Learn about MET, the definition, types and reconstruction algorithms.
Learn about extracting MET in MiniAOD files.
After following the instructions in the setup, make sure you have the CMS environment:
cd$CMSSW_BASE/src/METDAS
cmsenv
Event Reconstruction
Event reconstruction in CMS is achieved using the Particle Flow (PF) algorithm, which integrates information from all CMS subdetectors to reconstruct individual particles.
The algorithm produces a list of PF candidates classified as electrons, photons, muons, neutral hadrons, or charged hadrons.
These PF candidates are then used to reconstruct high-level physics objects, including jets and missing transverse momentum (MET).
Schematic of the CMS particle flow reconstruction algorithm.
Missing Transverse Energy
MET quantifies the imbalance in the transverse momentum of all visible particles in the final state of collisions—those interacting via electromagnetic or strong forces.
Due to momentum conservation in the transverse plane (the plane perpendicular to the beam), MET reflects the transverse momentum carried by undetected weakly interacting particles, such as neutrinos or potential dark matter candidates.
Although these invisible particles leave no direct signature in the CMS detector, their presence is inferred from the observed net momentum imbalance in the event.
An example of event with MET is shown in the figure below where two top quarks are produced. Each top quark decays into a b-jet and a W boson. The leptonic decay of a W boson leads to a lepton and its corresponding neutrino. So, the final state contains two jets, two leptons and missing transverse energy from two neutrinos.
Event display of a ttbar event recorded by CMS shows the dileptonic decay channel with two jets, one electron, one muon, and missing transverse energy from two neutneutrinosrinoes.
MET is a vital variable in many CMS analyses, playing a key role in both Standard Model measurements and Beyond Standard Model searches.
In the Standard Model, MET is used to study processes involving neutrinos in the final state, such as the W boson mass measurement.
In searches for new physics, MET helps identify potential signatures where weakly interacting particles escape detection, such as dark matter, resulting in an imbalance in transverse momentum.
The images below illustrate two such cases: on the left, a candidate W boson event with $W \rightarrow \mu \nu$, used in the W mass measurement, and on the right, a candidate event for dark matter production, featuring a hard jet recoiling against large missing energy.
W boson candidate event with a muon and neutrino.Dark matter search event with a hard jet recoiling against large MET.
Event displays of analyses involving MET.
Raw PF MET
The most widely used MET reconstruction algorithm in CMS is the PF MET.
PF MET is reconstructed as the negative vector sum of the pT of all PF candidates in the event, which is summarized in the following equation:
Multiple simultaneous proton-proton collisions occurring in the same bunch crossing, referred to as pileup, adversely affect MET resolution, leading to poorer performance at higher pileup levels. To mitigate these effects and improve MET performance with respect to pileup, CMS employs an alternative reconstruction algorithm known as PUPPI MET.
The PUPPI (Pileup Per Particle Identification) algorithm applies inherently local corrections by leveraging specific properties of particles. Particles originating from the hard scatter process are typically geometrically close to other particles from the same interaction and generally exhibit higher pT. In contrast, pileup particles lack shower structures, have lower pT on average, and are uncorrelated with particles from the leading vertex.
Using this information, the PUPPI algorithm removes charged particles associated with pileup vertices and assigns weights (ranging between 0 and 1) to neutral particles based on their likelihood of originating from pileup, thus enhancing MET reconstruction in high-pileup environments. The PUPPI MET is calculated using particle weights and can be summarized in the following equation:
The figure below presents the MET distribution for both PF MET and PUPPI MET in events with leptonically decaying W bosons, demonstrating the improved performance achieved with PUPPI MET.
Remember
PUPPI MET is the default MET algorithm in Run~3.
Exercise 1
The goal of this part is to get familiar:
with the event content of the miniAOD data tier,
the MET collections stored by default in miniAOD,
how to use tools to easily browse through the miniAOD file.
To view the event content of a miniAOD file one can use the edmDumpEventContent command and since we are interested in the MET collections only we use grep to avoid long printouts.
edmDumpEventContent root://cmseos.fnal.gov//eos/uscms/store/user/cmsdas/2025/short_exercises/MET/DYJetsToLL_M50_amcatnloFXFX.root | grep MET
Question 1
What MET collections do you see inside a MiniAOD file?
