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| CMS-SMP-18-003 ; CERN-EP-2020-223 | ||
| Measurement of the Z boson differential production cross section using its invisible decay mode (Z $\to \nu\bar{\nu}$) in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 16 December 2020 | ||
| JHEP 05 (2021) 205 | ||
| Abstract: Measurements of the total and differential fiducial cross sections for the Z boson decaying into two neutrinos are presented at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV. The data were collected by the CMS detector in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. In these measurements, events are selected containing an imbalance in transverse momentum and one or more energetic jets. The fiducial differential cross section is measured as a function of the Z boson transverse momentum. The results are combined with a previous measurement of charged-lepton decays of the Z boson. | ||
| Links: e-print arXiv:2012.09254 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures & Tables | Summary | Additional Figures & Tables | References | CMS Publications |
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| Figures | |
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Figure 1:
Comparison of data and simulation in the single-muon (upper left), single-electron (upper right) CRs and in the SR (lower), before and after performing the simultaneous fit across all the signal and control regions. The hadronic recoil $ {p_{\mathrm {T}}} $ in single lepton events is used as an estimator for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the SR. For the distributions in the CRs, the other backgrounds include top quark, diboson, and QCD multijet events. Ratios of data with the pre-fit expectation (red points) and post-fit prediction (blue points) are shown. The gray band in the ratio panel indicates the post-fit uncertainty after combining all systematic uncertainties. The distribution of the pulls, defined as the difference between data and the post-fit expectation relative to the quadratic sum of the post-fit uncertainties in the expectation, and statistical uncertainty in data, are shown in the lower panel. |
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Figure 1-a:
Comparison of data and simulation in the single-muon (upper left), single-electron (upper right) CRs and in the SR (lower), before and after performing the simultaneous fit across all the signal and control regions. The hadronic recoil $ {p_{\mathrm {T}}} $ in single lepton events is used as an estimator for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the SR. For the distributions in the CRs, the other backgrounds include top quark, diboson, and QCD multijet events. Ratios of data with the pre-fit expectation (red points) and post-fit prediction (blue points) are shown. The gray band in the ratio panel indicates the post-fit uncertainty after combining all systematic uncertainties. The distribution of the pulls, defined as the difference between data and the post-fit expectation relative to the quadratic sum of the post-fit uncertainties in the expectation, and statistical uncertainty in data, are shown in the lower panel. |
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Figure 1-b:
Comparison of data and simulation in the single-muon (upper left), single-electron (upper right) CRs and in the SR (lower), before and after performing the simultaneous fit across all the signal and control regions. The hadronic recoil $ {p_{\mathrm {T}}} $ in single lepton events is used as an estimator for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the SR. For the distributions in the CRs, the other backgrounds include top quark, diboson, and QCD multijet events. Ratios of data with the pre-fit expectation (red points) and post-fit prediction (blue points) are shown. The gray band in the ratio panel indicates the post-fit uncertainty after combining all systematic uncertainties. The distribution of the pulls, defined as the difference between data and the post-fit expectation relative to the quadratic sum of the post-fit uncertainties in the expectation, and statistical uncertainty in data, are shown in the lower panel. |
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Figure 1-c:
Comparison of data and simulation in the single-muon (upper left), single-electron (upper right) CRs and in the SR (lower), before and after performing the simultaneous fit across all the signal and control regions. The hadronic recoil $ {p_{\mathrm {T}}} $ in single lepton events is used as an estimator for $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the SR. For the distributions in the CRs, the other backgrounds include top quark, diboson, and QCD multijet events. Ratios of data with the pre-fit expectation (red points) and post-fit prediction (blue points) are shown. The gray band in the ratio panel indicates the post-fit uncertainty after combining all systematic uncertainties. The distribution of the pulls, defined as the difference between data and the post-fit expectation relative to the quadratic sum of the post-fit uncertainties in the expectation, and statistical uncertainty in data, are shown in the lower panel. |
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Figure 2:
The likelihood scan for the fiducial Z boson production cross section in the $\mathrm{Z} \to \nu \bar{\nu} $ channel $ {\mathrm{Z} \to \nu \bar{\nu}} $. |
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Figure 3:
The measured absolute (left) and normalized (right) fiducial cross sections as a function of $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands around the data points correspond to the total experimental uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 3-a:
The measured absolute (left) and normalized (right) fiducial cross sections as a function of $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands around the data points correspond to the total experimental uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 3-b:
The measured absolute (left) and normalized (right) fiducial cross sections as a function of $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands around the data points correspond to the total experimental uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 4:
Measured $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ absolute cross section for $\mathrm{Z} \to \ell ^+\ell ^-$ (left), and the combination (right) being compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands around the data points correspond to the total experimental uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 4-a:
Measured $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ absolute cross section for $\mathrm{Z} \to \ell ^+\ell ^-$ (left), and the combination (right) being compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands around the data points correspond to the total experimental uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 4-b:
Measured $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ absolute cross section for $\mathrm{Z} \to \ell ^+\ell ^-$ (left), and the combination (right) being compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands around the data points correspond to the total experimental uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 5:
Measured $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ normalized cross section for $\mathrm{Z} \to \ell ^+\ell ^-$ (left), and the combination (right) compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands correspond to the total systematic uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 5-a:
Measured $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ normalized cross section for $\mathrm{Z} \to \ell ^+\ell ^-$ (left), and the combination (right) compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands correspond to the total systematic uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
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Figure 5-b:
Measured $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ normalized cross section for $\mathrm{Z} \to \ell ^+\ell ^-$ (left), and the combination (right) compared with MadGraph 5_aMC@NLO and fixed-order calculations. The shaded bands correspond to the total systematic uncertainty. The vertical bars around the predictions correspond to the combined statistical, PDF, and QCD-scale uncertainties. |
| Tables | |
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Table 1:
Summary of the signal region definition. |
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Table 2:
Experimental uncertainties affecting transfer factors in the analysis that is used to estimate the $ {\mathrm{W} \to \ell \nu} $ background in the SR. The number of W boson events are denoted as $\mathrm{W} _{\mathrm {SR}}$ for the SR and in analogy as $\mathrm{W} _{\mu \nu}$ ($\mathrm{W} _{\mathrm{e} \nu}$) for the single-muon (single-electron) CR. |
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Table 3:
Uncertainties assigned to simulation-based processes in SR and CRs. |
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Table 4:
Cross sections (fb) at large $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ values in the $\mathrm{Z} \to \ell \ell $ and $\mathrm{Z} \to \nu \bar{\nu} $ channels, and their combination. The theoretical predictions from MadGraph 5_aMC@NLO at NLO in QCD and corrected to NLO in EW [9] using the NNPDF 3.0 are also reported. With the exception of the largest $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ bin, the statistical uncertainties in the measurements are much smaller than the systematic uncertainties. Both measurements and predictions correspond to $\sigma \mathcal {B}(\mathrm{Z} \to \ell \ell)$, where $\sigma $ is the total fiducial cross section, $\mathcal {B}$ is the branching fraction, and $\ell $ is a charged lepton. The $\mathrm{Z} \to \nu \bar{\nu} $ measurement corresponds to $\sigma \mathcal {B}(\mathrm{Z} \to \ell \ell)/\mathcal {B}(\mathrm{Z} \to \nu \bar{\nu})$. |
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Table 5:
Cross sections normalized to the total cross section measurements at high $ {{p_{\mathrm {T}}} ^{\mathrm{Z}}} $ values in the $\mathrm{Z} \to \ell \ell $ and $\mathrm{Z} \to \nu \bar{\nu} $ channels, and in their combination. |
| Summary |
| Total, differential, and normalized fiducial cross section measurements for a Z boson produced in association with one or more jets in proton-proton collisions at a center-of-mass energy of 13 TeV at high Z boson ${p_{\mathrm{T}}}$ in the invisible decay channel (Z $\to \nu\bar{nu}$) have been presented. The data collected with the CMS detector at the LHC correspond to an integrated luminosity of 35.9 fb$^{-1}$. The precision of this result is improved by combining the cross section measured with those extracted from charged-lepton final states. The results agree within uncertainties with the theoretical predictions from MadGraph5+MCatNLO, FEWZ and Z+1 jet at next-to-next-to-leading order in perturbative quantum chromodynamics. These are the most precise measurements of the ${{p_{\mathrm{T}}}^{\mathrm{Z}}} $ spectrum to date in proton-proton collisions at 13 TeV. |
| Additional Figures | |
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Additional Figure 1:
The relative statistical and systematic uncertainties from various sources in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {Z}}}$, for the absolute (left) and normalized (right) cross section measurements in the $ {\mathrm {Z}}\to \ell \ell $ (upper), $ {\mathrm {Z}}\to {\nu} {\nu} $ (center), and $ {\mathrm {Z}}\to {\nu} {\nu} +\ell \ell $ (lower) channels. |
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Additional Figure 1-a:
The relative statistical and systematic uncertainties from various sources in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {Z}}}$, for the absolute cross section measurements in the $ {\mathrm {Z}}\to \ell \ell $ channel. |
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Additional Figure 1-b:
The relative statistical and systematic uncertainties from various sources in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {Z}}}$, for the normalized cross section measurements in the $ {\mathrm {Z}}\to \ell \ell $ channel. |
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Additional Figure 1-c:
The relative statistical and systematic uncertainties from various sources in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {Z}}}$, for the absolute cross section measurements in the $ {\mathrm {Z}}\to {\nu} {\nu} $ channel. |
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Additional Figure 1-d:
The relative statistical and systematic uncertainties from various sources in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {Z}}}$, for the normalized cross section measurements in the $ {\mathrm {Z}}\to {\nu} {\nu} $ channel. |
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Additional Figure 1-e:
The relative statistical and systematic uncertainties from various sources in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {Z}}}$, for the absolute cross section measurements in the $ {\mathrm {Z}}\to {\nu} {\nu} +\ell \ell $ channels. |
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Additional Figure 1-f:
The relative statistical and systematic uncertainties from various sources in bins of $ {p_{\mathrm {T}}} ^{{\mathrm {Z}}}$, for the normalized cross section measurements in the $ {\mathrm {Z}}\to {\nu} {\nu} +\ell \ell $ channels. |
| Additional Tables | |
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Additional Table 1:
Systematic uncertainties of the total fiducial cross section in the $ {\mathrm {Z}}\to \ell \ell $, $ {\mathrm {Z}}\to {\nu} {\nu} $, and $ {\mathrm {Z}}\to {\nu} {\nu} +\ell \ell $ channels in units of percent. The data statistical uncertainty is below 0.1%. |
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