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| CMS-SMP-20-007 ; CERN-EP-2021-171 | ||
| Measurement of double-parton scattering in inclusive production of four jets with low transverse momentum in proton-proton collisions at $\sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 29 September 2021 | ||
| JHEP 01 (2022) 177 | ||
| Abstract: A measurement of inclusive four-jet production in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. The transverse momenta of jets within $| \eta | < $ 4.7 reach down to 35, 30, 25, and 20 GeV for the first-, second-, third-, and fourth-leading jet, respectively. Differential cross sections are measured as functions of the jet transverse momentum, jet pseudorapidity, and several other observables that describe the angular correlations between the jets. The measured distributions show sensitivity to different aspects of the underlying event, parton shower, and matrix element calculations. In particular, the interplay between angular correlations caused by parton shower and double-parton scattering contributions is shown to be important. The double-parton scattering contribution is extracted by means of a template fit to the data, using distributions for single-parton scattering obtained from Monte Carlo event generators and a double-parton scattering distribution constructed from inclusive single-jet events in data. The effective double-parton scattering cross section is calculated and discussed in view of previous measurements and of its dependence on the models used to describe the single-parton scattering background. | ||
| Links: e-print arXiv:2109.13822 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
A schematic depiction of inclusive four-jet production through SPS (left) and DPS (right). In the case of SPS, one hard scattering produces the jets $a$ through $d$, whereas two independent hard scatterings create two jets each in the case of DPS. Since the two jet pairs are created independently in a DPS event, they are expected to show different kinematic correlations compared with the four jets originating from an SPS event. |
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Figure 1-a:
A schematic depiction of inclusive four-jet production through SPS. One hard scattering produces the jets $a$ through $d$. |
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Figure 1-b:
A schematic depiction of inclusive four-jet production through DPS. Two independent hard scatterings create two jets each. Since the two jet pairs are created independently, they are expected to show different kinematic correlations compared with the four jets originating from an SPS event. |
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Figure 2:
Comparison of the ${p_{\mathrm {T}}}$ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the leading (upper left), subleading (upper right), third leading (lower left), and fourth leading (lower right) jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 2-a:
Comparison of the ${p_{\mathrm {T}}}$ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 2-b:
Comparison of the ${p_{\mathrm {T}}}$ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the subleading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 2-c:
Comparison of the ${p_{\mathrm {T}}}$ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the third leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 2-d:
Comparison of the ${p_{\mathrm {T}}}$ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the fourth leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 3:
Comparison of the $\eta $ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the leading (upper left), subleading (upper right), third leading (lower left), and fourth leading (lower right) jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 3-a:
Comparison of the $\eta $ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 3-b:
Comparison of the $\eta $ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the subleading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 3-c:
Comparison of the $\eta $ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the third leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 3-d:
Comparison of the $\eta $ spectra from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes, for the fourth leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 4:
Comparison of the ${\Delta \phi _\text {Soft}}$, ${\Delta \phi _\mathrm {3j}^\text {min}}$, ${\Delta Y}$, and ${\phi _{ij}}$ distributions from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region I. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 4-a:
Comparison of the ${\Delta \phi _\text {Soft}}$ distribution from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region I. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 4-b:
Comparison of the ${\Delta \phi _\mathrm {3j}^\text {min}}$ distribution from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region I. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 4-c:
Comparison of the ${\Delta Y}$ distribution from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region I. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 4-d:
Comparison of the ${\phi _{ij}}$ distribution from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region I. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 5:
Comparison of the ${\Delta p_{\text {T,Soft}}}$ and ${\Delta S}$ distributions from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region I and Region II, respectively. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 5-a:
Comparison of the ${\Delta p_{\text {T,Soft}}}$ distribution from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region I. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 5-b:
Comparison of the ${\Delta S}$ distribution from data to different PYTHIA-8 (P8), HERWIG++ (H++), and HERWIG-7 (H7) tunes in Region II. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 6:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the leading (upper left), subleading (upper right), third leading (lower left), and fourth leading (lower right) jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 6-a:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 6-b:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the subleading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 6-c:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the third leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 6-d:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the fourth leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 7:
Comparison of the unfolded $\eta $ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the leading (upper left), subleading (upper right), third leading (lower left), and fourth leading (lower right) jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 7-a:
Comparison of the unfolded $\eta $ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 7-b:
Comparison of the unfolded $\eta $ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the subleading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 7-c:
Comparison of the unfolded $\eta $ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the third leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 7-d:
Comparison of the unfolded $\eta $ spectra of data with different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) models, for the fourth leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 8:
Comparison of the ${\Delta \phi _\text {Soft}}$, ${\Delta \phi _\mathrm {3j}^\text {min}}$, ${\Delta Y}$, and ${\phi _{ij}}$ distributions from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region I. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-a:
Comparison of the ${\Delta \phi _\text {Soft}}$ distribution from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region I. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-b:
Comparison of the ${\Delta \phi _\mathrm {3j}^\text {min}}$ distribution from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region I. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-c:
Comparison of the ${\Delta Y}$ distribution from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region I. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-d:
Comparison of the ${\phi _{ij}}$ distribution from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region I. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 9:
Comparison of the ${\Delta p_{\text {T,Soft}}}$ and ${\Delta S}$ distributions from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region I and Region II, respectively. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 9-a:
Comparison of the ${\Delta p_{\text {T,Soft}}}$ distribution from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region I. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 9-b:
Comparison of the ${\Delta S}$ distribution from data to different KaTie (KT), MadGraph 5_aMC@NLO (MG5), and POWHEG (PW) implementations in Region II. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 10:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the leading (upper left), subleading (upper right), third leading (lower left), and fourth leading (lower right) jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 10-a:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectrum of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 10-b:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectrum of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the subleading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 10-c:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectrum of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the third leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 10-d:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectrum of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the fourth leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 11:
Comparison of the unfolded $\eta $ spectra of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the leading (upper left), subleading (upper right), third leading (lower left), and fourth leading (lower right) jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 11-a:
Comparison of the unfolded $\eta $ spectra of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 11-b:
Comparison of the unfolded $\eta $ spectra of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the subleading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 11-c:
Comparison of the unfolded $\eta $ spectra of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the third leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 11-d:
Comparison of the unfolded $\eta $ spectra of data with different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models, for the fourth leading jet in Region I. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty in the measurement. |
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Figure 12:
Comparison of the distributions in DPS-sensitive observables obtained from data to different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models. All distributions have been determined in Region I, except for the ${\Delta S}$ distribution which has been measured in Region II. All distributions have been normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-a:
Comparison of the distribution in a DPS-sensitive observable obtained from data to different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models. The distributions have been determined in Region I and have been normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-b:
Comparison of the distribution in a DPS-sensitive observable obtained from data to different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models. The distributions have been determined in Region I and have been normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-c:
Comparison of the distribution in a DPS-sensitive observable obtained from data to different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models. The distributions have been determined in Region I and have been normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-d:
Comparison of the distribution in a DPS-sensitive observable obtained from data to different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models. The distributions have been determined in Region I and have been normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-e:
Comparison of the distribution in a DPS-sensitive observable obtained from data to different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models. The distributions have been determined in Region I and have been normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-f:
Comparison of the distribution in a DPS-sensitive observable obtained from data to different SPS+DPS KaTie (KT) and PYTHIA-8 (P8) models. The distributions have been determined in Region II and have been normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 13:
The ${\Delta S}$ distribution obtained from the mixed data sample compared to predictions from the pure DPS sample in PYTHIA-8 (P8) and KaTie (KT). The distributions are normalized to unity. The error bars represent the statistical uncertainty, and the yellow band indicates the total (statistical+systematic) uncertainty on the data. |
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Figure 14:
The results of the template fit for the POWHEG (PW) NLO 2 $\to$ 2 model without the hard MPI removed. The yellow bands represent the total uncertainty of the distribution. The ratio of the scaled MC model and of the total fitted result over the data are shown in the bottom plot. Since the ${\Delta S}$ distribution obtained from the mixed data sample carries a statistical and systematic uncertainty, so does the total fitted sample. The total uncertainty in the ratio is shown on the plot. |
