} $ (upper right), $ u_{\parallel} $ (lower left), and $ u_{\perp} $ (lower right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin. The gray band represents the systematic uncertainties discussed in Section 8.4. |
png pdf |
Figure 11-c:
Data-to-simulation comparisons of DEEPMET $ p_{\mathrm{T}}^\text{miss} $ (upper left), recoil $ p_{\mathrm{T}} $ (upper right), $ u_{\parallel} $ (lower left), and $ u_{\perp} $ (lower right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin. The gray band represents the systematic uncertainties discussed in Section 8.4. |
png pdf |
Figure 11-d:
Data-to-simulation comparisons of DEEPMET $ p_{\mathrm{T}}^\text{miss} $ (upper left), recoil $ p_{\mathrm{T}} $ (upper right), $ u_{\parallel} $ (lower left), and $ u_{\perp} $ (lower right) after the quantile correction. The underflow (overflow) contents are included in the first (last) bin. The gray band represents the systematic uncertainties discussed in Section 8.4. |
png pdf |
Figure 12:
Response (upper) and response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections. |
png pdf |
Figure 12-a:
Response (upper) and response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections. |
png pdf |
Figure 12-b:
Response (upper) and response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators in data after the $ \mathrm{Z}\to\mu\mu $ selections. |
png pdf |
Figure 12-c:
Response (upper) and response-corrected resolutions of $ u_{\parallel} $ (lower left) and $ u_{\perp} $ (lower right) of different $ {\vec 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. |
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Table 2:
Higher half width at half maximum in $ p_{\mathrm{T}}^\text{miss} $ and $ m_\mathrm{T} $ in data after the $ \mathrm{W}\to\mu\nu $ selections. |
| Summary |
| This paper presents a new $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimator, DEEPMET, which is based on a deep neural network. The DEEPMET algorithm 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} $ and $ b_{i,y} $, to each candidate. The estimated $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ is the negative vector sum of the weighted transverse momenta of all candidates, plus their bias contributions. With 4541 trainable parameters, the training and deployment of DEEPMET is computationally efficient. DEEPMET is trained using Z+jets and $ \mathrm{t} \overline{\mathrm{t}} $ samples, but achieves 10-30% better resolution compared with the current PF and PUPPI $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ estimators across multiple physics processes, such as Z+jets, W+jets, Higgs boson production, and processes with dark matter candidates. Another important feature of the DEEPMET algorithm is its high resilience to pileup, improving the physics reach in LHC Run 2 and Run 3, and future High-Luminosity LHC conditions. Specifically for the measurement of the W boson mass, a PV-Agnostic version of DEEPMET is designed to be more robust in $ \mathrm{W} \to \mu\nu $ events where the LPV is not always identified correctly. Events containing $ \mathrm{Z} \to \mu\mu $ decays are used to calibrate $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $, including corrections for asymmetries in detector response, as well as for $ {\vec p}_{\mathrm{T}}^{\, \text{miss}} $ scale and resolution. Good agreement between data and simulation is found. The DEEPMET estimator demonstrates the potential to improve the precision of SM measurements and to achieve higher sensitivity in beyond the standard model physics searches. |
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