Performance of missing transverse momentum reconstruction in events containing a photon and jets collected by CMS during proton-proton collisions at √s = 13 TeV in 2018

Link to DPS note on CDS (CMS DP-2020/031)

Abstract

The performance is presented of the measurement of the missing transverse momentum ($\mathrm{p_{T}^{miss}}$) in events containing a photon and jets collected by the CMS experiment in proton-proton collisions at √s = 13 CMS.TeV in 2018 (End Of Year (EOY) and Prompt reconstruction). The dataset studied corresponds to an integrated luminosity of 60 $\mathrm{fb^{-1}}$, with on average 32 simultaneous “pileup” collisions happening in the same bunch crossing, allowing us to probe events with up to 60 collision vertices. Several estimates of $\mathrm{p_{T}^{miss}}$ are compared, based on the Particle Flow (PF) and Pile Up Per Particle Identification (PUPPI) algorithms. The $\mathrm{p_{T}^{miss}}$ distribution in data is compared to simulation and its response and resolution are also measured.

Introduction

Particles produced in proton-proton collisions that escape detection by the CMS detector can be inferred from the momentum imbalance in the transverse plane to the beam direction, also referred to as the missing transverse momentum ($\mathrm{\vec{p}_{T}^{~miss}}$), whose magnitude is simply denoted as $\mathrm{p_{T}^{miss}}$. These include neutrinos and possibly undiscovered particles such as dark matter candidates. A precise measurement of $\mathrm{\vec{p}_{T}^{~miss}}$ is therefore a crucial aspect in many measurements of standard model processes or searches for new physics.

The resolution of the $\mathrm{p_{T}^{miss}}$ is however very sensitive to detector noise or detector inhomogeneities, as well as to the presence of pileup collisions.

In this note, the performance of the $\mathrm{p_{T}^{miss}}$ reconstructed with various methods is assessed using a sample of events containing one well identified and isolated photon (γ) with a transverse momentum ($\mathrm{q_{T}}$) > 50 CMS.GeV lying within the pseudorapidity range of |η| < 1.44 along with any number of hadronic jets, collected with a set of prescaled or unprescaled single photon triggers. Data events are weighted according to the prescale factor of the trigger. The dataset recorded by the CMS experiment in proton-proton collisions at √s = 13 CMS.TeV in 2018 (End Of Year (EOY) and Prompt reconstruction) corresponding to an integrated luminosity of 60 $\mathrm{fb^{-1}}$ is used for this study. The $\mathrm{p_{T}^{miss}}$ distribution in data is compared to simulation and its response and resolution are also estimated after subtracting the photon $\mathrm{q_{T}}$ from the momentum balance.

The events selected for this study are also required to pass a set of filters that are designed to reject events containing anomolous $\mathrm{p_{T}^{miss}}$ that can be attributed to detector noise or misreconstruction, as described in [1], and more recently studied in [2].

Reconstruction of $\mathrm{p_{T}^{miss}}$

Four $\mathrm{p_{T}^{miss}}$ estimates are studied :

  • Raw PF $\mathrm{p_{T}^{miss}}$ : the negative vectorial $\mathrm{p_{T}}$ sum of all particles reconstructed with the particle flow (PF) algorithm [1].
  • Type-1 PF $\mathrm{p_{T}^{miss}}$ with XY corrections : the same as Raw PF $\mathrm{p_{T}^{miss}}$ , replacing the vectorial $\mathrm{p_{T}}$ sum of all PF particles clustered in jets with $\mathrm{p_{T}}$ >15 CMS.GeV by the corresponding jet $\mathrm{p_{T}}$, after the jet energy corrections are applied. A slight inhomogeneity of the detector response (and in particular of the tracker) results in a gradual shift of the average x and y component of $\mathrm{p_{T}^{miss}}$ with increasing pileup, introducing a modulation in the distribution of the azimuthal angle (φ) of PF $\mathrm{p_{T}^{miss}}$ . An additional correction, referred to as the XY correction, is therefore applied to mitigate this effect.
  • Raw PUPPI $\mathrm{p_{T}^{miss}}$ : the negative vectorial sum of the weighted $\mathrm{p_{T}}$ of all PF particles, where the weights (between 0 and 1) are related to their likelihood to come from the primary vertex (PV) [2]. In particular, all charged particles associated to the PV (to another vertex) are assigned a weight of 1 (0).
  • Type-1 PUPPI $\mathrm{p_{T}^{miss}}$ : The same as Raw PUPPI $\mathrm{p_{T}^{miss}}$, replacing the vectorial $\mathrm{p_{T}}$ sum of all PF particles clustered in jets with $\mathrm{p_{T}}$ >15 CMS.GeV by the corresponding jet $\mathrm{p_{T}}$, after the jet energy corrections are applied. The XY corrections are not required for PUPPI $\mathrm{p_{T}^{miss}}$ due to the better pileup mitigation of the PUPPI $\mathrm{p_{T}^{miss}}$ algorithm.

