CMS-SMP-17-002 ; CERN-EP-2017-234 | ||
Measurement of differential cross sections in the $\phi^*$ variable for inclusive $\mathrm{Z}$ boson production in pp collisions at $\sqrt{s} = $ 8 TeV | ||
CMS Collaboration | ||
22 October 2017 | ||
JHEP 03 (2018) 172 | ||
Abstract: Measurements of differential cross sections ${\mathrm{d}}\sigma / {\mathrm{d}}\phi^*$ and double-differential cross sections ${\mathrm{d}}^2\sigma / {\mathrm{d}}\phi^*{\mathrm{d}}{|y|}$ for inclusive Z boson production are presented using the dielectron and dimuon final states. The kinematic observable $\phi^*$ correlates with the dilepton transverse momentum but has better resolution, and $y$ is the dilepton rapidity. The analysis is based on data collected with the CMS experiment at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 19.7 fb$^{-1}$. The normalised cross section $(1 / \sigma)\,{\mathrm{d}}\sigma / {\mathrm{d}}\phi^*$, within the fiducial kinematic region, is measured with a precision of better than 0.5% for $\phi^* < $ 1. The measurements are compared to theoretical predictions and they agree, typically, within few percent. | ||
Links: e-print arXiv:1710.07955 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; |
Figures | Summary | Additional Figures & Tables | References | CMS Publications |
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Figures | |
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Figure 1:
Distributions of dilepton transverse momentum $ {q_{\mathrm {T}}} $ (upper), $\phi ^*$ (middle), and rapidity $ {< y >}$ (lower) in the dielectron (left) and dimuon (right) channels. The points represent the data and the shaded histograms represent the expectations which are based on simulation, except for the contributions from QCD multijet and W+jets events in the dielectron channel, which are obtained from control samples in data. Here "MG+PY6'' refers to a sample produced with MadGraph interfaced with PYTHIA-6 (Z2* tune). The error bars indicate the statistical uncertainties for data and for simulation only. No unfolding procedure has been applied to these distributions. |
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Figure 1-a:
Distribution of the dilepton transverse momentum $ {q_{\mathrm {T}}} $ in the dielectron channel. The points represent the data and the shaded histograms represent the expectations which are based on simulation, except for the contributions from QCD multijet and W+jets events in the dielectron channel, which are obtained from control samples in data. Here "MG+PY6'' refers to a sample produced with MadGraph interfaced with PYTHIA-6 (Z2* tune). The error bars indicate the statistical uncertainties for data and for simulation only. No unfolding procedure has been applied to these distributions. |
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Figure 1-b:
Distribution of the dilepton transverse momentum $ {q_{\mathrm {T}}} $ in the dimuon channel. The points represent the data and the shaded histograms represent the expectations which are based on simulation, except for the contributions from QCD multijet and W+jets events in the dielectron channel, which are obtained from control samples in data. Here "MG+PY6'' refers to a sample produced with MadGraph interfaced with PYTHIA-6 (Z2* tune). The error bars indicate the statistical uncertainties for data and for simulation only. No unfolding procedure has been applied to these distributions. |
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Figure 1-c:
Distribution of the dilepton $\phi ^*$ in the dielectron channel. The points represent the data and the shaded histograms represent the expectations which are based on simulation, except for the contributions from QCD multijet and W+jets events in the dielectron channel, which are obtained from control samples in data. Here "MG+PY6'' refers to a sample produced with MadGraph interfaced with PYTHIA-6 (Z2* tune). The error bars indicate the statistical uncertainties for data and for simulation only. No unfolding procedure has been applied to these distributions. |
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Figure 1-d:
Distribution of the dilepton $\phi ^*$ in the dimuon channel. The points represent the data and the shaded histograms represent the expectations which are based on simulation, except for the contributions from QCD multijet and W+jets events in the dielectron channel, which are obtained from control samples in data. Here "MG+PY6'' refers to a sample produced with MadGraph interfaced with PYTHIA-6 (Z2* tune). The error bars indicate the statistical uncertainties for data and for simulation only. No unfolding procedure has been applied to these distributions. |
