CMS-SMP-18-003

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

Figures
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	Figure 2: The likelihood scan for the fiducial Z boson production cross section in the $\mathrm{Z} \to \nu \bar{\nu}$ channel ${\mathrm{Z} \to \nu \bar{\nu}}$ .
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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
png pdf	Table 1: Summary of the signal region definition.
png pdf	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.
png pdf	Table 3: Uncertainties assigned to simulation-based processes in SR and CRs.
png pdf	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 $\sigma \mathcal {B}(\mathrm{Z} \to \ell \ell)/\mathcal {B}(\mathrm{Z} \to \nu \bar{\nu})$ .
png pdf	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
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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.
png pdf	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
png pdf	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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