Measurement of the $\mathrm{p_{T}^{miss}}$ response and resolution

The same method as described in [3] is used. The selected sample is strongly enriched in events from the γ+jets process where no genuine $\mathrm{p_{T}^{miss}}$ is expected.

In such events, the hadronic recoil ($\mathrm{\vec{u}_{T}}$) is defined through the following equation : $\mathrm{\vec{q_{T}} + \vec{u_{T}} + \vec{p_{T}^{miss}} = \vec{0}}$

Since the response (resolution) of the transverse momentum of the photon $\mathrm{q_{T}}$ is much better measured (is much smaller) than that of $\mathrm{u_{T}}$, the latter provides a direct proxy for the $\mathrm{p_{T}^{miss}}$ response (resolution). The $\mathrm{\vec{u_{T}}}$ can be projected into a component parallel (perpendicular) to $\mathrm{q_{T}}$, denoted as $\mathrm{u_{\parallel}}$ ($\mathrm{u_{perp}}$).

The $\mathrm{p_{T}^{miss}}$ response is then defined as the average of the distribution of $\mathrm{-u_{||}/q_{T}}$ ($\mathrm{-&amp;lt;u_{||}&amp;gt; / &amp;lt;q_{T}&amp;gt;}$) while its resolution can be quantified through the RMS of the $\mathrm{u_{\parallel}+q_{T}}$ and $\mathrm{u_{\perp}}$ distributions ($\mathrm{\sigma(u_{\parallel}+q_{T})}$, $\mathrm{\sigma(u_{\perp})}$), corrected for the corresponding $\mathrm{p_{T}^{miss}}$ response.

Summary

Several estimates of $\mathrm{p_{T}^{miss}}$ are studied in events containing a photon and jets in the dataset collected by the CMS experiment in proton-proton collisions at √s = 13 CMS.TeV in 2018 (EOY and Prompt reconstruction).

The distributions for Type-1 & XY corrected PF $\mathrm{p_{T}^{miss}}$ and Type-1 corrected PUPPI $\mathrm{p_{T}^{miss}}$ in data and simulation are found to agree within the uncertainties.

The responses of PF $\mathrm{p_{T}^{miss}}$ and PUPPI $\mathrm{p_{T}^{miss}}$, when applying the Type-1 corrections, are found to be close to unity. This indicates the importance of propagating the jet energy corrections to the $\mathrm{p_{T}^{miss}}$ calculation (Type-1 corrections) to achieve a response close to unity.

The better pileup mitigation of the PUPPI $\mathrm{p_{T}^{miss}}$ algorithm is found to result in a better resolution for PUPPI $\mathrm{p_{T}^{miss}}$ compared to PF $\mathrm{p_{T}^{miss}}$.

Bibliography

[1] CMS Collaboration, “Performance of missing transverse momentum reconstruction in proton-proton collisions at √s =13 CMS.TeV using the CMS detector”, JINST 14, P07004 (2019), arXiv:1903.06078.

[2] CMS Collaboration, “Mitigation of anomalous missing transverse momentum measurements in data collected by CMS at √s = 13 CMS.TeV during the LHC Run 2”, CMS-DP-2020-018, https://cds.cern.ch/record/2714938.

[3] CMS Collaboration, “Particle-flow reconstruction and global event description with the CMS detector”, JINST 12 (2017) P10003, arXiv:1706.04965.

[4] CMS Collaboration, “Pileup mitigation at CMS in 13 CMS.TeV data”, submitted to JINST (2019), arXiv:2003.00503.

Figures

Event kinematics for γ+jet events in the transverse plane. $\mathrm{\vec{q}_{T}}$ is the transverse momentum of the photon, $\mathrm{\vec{p}_{T}^{~miss}}$ is the missing transverse momentum, $\mathrm{\vec{u}_{T}}$ is the hadronic recoil in the transverse plane, $\mathrm{u_{\parallel}}$ ($\mathrm{u_{\perp}}$) is the parallel (perpendicular) component of the hadronic recoil with respect to the direction of the photon transverse momentum.

Distribution of PF $\mathrm{p_{T}^{miss}}$ with Type-1 and XY corrections in γ+jets events for data (black points) and simulation (colored histograms). The shaded region corresponds to the total uncertainty on the simulation.

The bottom panel shows the ratio between the data and simulation along with the uncertainties corresponding to the statistical uncertainty of the simulation (Sim. stat.), the jet energy scale (JES) and the momentum scale of particles not clustered in jets (Uncl. $\mathrm{p_{T}^{miss}}$) that make up the total uncertainty on the simulation.

The data and the simulation are compatible within the uncertainties, as seen from the bottom panel.

Distribution of PUPPI $\mathrm{p_{T}^{miss}}$ with Type-1 corrections in γ+jets events for data (black points) and simulation (colored histograms). The shaded region corresponds to the total uncertainty on the simulation.