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Figure 1-e:
Distribution of the dilepton rapidity $ {< y >}$ in the dielectron channel. The points represent the data and the shaded histograms represent the expectations which are based on simulation, except for the contributions from QCD multijet and W+jets events in the dielectron channel, which are obtained from control samples in data. Here "MG+PY6'' refers to a sample produced with MadGraph interfaced with PYTHIA-6 (Z2* tune). The error bars indicate the statistical uncertainties for data and for simulation only. No unfolding procedure has been applied to these distributions. |
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Figure 1-f:
Distribution of the dilepton rapidity $ {< y >}$ in the dimuon channel. The points represent the data and the shaded histograms represent the expectations which are based on simulation, except for the contributions from QCD multijet and W+jets events in the dielectron channel, which are obtained from control samples in data. Here "MG+PY6'' refers to a sample produced with MadGraph interfaced with PYTHIA-6 (Z2* tune). The error bars indicate the statistical uncertainties for data and for simulation only. No unfolding procedure has been applied to these distributions. |
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Figure 2:
The variation of statistical and systematic uncertainties with $\phi ^*$. The upper row shows the relative uncertainty for the absolute cross section while the lower one shows the relative uncertainty for the normalised cross section. The left plots pertain to the dielectron channel and the right plots pertain to the dimuon channel. The uncertainties from the background, pileup, the electron energy scale or the muon $ {p_{\mathrm {T}}} $ resolution, and from QED-FSR modelling are combined under the label "Other''. |
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Figure 2-a:
The variation of statistical and systematic uncertainties with $\phi ^*$. The plot shows the relative uncertainty for the absolute cross section, and pertains to the dielectron channel. The uncertainties from the background, pileup, the electron energy scale, and from QED-FSR modelling are combined under the label "Other''. |
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Figure 2-b:
The variation of statistical and systematic uncertainties with $\phi ^*$. The plot shows the relative uncertainty for the absolute cross section, and pertains to the dimuon channel. The uncertainties from the background, pileup, the muon $ {p_{\mathrm {T}}} $ resolution, and from QED-FSR modelling are combined under the label "Other''. |
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Figure 2-c:
The variation of statistical and systematic uncertainties with $\phi ^*$. The plot shows the relative uncertainty for the normalised cross section, and pertains to the dielectron channel. The uncertainties from the background, pileup, the electron energy scale, and from QED-FSR modelling are combined under the label "Other''. |
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Figure 2-d:
The variation of statistical and systematic uncertainties with $\phi ^*$. The plot shows the relative uncertainty for the normalised cross section, and pertains to the dimuon channel. The uncertainties from the background, pileup, the muon $ {p_{\mathrm {T}}} $ resolution, and from QED-FSR modelling are combined under the label "Other''. |
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Figure 3:
The variation of statistical and systematic uncertainties, in representative $ {< y >}$ bins, for the ${{\mathrm {d}}}^2 \sigma / {{\mathrm {d}}} \phi ^* {{\mathrm {d}}} {< y >}$ measurements, in the dielectron (left) and dimuon (right) channels. The main components are shown individually while uncertainties from the background, pileup, the electron energy scale or the muon $ {p_{\mathrm {T}}} $ resolution, and from QED-FSR are combined under the label "Other''. |
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Figure 3-a:
The variation of statistical and systematic uncertainties, in representative $ {< y >}$ bins, for the ${{\mathrm {d}}}^2 \sigma / {{\mathrm {d}}} \phi ^* {{\mathrm {d}}} {< y >}$ measurements, in the dielectron channel. The main components are shown individually while uncertainties from the background, pileup, the electron energy scale, and from QED-FSR are combined under the label "Other''. |
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Figure 3-b:
