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| CMS-SMP-21-006 ; CERN-EP-2022-144 | ||
| Measurements of jet multiplicity and jet transverse momentum in multijet events in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 24 October 2022 | ||
| Eur. Phys. J. C 83 (2023) 742 | ||
| Abstract: Multijet events at large transverse momentum ($ p_{\mathrm{T}} $) are measured at $ \sqrt{s}= $ 13 TeV using data recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The multiplicity of jets with $ p_{\mathrm{T}} > $ 50 GeV that are produced in association with a high-$ p_{\mathrm{T}} $ dijet system is measured in various ranges of the $ p_{\mathrm{T}} $ of the jet with the highest transverse momentum and as a function of the azimuthal angle difference $ \Delta\phi_{1,2} $ between the two highest $ p_{\mathrm{T}} $ jets in the dijet system. The differential production cross sections are measured as a function of the transverse momenta of the four highest $ p_{\mathrm{T}} $ jets. The measurements are compared with leading and next-to-leading order matrix element calculations supplemented with simulations of parton shower, hadronization, and multiparton interactions. In addition, the measurements are compared with next-to-leading order matrix element calculations combined with transverse-momentum dependent parton densities and transverse-momentum dependent parton shower. | ||
| Links: e-print arXiv:2210.13557 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Distribution of $ E_{\mathrm{T}}^{\text{miss}}/\sum{E_{\mathrm{T}}} $ for data and simulated jet production for three regions of $ \Delta\phi_{1,2} $. Shown are the contributions from QCD, $ \mathrm{W}/\mathrm{Z} $ and $ {\mathrm{t}\overline{\mathrm{t}}} $ events. The main contributions of events with large $ E_{\mathrm{T}}^{\text{miss}} $ in the final state come from processes like $ \mathrm{Z} \to \nu \overline{\nu} $ and $ \mathrm{W} \to \ell\nu $. The data (MC prediction) statistical uncertainty is shown as a vertical line (grey shaded bar in the ratio). |
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Figure 2:
Probability matrix (condition number: 3.0) for the jet multiplicity distribution constructed with the MADGRAPH+PY8 sample. The global 3$ \times $3 sectors (separated by the thick black lines) correspond to the $ p_{\mathrm{T1}} $ bins, indicated by the labels in the x (lower) and y (left) axes; the smaller 3$ \times $3 structures correspond to the $ \Delta\phi_{1,2} $ bins, indicated in the leftmost row and lowest column, the x(y) axis of these $ \Delta\phi_{1,2} $ cells corresponds to the jet multiplicity at particle (detector) level. The z axis covers a range from 10$^{-6} $ to 1 indicating the probability of migrations from the particle-level bin to the corresponding detector-level bin. |
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Figure 3:
Probability matrix (condition number: 4.9) for the $ p_{\mathrm{T}} $ of the four leading jets constructed with the MADGRAPH+PY8 sample. The global 4$ \times $4 sectors correspond to the $ p_{\mathrm{T}} $ distributions each of the first four jets, the x axis corresponds to the particle (gen) level and y axis corresponds to the detector (rec) level. The z axis covers a range from 10$^{-6} $ to 1 indicating the probability of migrations from the particle-level bin to the corresponding detector-level bin. |
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Figure 4:
Correlation matrix at the particle-level for the jet multiplicity distribution. It contains contributions from the data and from the limited-size MADGRAPH+PY8 sample. The global 3$ \times $3 sectors (separated by the thick black lines) correspond to the $ p_{\mathrm{T1}} $ bins, indicated by the labels next to the x (lower) and y (left) axes; the smaller 3$ \times $3 structures correspond to the $ \Delta\phi_{1,2} $ bins, indicated in the leftmost row and lowest column, the x and y axes correspond to the jet multiplicity. The z axis covers a range from-1 to 1 indicating the correlations in blue shades and anticorrelations in red shades, the values between-0.1 and 0.1 are represented in white. |
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Figure 5:
