CMSSMP21003 ; CERNEP2022178  
Azimuthal correlations in Z+jets events in protonproton collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
28 October 2022  
Eur. Phys. J. C 83 (2023) 722  
Abstract: The production of Z bosons associated with jets is measured in pp collisions at $ \sqrt{s}= $ 13 TeV with data recorded with the CMS experiment at the LHC corresponding to an integrated luminosity of 36.3 fb$ ^{1} $. The multiplicity of jets with transverse momentum $ p_{\mathrm{T}} > $ 30 GeV is measured for different regions of the Z boson's $ p_{\mathrm{T}}(\mathrm{Z}) $, from lower than 10 GeV to higher than 100 GeV. The azimuthal correlation $ \Delta \phi $ between the Z boson and the leading jet, as well as the correlations between the two leading jets are measured in three regions of $ p_{\mathrm{T}}(\mathrm{Z}) $. The measurements are compared with several predictions at leading and nexttoleading orders, interfaced with parton showers. Predictions based on transversemomentum dependent parton distributions and corresponding parton showers give a good description of the measurement in the regions where multiple parton interactions and higher jet multiplicities are not important. The effects of multiple parton interactions are shown to be important to correctly describe the measured spectra in the low $ p_{\mathrm{T}}(\mathrm{Z}) $ regions.  
Links: eprint arXiv:2210.16139 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; 
Figures  
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Figure 1:
The exclusive jet multiplicity distribution before unfolding in three different regions of $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (middle), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower) for the $ \mu^{+} \mu^{} $ channel (left) and the $ \mathrm{e}^+ \mathrm{e}^ $ channel (right). The error bars around the data points represent the statistical uncertainties. 
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Figure 1a:
The exclusive jet multiplicity distribution before unfolding for $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV for the $ \mu^{+} \mu^{} $ channel. The error bars around the data points represent the statistical uncertainties. 
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Figure 1b:
The exclusive jet multiplicity distribution before unfolding for $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV for the $ \mathrm{e}^+ \mathrm{e}^ $ channel. The error bars around the data points represent the statistical uncertainties. 
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Figure 1c:
The exclusive jet multiplicity distribution before unfolding for $ p_{\mathrm{T}}(\mathrm{Z}) $: 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV for the $ \mu^{+} \mu^{} $ channel. The error bars around the data points represent the statistical uncertainties. 
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Figure 1d:
The exclusive jet multiplicity distribution before unfolding for $ p_{\mathrm{T}}(\mathrm{Z}) $: 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV for the $ \mathrm{e}^+ \mathrm{e}^ $ channel. The error bars around the data points represent the statistical uncertainties. 
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Figure 1e:
The exclusive jet multiplicity distribution before unfolding for $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV for the $ \mu^{+} \mu^{} $ channel. The error bars around the data points represent the statistical uncertainties. 
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Figure 1f:
The exclusive jet multiplicity distribution before unfolding for $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV for the $ \mathrm{e}^+ \mathrm{e}^ $ channel. The error bars around the data points represent the statistical uncertainties. 
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Figure 2:
Jet multiplicity in three different regions of $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without MPI are shown. 
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Figure 2a:
Jet multiplicity for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without MPI are shown. 
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Figure 2b:
Jet multiplicity for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without MPI are shown. 
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Figure 2c:
Jet multiplicity for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without MPI are shown. 
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Figure 3:
Jet multiplicity in three different regions of $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 3a:
Jet multiplicity for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 3b:
Jet multiplicity for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 3c:
Jet multiplicity for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 4:
Jet multiplicity in three different regions of $ p_{\mathrm{T}}(\mathrm{Z}) $: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 4a:
Jet multiplicity in three different regions for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 4b:
Jet multiplicity in three different regions for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 4c:
Jet multiplicity in three different regions for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 5:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet in the three $ p_{\mathrm{T}}(\mathrm{Z}) $ bins: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 5a:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 5b:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 5c:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 6:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet in the three $ p_{\mathrm{T}}(\mathrm{Z}) $ bins: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from GENEVA (Z+0 NNLO), MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 6a:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from GENEVA (Z+0 NNLO), MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 6b:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from GENEVA (Z+0 NNLO), MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 6c:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from GENEVA (Z+0 NNLO), MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) are shown. An overall normalization factor of 1.2 is applied to MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO). 
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Figure 7:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet in three $ p_{\mathrm{T}}(\mathrm{Z}) $ bins: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 7a:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 7b:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 7c:
Cross section as a function of $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 8:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets in three $ p_{\mathrm{T}}(\mathrm{Z}) $ regions: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 8a:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 8b:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 8c:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions using MG5_AMC+PY8 ($ \leq $ 2j NLO) with and without multiparton interactions are shown. 