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Figure 15:
Comparison of the values for ${\sigma _\text {eff}}$ extracted from data using different SPS models where events that have generated one or more hard MPI partons with $ {p_{\mathrm {T}}} ^\text {parton} \geq $ 20 GeV, have been removed. The results from four-jet measurements performed at lower center-of-mass energies [20,6,24,51] are shown alongside the newly extracted values. The error bars in each of the values of ${\sigma _\text {eff}}$ represent the total (statistical+systematic) uncertainties. |
| Tables | |
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Table 1:
Systematic uncertainties, along with the statistical and the total uncertainties for the ${p_{\mathrm {T}}}$ spectra, the $\eta $ spectra, and the DPS sensitive observables, in percent. The JES uncertainty leads to asymmetric uncertainties (an upper and a lower error), while all other systematic uncertainties, as well as the statistical uncertainty, are symmetric. |
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Table 2:
Systematic uncertainties, along with the statistical and the total uncertainties for the cross sections of the two phase space regions, along with the observables needed for the extraction of $ {\sigma _\mathrm {A,B}^\mathrm {DPS}} $, in percent. The JES uncertainty leads to asymmetric uncertainties (an upper and a lower error): all other systematic uncertainties, as well as the statistical uncertainty, are symmetric. An additional uncertainty in ${\epsilon _\mathrm {4j}}$ because of possible differences between generator- and detector-level events, is estimated to be 2%. |
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Table 3:
Cross sections obtained from data and from the PYTHIA-8, HERWIG++, and HERWIG-7 models in Region I and Region II of the phase space, where ME stands for matrix element. |
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Table 4:
Cross sections obtained from data and from KaTie, MadGraph 5_aMC@NLO, and POWHEG in region Region I and Region II of the phase space, where ME stands for matrix element. |
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Table 5:
Cross sections obtained from data and from models with an explicit DPS contribution in Region I and Region II of the phase space, where ME stands for matrix element. |
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Table 6:
The values of the DPS fraction $ {f_\mathrm {DPS}} $ extracted from data using different SPS models, along with their statistical and systematic uncertainties. The results are shown for the model where the full tune is used, and for the same models where the hard MPI have been removed. The last column shows the net difference between the two first columns, and is interpreted as the fraction of DPS inherent to the tune. |
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Table 7:
The values of the DPS cross section $ {\sigma _\mathrm {A,B}^\mathrm {DPS}} $ extracted from data using different SPS models, along with their statistical and systematic uncertainties. The results are shown for the model where the full tune is used, and for the same models where the hard MPI have been removed The last column shows the net difference between the two first columns and is interpreted as the amount of DPS inherent to the tune. |
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Table 8:
The values of the effective cross section $ {\sigma _\text {eff}} $ extracted from data using different SPS models, along with their statistical and systematic uncertainties. The results are shown for the model where the full tune is used, and for the same models where the hard MPI have been removed |
| Summary |
|
A study of the inclusive production of four-jet events at low transverse momentum has been presented based on data from proton-proton collisions collected with the CMS detector at a center-of-mass energy of 13 TeV. Various observables sensitive to double-parton scattering (DPS) are studied and values for its effective cross section have been extracted. Models based on leading order (LO) 2 $\to$ 2 matrix elements significantly overestimate the absolute four-jet cross section in the phase space domains studied in this paper. This excess is related to an abundance of low-${p_{\mathrm{T}}}$ and forward jets. The predictions of the absolute cross section generally improve when next-to-leading order (NLO) and/or higher-multiplicity matrix elements are used. The azimuthal angle between the jets with the largest separation in $\eta$, ${\phi_{ij}}$, has a strong discriminating power for different parton-shower approaches and the data favor the angular-ordered and dipole-antenna parton-shower models over those with a ${p_{\mathrm{T}}}$-ordered parton shower. The yield of jet pairs with large rapidity separation ${\Delta Y}$ is, however, overestimated by all models, although models based on NLO and/or higher-multiplicity matrix elements are closer to the data. The distribution of the minimal combined azimuthal angular range of three jets, ${\Delta \phi_\mathrm{3j}^\text{min}} $, also exhibits sensitivity to the parton-shower implementation, with data favoring ${p_{\mathrm{T}}}$-ordered parton showers with the LO 2 $\to$ 2 models for this observable. In the case of models based on NLO and/or higher-multiplicity matrix elements the comparisons are less conclusive. Other observables, such as the azimuthal angle between the two softest jets, ${\Delta \phi_\text{Soft}}$, and their transverse momentum balance, ${\Delta p_{\text{T,Soft}}}$, indicate the need for a DPS contribution in the models to various degrees, as confirmed by the extracted values of ${\sigma_\text{eff}}$. The distribution of the azimuthal angle between the hard and soft jet pairs, ${\Delta S}$, is the least sensitive to the details of the parton-shower modeling, and it is used for the extraction of the effective cross section, ${\sigma_\text{eff}}$. A dependence is observed of the extracted values of ${\sigma_\text{eff}}$ on the model used to describe the SPS contribution. Models based on NLO 2 $\to$ 2 matrix elements yield the smallest ($\sim$7 mb) values of ${\sigma_\text{eff}}$ and need the largest DPS contribution. However, models using a 2 $\to$ 2 matrix element along with older underlying event descriptions and older PDFs, tend to need the smallest DPS contribution. The sensitivity to the underlying event description, parton showers, and the PDFs is observed to be small when including higher-order matrix elements, since both models using the 2 $\to$ 2, 3, 4 matrix elements show agreement with each other. These results demonstrate the need for further development of models to accurately describe final states with multiple jets in phase space regions with large potential DPS contributions. |
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