Each entry (line) corresponds to a separate MET collection.
The first column, pat::MET, shows the class of the MET object, where one finds the properties of the MET object.
The second column shows the MET collection, and finally PAT is the namespace (in MiniAOD it is PAT).
In this exercise we will focus on the slimmedMETs and slimmedMETsPuppi collections.
Key Points
Weakly interacting neutral particles produced in proton-proton (pp) collisions at the LHC traverse the CMS detector unobserved.
Their presence is inferred from the measurable momentum imbalance in the plane perpendicular to the beam direction when produced alongside electromagnetically charged or neutral particles. This measurable transverse momentum imbalance is referred to as missing transverse momentum (MET).
Precise determination of MET is critical for Standard Model measurements involving final states with neutrinos and searches for physics beyond the SM targeting new weakly interacting particles.
MET reconstruction is sensitive to experimental resolutions and mis-measurements of reconstructed particles, detector artifacts, and the effects of additional pp interactions within the same or nearby bunch crossings (pileup).
MET Calibrations
Overview
Teaching: 20 min
Exercises: 10 min
Questions
Why do we need to calibrate MET? How is the performance measured?
What are the different ways of calibrating MET at CMS?
What is MET phi modulation? How to correct for it?
How is the uncertainty on MET estimated?
Objectives
Learn about the MET calibration procedure and techniques used at CMS.
Learn about measuring MET performance.
Understand MET phi modulation and how to account for it.
Learn about MET uncertainty sources and to get the MET uncertainty in MiniAOD analyses.
After following the instructions in the setup, make sure you have the CMS environment:
The MET objects described earlier (PF-MET and PUPPI-MET) are referred to as raw MET, and they are systematically different from the true MET, which corresponds to the transverse momentum carried by invisible particles.
This difference arises from factors such as the non-compensating nature of the calorimeters, calorimeter thresholds, and detector misalignment, among others.
To improve the MET estimate and make it closer to the true MET, corrections can be applied.
Type-1 Correction
The Type-I correction is the most commonly used MET correction in CMS.
It propagates the jet energy corrections (JEC) to MET. Specifically, the Type-I correction replaces the vector sum of the transverse momenta of particles clustered as jets with the vector sum of the transverse momenta of the jets, which have been corrected with JEC.
Particles can be classified into two disjoint sets: those that are clustered as jets and those that remain unclustered.
The superscript “uncorr” indicates that the jet energy correction (JEC) has not yet been applied to these jets.
The Type-I correction replaces the raw jet pT with the corrected jet pT. The Type-I correction can be expressed as the difference between two vector sums:
We will revisit this in MET performance, but this figure shows a comarison between the MET scale for raw PF MET vs Type-1 PF MET.
Type-1 Smear MET (For MC only)
In MC simulations, jets are smeared to achieve better agreement with data. This smearing of MC jets can additionally be propagated to MET, resulting in Type-1 smear MET.
Remember
PF MET is the recommended MET algorithm in Run 2, and PUPPI MET is recommended for Run 3 analyses.
Type-I corrected MET is the default MET calibration required in all analyses.
XY corrections
The XY correction reduces the MET $\phi$ modulation. This correction also helps mitigate pile-up effects.
The distribution of true MET is independent of $\phi$ due to the rotational symmetry of collisions around the beam axis.
However, we observe that the reconstructed MET does depend on $\phi$.
The MET $\phi$ distribution follows roughly a sinusoidal curve with a period of $2\pi$.
The possible causes of this modulation include:
Anisotropic detector responses
Inactive calorimeter cells
Detector misalignment
Displacement of the beam spot
The amplitude of the modulation increases roughly linearly with the number of pile-up interactions.
MET Uncertainty
For analyses sensitive to missing transverse energy — those involving large MET contributions from neutrinos or other signatures — it is necessary to break MET into its individual components.
Since MET is calculated as the vector sum of contributions from jets, electrons, muons, taus, photons, and “unclustered energy” (energy not associated with reconstructed objects), the resolution and scale of each component must be propagated to MET.
These uncertainties are then treated as separate nuisance parameters each arising from a different physics object.
The physics objects that contribute the most are:
Jets: Jet energy scale (JES) and jet energy resolution (JER) uncertainties directly impact MET, as jets typically contribute significantly to the total energy.
