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| CMS-PAS-SMP-20-007 | ||
| Study of double-parton scattering in the inclusive production of four jets with low transverse momentum in proton-proton collisions at $\sqrt{s}$ = 13 TeV | ||
| CMS Collaboration | ||
| March 2021 | ||
| Abstract: A study of inclusive four-jet production in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. The transverse momentum of jets within $|\eta| < $ 4.7 reaches down to 35, 30, 25, and 20 GeV for the first, second, third, and fourth leading jet, respectively. Differential cross sections are measured as a function of the jet transverse momentum and pseudorapidity, and of several other observables that exploit angular correlations between the jets. It is found that the measured distributions show sensitivity to different aspects of the underlying event, parton shower, and matrix element calculations. In particular, the interplay between decorrelations 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 of 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. Values of the effective cross section are calculated and discussed in view of earlier measurements and of their dependence on the models used for the single-parton scattering background. | ||
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Links:
CDS record (PDF) ;
inSPIRE record ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| 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 $d$, while two independent hard scatterings create two jets each in the case of DPS. As the two jet pairs are created independently in a DPS event, they are expected to show different kinematic correlations compared to the four jets originating from a 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 (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on 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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 4:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different PYTHIA 8 (P8), HERWIG++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 4-a:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different PYTHIA 8 (P8), HERWIG++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 4-b:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different PYTHIA 8 (P8), HERWIG++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 4-c:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different PYTHIA 8 (P8), HERWIG++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 4-d:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different PYTHIA 8 (P8), HERWIG++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 5-a:
Comparison of the ${\Delta p_{\mathrm {T,soft}}}$ and ${\Delta \mathrm {S}}$ distributions from data to different PYTHIA 8 (P8), HERWIG++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 5-b:
Comparison of the ${\Delta p_{\mathrm {T,soft}}}$ and ${\Delta \mathrm {S}}$ distributions from data to different PYTHIA 8 (P8), HERWIG++ (H++), and HERWIG 7 (H7) tunes. All distributions have been normalized to regions where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 6:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 6-a:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 6-b:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 6-c:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 6-d:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 7:
Comparison of the unfolded $\eta $ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 7-a:
Comparison of the unfolded $\eta $ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 7-b:
Comparison of the unfolded $\eta $ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 7-c:
Comparison of the unfolded $\eta $ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 7-d:
Comparison of the unfolded $\eta $ spectra of data with different KATIE (KT), MadGraph 5 (MG5) and POWHEG (PW) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 8:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-a:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-b:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-c:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 8-d:
Comparison of the ${\Delta \phi _\mathrm {soft}}$, ${\Delta \phi _\mathrm {3j}^\mathrm {min}}$, ${\Delta \mathrm {Y}}$, and ${\phi _{ij}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 9:
Comparison of the ${\Delta p_{\mathrm {T,soft}}}$ and ${\Delta \mathrm {S}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 9-a:
Comparison of the ${\Delta p_{\mathrm {T,soft}}}$ and ${\Delta \mathrm {S}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 9-b:
Comparison of the ${\Delta p_{\mathrm {T,soft}}}$ and ${\Delta \mathrm {S}}$ distributions from data to different KATIE (KT), MadGraph 5 (MG5), and POWHEG (PW) implementations. All distributions have been normalized to regions where a reduced DPS sensitivity is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 10-a:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 10-b:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 10-c:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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Figure 10-d:
Comparison of the unfolded ${p_{\mathrm {T}}}$ spectra of data with different SPS+DPS KATIE (KT) and PYTHIA 8 (P8) models, for the leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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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 (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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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 (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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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 leading (top left), subleading (top right), third leading (bottom left), and fourth leading (bottom right) jet. The error bars and bands are shown similarly to Fig. 2. |
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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 normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-a:
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 normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-b:
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 normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-c:
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 normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-d:
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 normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-e:
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 normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 12-f:
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 normalized to the region where a reduced DPS contribution is expected. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the measurement. |
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Figure 13:
The ${\Delta \mathrm {S}}$ distribution obtained from the mixed data sample compared to predictions from the DPS component in PYTHIA 8 and KATIE. The distributions are normalized to unity. The error bars represent the statistical uncertainty, while the yellow band indicates the total (statistical+systematic) uncertainty on the data. |
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Figure 14:
Comparison of the values for ${\sigma _\mathrm {eff}}$ extracted from data using different SPS models, along with the results from four-jet measurements performed at lower center-of-mass energies [18,5,22,43]. |
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Figure 15:
The results of the template fit for the POWHEG (PW) NLO 2$\to $2 model. The yellow bands represent the total uncertainty of the distribution. In the ratio of the fitted MC model and of the total fitted result over the data are show in the bottom plot. As the ${\Delta \mathrm {S}_\mathrm {DPS}}$ carries a statistical and systematical uncertainty, so does the total fitted sample. The total uncertainty of the ratio is shown on the plot. |
| Tables | |
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Table 1:
Systematic uncertainties, along with the statistical and the total uncertainties, in percent. The JES uncertainty leads to asymmetric errors, while all other systematic uncertainties as well as the statistical uncertainty are symmetric. An additional uncertainty on $\epsilon _{4j}$ due to possible differences between generator and detector level is estimated at 2%. |
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Table 2:
Cross sections obtained from data and from the PYTHIA 8, HERWIG++, and HERWIG 7 models in phase space region I and region II. |
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Table 3:
Cross sections obtained from data and from KATIE, MadGraph 5, and POWHEG in phase space region region I and region II. |
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Table 4:
Cross sections obtained from data and from models with an explicit DPS contribution in phase space region I and region II. |
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Table 5:
The values of the DPS fraction $f_\mathrm {DPS}$, the DPS cross section $\sigma _\mathrm {A,B}^\mathrm {DPS}$, and the effective cross section $\sigma _\mathrm {eff}$ extracted from data using different SPS models, along with their statistical and systematic uncertainties. |
| Summary |
|
A measurement of the inclusive production of four jet at low transverse momentum has been presented based on data from pp collisions collected with the CMS detector at a center-of-mass energy of $\sqrt{s}= $ 13 TeV. Various observables sensitive to double-parton scattering (DPS) have been studied and values for the effective cross section have been extracted. Models based on leading order (LO) 2$\to $2 matrix elements significantly overestimate the absolute four-jet cross section in the phase space domains studied in this note. This excess can be related to an abundance of low-${p_{\mathrm{T}}}$ and forward/backward jets. The predictions of the absolute cross section improve when next-to-leading order (NLO) and/or higher-multiplicity matrix elements are used, but not for all models and for all regions of phase space. The azimuthal-angle difference between the jets with the largest separation in pseudorapidity, $\phi_{ij}$, is found to have a strong discriminating power for different parton shower approaches and results from data favor the angular ordered/dipole antenna parton shower models over those with a ${p_{\mathrm{T}}}$-ordered 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, $\Delta \phi^{\text{min}}_{3j}$, also exhibits sensitivity to the parton shower implementation, with data favoring ${p_{\mathrm{T}}}$-ordered 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 distributions are less conclusive. Other observables, such as the azimuthal-angle difference between the two softest jets, $\Delta \phi_{\text{soft}}$, and their transverse momentum balance, $\Delta p_{\mathrm{T},\text{soft}}$, indicate the need for a DPS contribution in the models to various degrees, as confirmed by the extracted values of ${\sigma_\mathrm{eff}} $. The distribution of the azimuthal-angle separation between the hard and soft jet pairs, $\Delta S$, is found to be the most insensitive to the details of the parton shower modeling and is used for the extraction of the effective cross section, ${\sigma_\mathrm{eff}} $. A strong dependence of the extracted values of ${\sigma_\mathrm{eff}}$ on the model used to the describe the SPS contribution is observed. Models based on NLO 2$\to $2 or 2$\to $3 matrix elements yield the smallest ($\sim $10 mb) values of ${\sigma_\mathrm{eff}} $ and need the largest DPS contribution. Including 4 partons in the matrix element calculation of the SPS model introduces DPS-like correlations in the distributions of DPS-sensitive observables and yields values of ${\sigma_\mathrm{eff}}$ around 15 mb. The largest values of ${\sigma_\mathrm{eff}} $ ($\gtrsim $ 20 mb) are found for the models based on LO 2$\to $2 models with dedicated tunes of the parameters controlling the parton shower and multiple-parton interactions modeling. These results demonstrate the need for further development of models in order to accurately describe final states with multiple jets and the kinematic correlations between the jets. |
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