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Figure 9:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets in three $ p_{\mathrm{T}}(\mathrm{Z}) $ regions: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to the MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) predictions. 
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Figure 9a:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to the MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) predictions. 
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Figure 9b:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to the MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) predictions. 
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Figure 9c:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+CA3 (Z+1 NLO), MG5_AMC+CA3 (Z+2 NLO) and GENEVA (Z+0 NNLO) are shown. An overall normalization factor of 1.2 is applied to the MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) predictions. 
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Figure 10:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets in three $ p_{\mathrm{T}}(\mathrm{Z}) $ regions: $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV (upper left), 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV (upper right), $ p_{\mathrm{T}}(\mathrm{Z}) > $ 100 GeV (lower). The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 10a:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 10b:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
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Figure 10c:
Cross section as a function of $ \Delta\phi (j_1j_2) $ between two leading jets for $ p_{\mathrm{T}}(\mathrm{Z}) > $. The error bars on the data points represent the statistical uncertainty of the measurement, and the hatched band shows the total statistical and systematic uncertainties added in quadrature. Predictions from MG5_AMC+PY8 ($ \leq $ 4j LO) and MG5_AMC+CA3 (Z $ \leq $ 3j LO) are shown. Different normalization factors are applied, as described in the text. 
Tables  
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Table 1:
Description of the simulated samples used in the analysis. 
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Table 2:
Particlelevel phase space definition 
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Table 3:
Systematic uncertainties on the unfolded differential cross section 
Summary 
We have measured the Z+jet production cross section in protonproton collisions at the LHC at a centerofmass energy of 13 TeV. The associated jet multiplicity for various regions of the transverse momentum of the Z boson, $ p_{\mathrm{T}}(\mathrm{Z}) $, was measured. At $ p_{\mathrm{T}}(\mathrm{Z}) < $ 10 GeV only about 1% of the events have jets with $ p_{\mathrm{T}} > $ 30 GeV, with nonnegligible cross sections at high jet multiplicity. At 30 $ < p_{\mathrm{T}}(\mathrm{Z}) < $ 50 GeV, most of the events have at least one jet, with a significant tail to higher jet multiplicities. The azimuthal angle $ \Delta\phi (\mathrm{Z} j_1) $ between the Z boson and the leading jet, as well as the azimuthal angle $ \Delta\phi (j_1j_2) $ between the two leading jets, was measured for the three $ p_{\mathrm{T}}(\mathrm{Z}) $ regions. At low $ p_{\mathrm{T}}(\mathrm{Z}) $, the Z boson is only loosely correlated with the jets, but the two leading jets are strongly correlated. At large $ p_{\mathrm{T}}(\mathrm{Z}) $, the Z boson is highly correlated with the leading jet, but the two leading jets are only weakly correlated. The measurement shows that at low $ p_{\mathrm{T}}(\mathrm{Z}) $ the Z boson appears as an electroweak correction to high$ p_{\mathrm{T}} $ jet production, whereas at large $ p_{\mathrm{T}}(\mathrm{Z}) $ the dominant process is Z+jet production. The nexttoleading order (NLO) prediction of MG5_AMC+PY8 ($ \leq $ 2j NLO) with Z+0,1,2 partons, which is merged with the FxFx procedure and supplemented with parton showering (PS) and multiple parton interactions (MPI) from PYTHIA 8, agrees with the measurements. The predictions of MG5_AMC+CA3 (Z+1 NLO) and MG5_AMC+CA3 (Z+2 NLO) using the parton branching method with transversemomentum dependent (PB TMD) parton densities, which do not include MPI effects, and the corresponding PS agree with the measurements in the regions where MPI effects are negligible. The prediction from GENEVA (Z+0 NNLO) using matrix elements at nexttonexttoleading order for Z production, supplemented with resummation, PS and MPI from PYTHIA 8, agrees with the measurements in the low jet multiplicity region. The leading order prediction of MG5_AMC+PY8 ($ \leq $ 4j LO), including merging of jet multiplicities, describes the measurements well. The prediction of MG5_AMC+CA3 (Z $ \leq $ 3j LO) using PB TMD parton densities and PS with merging of jet multiplicities agrees well with the measurements in the regions where MPI is negligible. In summary, Z+jet measurements challenge theoretical predictions; a good agreement can be achieved by including contributions of multiparton interactions, parton showering, parton densities, as well as multijet matrix element merging. The differential measurements provided here help to disentangle the various contributions and illustrate where each contribution becomes important. 
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