Unclustered Energy: Unclustered energy includes contributions from particles not grouped into jets, leptons, or photons. The uncertainty arises from the resolution of individual particle types, such as charged hadrons, neutral hadrons, photons, and hadronic forward (HF) particles.
Leptons: This includes tau leptons, electrons, muons, and photons. Scale uncertainties for these objects need to be propagated to MET, as even small variations can affect its calculation.
The scale and resolution of each component must be systematically varied within their respective uncertainties. These variations are then propagated to the MET calculation to calculate their impact on the analysis.
Exercise 2.1
In this section, we will focus on accessing the MET object(s) in miniAOD, including:
Different MET calibrations
MET uncertainties
Firstly, we will access different MET flavors: the raw PFMET, the Type-1 PFMET (the default MET flavor in CMS), and the Type-1 smeared PFMET.
In Type-1 MET, corrections from the jet energy scale are propagated to MET, whereas in Type-1 smeared MET, corrections from both the jet energy scale and the jet energy resolution are applied.
MET relies on accurate momentum/energy measurements of reconstructed physics objects, including muons, electrons, photons, hadronically decaying taus, jets, and unclustered energy (UE). The latter refers to contributions from PF candidates not associated with any of the previously mentioned physics objects.
Since uncertainties in MET measurements strongly depend on the event topology, uncertainties in the momenta of all reconstructed objects are propagated to MET. This is done by varying the momentum estimate of each object within its uncertainty and recomputing MET.
In this exercise, we will consider three sources of uncertainty:
Print the transverse momentum ($p_T$) and azimuthal angle ($\phi$) of the MET object for each event
Print the values of various sources of systematic uncertainties
Additionally, the script demonstrates how to access MET with different levels of corrections applied. By default, Type-1 MET is selected.
The analyzer being run using is command is CMSDAS_MET_Analysis/plugins/CMSDAS_MET_AnalysisExercise2.cc. The printout looks like the following:
Begin processing the 1st record. Run 1, Event 138728702, LumiSection 513811 on stream 0 at 05-Jan-2025 14:40:03.942 CST
MET :
pt [GeV] = 4.42979
phi [rad] = 2.92774
MET uncertainties :
JES up/down [GeV] = 2.22909/6.63454
JER up/down [GeV] = 4.34603/4.51426
Unc up/down [GeV] = 9.2058/6.06604
MET corrections :
Raw PFMET pt [GeV] = 10.7137
PFMET-type1 pt [GeV] = 4.42979
Smeared PFMET-type1 pt [GeV] = 4.40847
.......
.......
Question 2.1
Compare the distributions of the above quantities and get a feeling about their effect. Wheer are these distrucutions being stored?
Solution 2.1
The various MET histograms (raw, Type-1, JES Up, JER down etc.) are being stored at ./outputs/cmsdas_met_exercise2.root
Exercise 2.2
Now we make the following modifications to the configuration script CMSDAS_MET_Analysis/test/run_CMSDAS_MET_Exercise2_cfg.py:
Prevent printouts by setting doprints to False.
Reduce the frequency of the report from “every” event to “every 10000” events by modifying process.MessageLogger.cerr.FwkReport.reportEvery.
Run over all events in the file by updating process.maxEvents from 10 to -1.
After these modifications, please re-run the configuration with the following command:
Once the process completes (it will take a few seconds), it will produce a ROOT file. We will then compare the 1D distribution of different MET flavors in a Z+jets sample (which has no genuine MET).
To generate the plot, run the following commands:
What do you observe looking at the different MET calibration algorithms?
Solution 2.2
Exercise 2.3
Next, we will focus on Type-1 PF MET and study the impact of various uncertainties, including Unclustered, JES, and JER.
To generate the corresponding plot, use the following command:
What do you observe looking at the different sources of MET uncertainty?
Solution 2.3
Key Points
Inaccurate MET estimation can result from sources such as non-linearity in the calorimeter’s response to hadrons, minimum energy thresholds in the calorimeters, and pT thresholds or inefficiencies in track reconstruction. These issues are mitigated through calibration procedures discussed in this exercise.
Type-1 MET is the default MET calibration recommended by CMS.