The variation of statistical and systematic uncertainties, in representative $ {< y >}$ bins, for the ${{\mathrm {d}}}^2 \sigma / {{\mathrm {d}}} \phi ^* {{\mathrm {d}}} {< y >}$ measurements, in the dimuon channel. The main components are shown individually while uncertainties from the background, pileup, the muon $ {p_{\mathrm {T}}} $ resolution, and from QED-FSR are combined under the label "Other''. |
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Figure 4:
The variation of statistical and systematic uncertainties, for the normalised double-differential cross section measurements, in representative $ {< y >}$ bins, in the dielectron (left) and dimuon (right) channel. The main components are shown individually while uncertainties from the background, pileup, the electron energy scale or the muon $ {p_{\mathrm {T}}} $ resolution, and from QED-FSR are combined under the label "Other''. |
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Figure 4-a:
The variation of statistical and systematic uncertainties, for the normalised double-differential cross section measurements, in representative $ {< y >}$ bins, in the dielectron channel. The main components are shown individually while uncertainties from the background, pileup, the electron energy scale, and from QED-FSR are combined under the label "Other''. |
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Figure 4-b:
The variation of statistical and systematic uncertainties, for the normalised double-differential cross section measurements, in representative $ {< y >}$ bins, in the dimuon channel. The main components are shown individually while uncertainties from the background, pileup, the muon $ {p_{\mathrm {T}}} $ resolution, and from QED-FSR are combined under the label "Other''. |
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Figure 5:
Comparison of theoretical values for the fiducial cross section with the measured value. The grey error bar represents the total experimental uncertainty for the measured value. The error bars for the theoretical values include the uncertainties due to statistical precision, the PDFs, and the scale choice. The fiducial cross section for FEWZ is obtained by multiplying the total cross section with the acceptance determined from the simulated MadGraph+PYTHIA-6 sample; the uncertainty in the prediction corresponds to that in the FEWZ calculation. |
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Figure 6:
The measured absolute (left) and the normalised (right) cross sections after the combination of dielectron and dimuon channels. The measurement is compared with the predictions from RESBOS, MadGraph and POWHEG interfaced with PYTHIA-6 (Z2* tune), and aMC@NLO and POWHEG interfaced with PYTHIA-8 (CUETP8M1 tune). In the lower panels, the horizontal bands correspond to the experimental uncertainty, while the error bars correspond to the statistical, PDF, and scale uncertainties in the theoretical predictions from RESBOS, POWHEG and aMC@NLO and only the statistical uncertainty for MadGraph. |
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Figure 6-a:
The measured absolute cross section after the combination of dielectron and dimuon channels. The measurement is compared with the predictions from RESBOS, MadGraph and POWHEG interfaced with PYTHIA-6 (Z2* tune), and aMC@NLO and POWHEG interfaced with PYTHIA-8 (CUETP8M1 tune). In the lower panels, the horizontal bands correspond to the experimental uncertainty, while the error bars correspond to the statistical, PDF, and scale uncertainties in the theoretical predictions from RESBOS, POWHEG and aMC@NLO and only the statistical uncertainty for MadGraph. |
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Figure 6-b:
The measured normalised cross section after the combination of dielectron and dimuon channels. The measurement is compared with the predictions from RESBOS, MadGraph and POWHEG interfaced with PYTHIA-6 (Z2* tune), and aMC@NLO and POWHEG interfaced with PYTHIA-8 (CUETP8M1 tune). In the lower panels, the horizontal bands correspond to the experimental uncertainty, while the error bars correspond to the statistical, PDF, and scale uncertainties in the theoretical predictions from RESBOS, POWHEG and aMC@NLO and only the statistical uncertainty for MadGraph. |
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Figure 7:
The combined absolute (left) and the normalised (right) double-differential cross sections as a function of $\phi ^*$ for six ranges of $ {< y >}$. Experimental data is compared with prediction from MadGraph+PYTHIA-6 with Z2* tune. |
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Figure 7-a:
The combined absolute double-differential cross section as a function of $\phi ^*$ for six ranges of $ {< y >}$. Experimental data is compared with prediction from MadGraph+PYTHIA-6 with Z2* tune. |
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Figure 7-b:
The combined normalised double-differential cross section as a function of $\phi ^*$ for six ranges of $ {< y >}$. Experimental data is compared with prediction from MadGraph+PYTHIA-6 with Z2* tune. |
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Figure 8:
The ratio of predicted over measured normalised differential cross sections, $(1 / \sigma) \, {{\mathrm {d}}}^2 \sigma / {{\mathrm {d}}} \phi ^* {{\mathrm {d}}} {< y >}$, as a function of $\phi ^*$ for six bins in $ {< y >}$. The theoretical predictions from MadGraph+PYTHIA-6, POWHEG+PYTHIA-6, POWHEG+PYTHIA-8, RESBOS, and aMC@NLO+PYTHIA-8 are shown. The horizontal band corresponds to the uncertainty in the experimental measurement. The vertical bars are dominated by the statistical uncertainties in the theoretical predictions. |
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Figure 9:
The ratio of ${{\mathrm {d}}}^2 \sigma / {{\mathrm {d}}} \phi ^* {{\mathrm {d}}} {< y >}$ for higher rapidity bins ($ {< y >} > 0.4$) normalised to the values in the most central bin $ {< y >} < 0.4$. The theoretical predictions from MadGraph+PYTHIA-6, POWHEG+PYTHIA-6, POWHEG+PYTHIA-8, RESBOS, and aMC@NLO+PYTHIA-8 are also shown. The uncertainties in the theoretical predictions at large $\phi ^*$ are dominated by the statistical component. |
Summary |
Measurements of the absolute differential cross sections ${\mathrm{d}}\sigma / {\mathrm{d}}\phi^*$ and ${{\mathrm{d}}}^2 \sigma / {{\mathrm{d}}} \phi^* {{\mathrm{d}}}{|y|}$ and the corresponding normalised differential cross sections in the combined dielectron and dimuon channels were presented for the dilepton mass range of 60 to 120 GeV. The measurements are based on a sample of proton-proton collision data at a centre-of-mass energy of 8 TeV collected with the CMS detector at the LHC and correspond to an integrated luminosity of 19.7 fb$^{-1}$. They provide a sensitive test of theoretical predictions. The normalised cross section $(1/\sigma)\,{\mathrm{d}}\sigma / {\mathrm{d}}\phi^*$ is precise at the level of 0.24-1.2%. Theoretical predictions differ from the measurements at the level of 3% (RESBOS), 3% (POWHEG+PYTHIA-8), 4% (MadGraph+PYTHIA-6), 6% (aMC@NLO+PYTHIA-8) and 11% (POWHEG+PYTHIA-6) for $\phi^* < $ 0.1. For higher values of $\phi^*$ the differences are larger: about 9, 8, 5, 10 and 15% respectively. These observations suggest that more advanced calculations of the hard-scattering process reproduce the data better. At the same time, the large difference in theoretical predictions from a single POWHEG sample interfaced with two different versions of PYTHIA and underlying event tunes indicates the combined importance of the showering method, nonperturbative effects and the need for soft-gluon resummation on the predicted values of cross sections reported in this paper. The variation of the cross section with $|y|$ is reproduced by RESBOS within 1%, while MadGraph+PYTHIA-6 differs from the data by 5% comparing the most central and most forward rapidity bins. The predictions from aMC@NLO+PYTHIA-8, POWHEG+PYTHIA-6, and POWHEG+PYTHIA-8 deviate from the measurement by at most 2%. This analysis validates the overall theoretical description of inclusive production of vector bosons at the LHC energies by the perturbative formalism of the standard model. Nevertheless, further tuning of the description of the underlying event is necessary for an accurate prediction of the kinematics of the Drell-Yan production of lepton pairs. |
Additional Figures | |
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Additional Figure 1:
Correlation matrix for the measured single-differential absolute cross section. |
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Additional Figure 2:
Covariance matrix for the measured single-differential absolute cross section. |
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Additional Figure 3:
Correlation matrix for the measured single-differential normalized cross section. |
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Additional Figure 4:
Covariance matrix for the measured single-differential normalized cross section. |
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Additional Figure 5:
Correlation matrix for the measured double-differential absolute cross section as a function of $\phi *$ and $y$. The axis bin numbers refer to the bin numbers as defined in the measurement tables. |