The bottom panel shows the ratio between the data and simulation along with the uncertainties corresponding to the statistical uncertainty of the simulation (Sim. stat.), the jet energy scale (JES) and the momentum scale of particles not clustered in jets (Uncl. $\mathrm{p_{T}^{miss}}$) that make up the total uncertainty on the simulation.

The data and the simulation are compatible within the uncertainties, as seen from the bottom panel.

The response of $\mathrm{p_{T}^{miss}}$ as a function of the transverse momentum of the photon $\mathrm{q_{T}}$ for γ+jets events, for each of the different $\mathrm{p_{T}^{miss}}$ estimates introduced.

The figure illustrates in particular the importance of propagating the jet energy corrections to the $\mathrm{p_{T}^{miss}}$ calculation (Type-1 corrections) to achieve a response close to unity.

The difference in the response between the Raw PF $\mathrm{p_{T}^{miss}}$ and the Raw PUPPI $\mathrm{p_{T}^{miss}}$ can be attributed to the fact that the $\mathrm{p_{T}}$ of particles associated with pileup vertices are included during the reconstruction of PF $\mathrm{p_{T}^{miss}}$, while the PUPPI $\mathrm{p_{T}^{miss}}$ can be affected by the non-inclusion of particles misidentified to originate from pileup vertices. This also explains the difference in the low $\mathrm{q_{T}}$ region for the PF $\mathrm{p_{T}^{miss}}$ and the PUPPI $\mathrm{p_{T}^{miss}}$ after the application of the Type-1 corrections.

The resolution of the parallel component of the recoil $\mathrm{u_{\parallel}+q_{T}}$ as a function of the number of vertices in the event for γ+jets events for Type-1 & XY corrected PF $\mathrm{p_{T}^{miss}}$ (blue) and Type-1 corrected PUPPI $\mathrm{p_{T}^{miss}}$ (green). To compare resolutions for the different types of $\mathrm{p_{T}^{miss}}$, the resolution is corrected for the differences observed in the response.

The pileup dependency of the PUPPI $\mathrm{p_{T}^{miss}}$ resolution is much weaker than the PF $\mathrm{p_{T}^{miss}}$ , resulting in a better resolution for ≥ 10 reconstructed vertices. However, at a lower number of vertices, the σ($\mathrm{u_{\parallel}}$), becomes worse for the PUPPI $\mathrm{p_{T}^{miss}}$ since some low $\mathrm{p_{T}}$ particles originating from the leading vertex can be mistakenly assumed to originate from pileup.

The resolution of the perpendicular component of the recoil $\mathrm{u_{\perp}}$ as a function of the number of vertices in the event for γ+jets events for Type-1 & XY corrected PF $\mathrm{p_{T}^{miss}}$ (blue) and Type-1 corrected PUPPI $\mathrm{p_{T}^{miss}}$ (green). To compare resolutions for the different types of $\mathrm{p_{T}^{miss}}$, the resolution is corrected for the differences observed in the response.

The pileup dependency of the PUPPI $\mathrm{p_{T}^{miss}}$ resolution is much weaker than the PF $\mathrm{p_{T}^{miss}}$ , resulting in a better resolution for ≥ 10 reconstructed vertices. However, at a lower number of vertices, the σ($\mathrm{u_{\parallel}}$), becomes worse for the PUPPI $\mathrm{p_{T}^{miss}}$ since some low $\mathrm{p_{T}}$ particles originating from the leading vertex can be mistakenly assumed to originate from pileup.

The resolution of the parallel component of the recoil $\mathrm{u_{\parallel}+q_{T}}$ as a function of the transverse momentum of the photon $q_{T}$ for γ+jets events for Type-1 & XY corrected PF $\mathrm{p_{T}^{miss}}$ (blue) and Type-1 corrected PUPPI $\mathrm{p_{T}^{miss}}$ (green). To compare resolutions for the different types of $\mathrm{p_{T}^{miss}}$, the resolution is corrected for the differences observed in the response.

The better pileup mitigation of the PUPPI $\mathrm{p_{T}^{miss}}$ algorithm results in a better resolution.

The resolution of the perpendicular component of the recoil $\mathrm{u_{\perp}}$ as a function of the transverse momentum of the photon $q_{T}$ for γ+jets events for Type-1 & XY corrected PF $\mathrm{p_{T}^{miss}}$ (blue) and Type-1 corrected PUPPI $\mathrm{p_{T}^{miss}}$ (green). To compare resolutions for the different types of $\mathrm{p_{T}^{miss}}$, the resolution is corrected for the differences observed in the response.


The better pileup mitigation of the PUPPI $\mathrm{p_{T}^{miss}}$ algorithm results in a better resolution.

Topic attachments
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PDFpdf EventKinematics.pdf r1 manage 16.4 K 2020-07-09 - 14:27 SaranyaGhosh  
PNGpng EventKinematics.png r1 manage 14.4 K 2020-07-09 - 14:27 SaranyaGhosh  
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PNGpng PFMET_Type1XY.png r1 manage 71.2 K 2020-07-09 - 14:26 SaranyaGhosh  
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