Type-1 smear MET enhances data-MC agreement, and JME POG advises analysts to assess its impact in their studies.
MET is influenced by uncertainties from all contributing objects, including jets, leptons, photons, and unclustered energy. Systematic variations in the scale and resolution of each component must be propagated to the MET calculation to evaluate their impact on the analysis.
MET performance
Overview
Teaching: 20 min
Exercises: 10 min
Questions
How do we measure the MET performance (i.e. MET scale and MET resolution) ?
Objectives
Learn about MET performance.
Measure the resolution and scale of MET for different MET algorithms and calibrations.
After following the instructions in the setup, make sure you have the CMS environment:
cd$CMSSW_BASE/src/METDAS
cmsenv
MET performance
A well-measured Z boson or photon provides a unique event axis and a precise momentum scale for evaluating MET performance.
To achieve this, the response and resolution of MET are studied in samples where a Z boson decays to a pair of electrons or muons, or in events with an isolated photon.
Such events should have little to no genuine MET.
The MET performance is then assessed by comparing the momentum of the vector boson to that of the hadronic recoil system.
The hadronic recoil system is defined as the vector sum of the transverse momenta of all PF candidates, excluding the vector boson (or its decay products in the case of Z boson decay).
Momentum conservation in the transverse plane imposes
where \(\vec{q}_{T}\) is the transverse momentum of the Z boson, and \(\vec{u}_{T}\) is the hadronic recoil.
Define two components of the hadronic recoil to study the MET response and resolution:
hadronic recoil parallel (\(u_{\parallel}\)) to the boson axis: sensitive to the scale of boson/jets
perpendicular (\(u_{\perp}\)) to the boson axis: sensitive to isotropic effects like pileup
Specifically, the mean of the distribution of the magnitude of \(q_{T} + u_{\parallel}\), is used to estimate the MET response, whereas the RMS of \(q_{T} + u_{\parallel}\) and \(u_{\perp}\) distributions are used to estimate the MET resolution in the axis parallel and perpendicular to the Z boson, respectively.
An example of the \(q_{T} + u_{\parallel}\) and $u_{\perp}$ distributions is shown in the following plots.
Use the distribution of the parallel and perpendicular components of the hadronic recoil to measure the MET scale and resolution
Get the mean of the parallel component to estimate MET scale.
The RMS of the distributions gives the MET resolution in each direction.
Exercise 3.1: MET Scale
In this exercise, we will measure the scale of the “uncorrected” (raw) PF MET as a function of the transverse momentum of the Z boson (pT(Z)).
For a fully calibrated MET object, what behavior would you expect to see in the distribution?
Solution 3.1 (a)
For a fully calibrated MET object, the scale is expected to be approximately 1, indicating an accurate representation of the true missing transverse energy with minimal systematic bias.
Next, measure the MET scale using the Type-1 calibrated MET. Run the following commands:
This command will generate distributions showing the resolution of the parallel ($u_{\parallel}$) and perpendicular ($u_{\perp}$) components of MET with respect to pT(Z) and pileup.
Question 3.2
How does the MET resolution depend on pileup?
Solution 3.2
The MET resolution degrades significantly as pileup increases, with an average deterioration of approximately 4 GeV per additional pileup vertex.
For more detailed insights, refer to the CMS MET paper based on 13 TeV data: CMS-JME-17-001.
Exercise 3.3
Equipped with the ability to evaluate MET performance through scale and resolution, we now aim to compare Type-1 PF MET with Type-1 PUPPI MET. Starting from Run 3, Type-1 PUPPI MET is the default MET algorithm in CMS. In this example, we will examine the performance of PF MET and PUPPI MET by comparing their scale and resolution.
To generate the corresponding plots, use the following command:
Compare the correlation between Type1 PFMET and Puppi MET. What do you observe?
Solution 3.3 (a)
Question 3.3 (b)
Compare the scale and resolution between Type1 PFMET and Puppi MET, especially the resolution as a function of \(N_{vtx}\). What do you observe?
Solution 3.3 (b)
Significantly improved MET resolution as a function of \(N_{vtx}\) compared to PFMET.
PUPPI-MET has 2x smaller degradation in resolution compared to PFMET.
Key Points
The performance of MET is studied in events with a well-measured Z boson (decaying to electrons or muons) or an isolated photon, which should have little to no genuine MET.