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Additional Figure 6:
Covariance matrix for the measured double-differential absolute cross section as a function of $\phi *$ and $y$. The axis bin numbers refer to the bin numbers as defined in the measurement tables. |
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Additional Figure 7:
Correlation matrix for the measured double-differential normalized cross section as a function of $\phi *$ and $y$. The axis bin numbers refer to the bin numbers as defined in the measurement tables. |
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Additional Figure 8:
Covariance matrix for the measured double-differential normalized cross section as a function of $\phi *$ and $y$. The axis bin numbers refer to the bin numbers as defined in the measurement tables. |
Additional Tables | |
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Additional Table 1:
The measured single-differential absolute cross section measurement as a function of $\phi *$ after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
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Additional Table 2:
The measured single-differential normalized cross section measurement as a function of $\phi *$ after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
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Additional Table 3:
The measured double-differential absolute cross section measurement as a function of $\phi *$ and $y$, for 0.0 $\le |y| < $ 0.4, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
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Additional Table 4:
The measured double-differential absolute cross section measurement as a function of $\phi *$ and $y$, for 0.4 $\le |y| < $ 0.8, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
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Additional Table 5:
The measured double-differential absolute cross section measurement as a function of $\phi *$ and $y$, for 0.8 $\le |y| < $ 1.2, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
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Additional Table 6:
The measured double-differential absolute cross section measurement as a function of $\phi *$ and $y$, for 1.2 $\le |y| < $ 1.6, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
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Additional Table 7:
The measured double-differential absolute cross section measurement as a function of $\phi *$ and $y$, for 1.6 $\le |y| < $ 2.0, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
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Additional Table 8:
The measured double-differential absolute cross section measurement as a function of $\phi *$ and $y$, for 2.0 $\le |y| < $ 2.4, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. |
png pdf |
Additional Table 9:
The measured double-differential normalized cross section measurement as a function of $\phi *$ and $y$, for 0.0 $\le |y| < $ 0.4, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. The bin numbers are used in the covarience plots. |
png pdf |
Additional Table 10:
The measured double-differential normalized cross section measurement as a function of $\phi *$ and $y$, for 0.4 $\le |y| < $ 0.8, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. The bin numbers are used in the covarience plots. |
png pdf |
Additional Table 11:
The measured double-differential normalized cross section measurement as a function of $\phi *$ and $y$, for 0.8 $\le |y| < $ 1.2, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. The bin numbers are used in the covarience plots. |
png pdf |
Additional Table 12:
The measured double-differential normalized cross section measurement as a function of $\phi *$ and $y$, for 1.2 $\le |y| < $ 1.6, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. The bin numbers are used in the covarience plots. |
png pdf |
Additional Table 13:
The measured double-differential normalized cross section measurement as a function of $\phi *$ and $y$, for 1.6 $\le |y| < $ 2.0, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. The bin numbers are used in the covarience plots. |
png pdf |
Additional Table 14:
The measured double-differential normalized cross section measurement as a function of $\phi *$ and $y$, for 2.0 $\le |y| < $ 2.4, after the combination of dielectron and dimuon channels, with the breakdown of uncertainties. The bin numbers are used in the covarience plots. |
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Compact Muon Solenoid LHC, CERN |