Transverse momentum conservation is used to study MET response and resolution along z-axis.
Handling Anomalous MET Events
Overview
Teaching: 20 min
Exercises: 10 min
Questions
What is anomalous MET?
How to identify these events?
Objectives
Learn about anomalous MET
Learn about the Noisy event filters and their implementation.
After following the instructions in the setup, make sure you have the CMS environment:
cd$CMSSW_BASE/src/METDAS
cmsenv
What is anomalous MET?
Anomalous MET refers to events where the measured MET deviates from what is expected due to various factors, such as reconstruction failures, detector malfunctions, or background noise.
These anomalous MET events can arise from:
Detector Issues: Malfunctions or mismeasurements in detectors, such as the electromagnetic calorimeter (ECAL) or hadronic calorimeter (HCAL), leading to spurious energy deposits.
Reconstruction Failures: Errors in reconstructing particle tracks or energy, including issues with jets, leptons, or unclustered energy, that result in inaccurate MET calculations.
Non-collision Origins: Spurious signals from sources unrelated to the particle collision, such as beam-halo particles, cosmic rays, or other environmental factors.
Dead or Malfunctioning Detector Cells: Areas of the detector that fail to register energy deposits correctly, leading to underestimation of the MET.
In such events, the MET value may be much higher than expected and does not reflect true missing energy from invisible particles (like neutrinos or dark matter candidates).
Noisy event filters
To identify false MET, several algorithms have been developed that analyze factors such as timing, pulse shape, and signal topology.
When fake MET is detected, the corresponding events are typically discarded.
These cleaning algorithms, or filters, run in separate processing paths, and the outcome (success or failure) is recorded as a filter decision bit.
Analyzers can use this decision bit to filter out noisy events. These filters are specifically designed to reject events with unusually large MET values caused by spurious signals.
Excercise 4
Noisy event filters (previously called MET Filters) are stored as trigger results, specifically in edm::TriggerResults of the RECO or PAT process. Each MET filter runs in a separate path, and the success or failure of the path is recorded as a filter decision bit. For more information, please refer to the provided link.
In this exercise, we will show how to access the MET Filters in miniAOD. Please run the following commands:
This example accesses the decision bits for the following MET Filters: Beam Halo, HBHE, HBHE (Iso), Ecal Trigger Primitives, EE SuperCluster, Bad Charged Hadron, and Bad PF Muon. A “true” decision means the event was not rejected by the filter. The analyzer used in this example is CMSDAS_MET_Analysis/plugins/CMSDAS_MET_AnalysisExercise5.cc. The printed result will look like this:
Begin processing the 1st record. Run 317626, Event 178458435, LumiSection 134 on stream 0 at 28-Jun-2020 10:39:20.656 CDT
MET Filters decision:
HBHE = 1
HBHE (Iso) = 1
Beam Halo = 1
Ecal TP = 1
EE SuperCluster = 1
Bad Charged Hadron = 1
Bad PF Muon = 1
.......
.......
Question 4
To see the output for a bad event, modify the input file in CMSDAS_MET_Analysis/test/run_CMSDAS_MET_Exercise5_cfg.py.
Comment out the line for the first input file cmsdas_met_METFilters1.root and uncomment the line for the second input file cmsdas_met_METFilters2.root.
Then run the code again. What changes do you notice?
Solution 4
The event does not pass the HBHE filter and for an event to qualify it must pass ALL filters.
Begin processing the 1st record. Run 317182, Event 1740596074, LumiSection 1226 on stream 0 at 06-Jan-2025 08:22:50.035 CST
MET Filters decision:
HBHE = 0
HBHE (Iso) = 1
Beam Halo = 1
Ecal TP = 1
EE SuperCluster = 1
Bad Charged Hadron = 1
Bad PF Muon = 1
.......
.......
Key Points
Large MET in an event may be caused by detector noise, cosmic rays, and beam-halo particles. Such MET with uninteresting origins is called false MET, anomalous MET, or fake MET and can be an indication of problematic event reconstruction.
Events with anomalos mets can be rejected using the Noisy event filters.
For a fully calibrated MET object, the scale is expected to be approximately 1, indicating an accurate representation of the true missing transverse energy with minimal systematic bias.