Correlation matrix for the particle-level $ p_{\mathrm{T}} $ of the four leading jets. It contains contributions from the data and from the limited-size MADGRAPH+PY8 sample. Here each one of the 4$ \times $4 sectors corresponds to one of the $ p_{\mathrm{T}} $ spectra measured, indicated by the x and y axis labels. The z axis covers a range from-1 to 1 indicating the correlations in blue shades and anticorrelations in red shades, the values between-0.1 and 0.1 are represented in white. |
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Figure 6:
Relative uncertainties for JES, JER, ``Other'' and total statistical uncertainty for the jet multiplicity distribution in bins of $ p_{\mathrm{T1}} $ and $ \Delta\phi_{1,2} $. Here ``Other'' indicates luminosity, pileup, prefiring, and model uncertainty. |
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Figure 7:
Relative uncertainties for JES, JER, ``Other'' and total statistical uncertainty for the $ p_{\mathrm{T}} $ distributions of the four leading jets. Here ``Other'' indicates luminosity, pileup, prefiring, and model uncertainty. |
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Figure 8:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of $ p_{\mathrm{T1}} $ and $ \Delta\phi_{1,2} $. The data are compared with LO predictions of PYTHIA 8, HERWIG++, MADGRAPH+PY8 and MADGRAPH+CA3. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. |
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Figure 8-a:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) for 200 $ < p_{\mathrm{T1}} < $ 400 GeV and 0 $ < \Delta\phi_{1,2} < $ 150$^{\text{o}}$ (left), 150 $ < \Delta\phi_{1,2} < $ 170$^{\text{o}}$ (middle), 170 $ < \Delta\phi_{1,2} < $ 180$^{\text{o}}$ (right). The data are compared with LO predictions of PYTHIA 8, HERWIG++, MADGRAPH+PY8 and MADGRAPH+CA3. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. |
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Figure 8-b:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) for 400 $ < p_{\mathrm{T1}} < $ 800 GeV and 0 $ < \Delta\phi_{1,2} < $ 150$^{\text{o}}$ (left), 150 $ < \Delta\phi_{1,2} < $ 170$^{\text{o}}$ (middle), 170 $ < \Delta\phi_{1,2} < $ 180$^{\text{o}}$ (right). The data are compared with LO predictions of PYTHIA 8, HERWIG++, MADGRAPH+PY8 and MADGRAPH+CA3. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. |
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Figure 8-c:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) for $ p_{\mathrm{T1}} > $ 800 GeV and 0 $ < \Delta\phi_{1,2} < $ 150$^{\text{o}}$ (left), 150 $ < \Delta\phi_{1,2} < $ 170$^{\text{o}}$ (middle), 170 $ < \Delta\phi_{1,2} < $ 180$^{\text{o}}$ (right). The data are compared with LO predictions of PYTHIA 8, HERWIG++, MADGRAPH+PY8 and MADGRAPH+CA3. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. |
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Figure 9:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of $ p_{\mathrm{T1}} $ and $ \Delta\phi_{1,2} $. The data are compared with NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. The shaded bands show the uncertainty from a variation of the renormalization and factorization scales. The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend. |
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Figure 9-a:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) for 200 $ < p_{\mathrm{T1}} < $ 400 GeV and 0 $ < \Delta\phi_{1,2} < $ 150$^{\text{o}}$ (left), 150 $ < \Delta\phi_{1,2} < $ 170$^{\text{o}}$ (middle), 170 $ < \Delta\phi_{1,2} < $ 180$^{\text{o}}$ (right). The data are compared with NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. The shaded bands show the uncertainty from a variation of the renormalization and factorization scales. The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend. |
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Figure 9-b:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) for 400 $ < p_{\mathrm{T1}} < $ 800 GeV and 0 $ < \Delta\phi_{1,2} < $ 150$^{\text{o}}$ (left), 150 $ < \Delta\phi_{1,2} < $ 170$^{\text{o}}$ (middle), 170 $ < \Delta\phi_{1,2} < $ 180$^{\text{o}}$ (right). The data are compared with NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. The shaded bands show the uncertainty from a variation of the renormalization and factorization scales. The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend. |
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Figure 9-c:
Differential cross section as a function of the exclusive jet multiplicity (inclusive for 7 jets) for $ p_{\mathrm{T1}} > $ 800 GeV and 0 $ < \Delta\phi_{1,2} < $ 150$^{\text{o}}$ (left), 150 $ < \Delta\phi_{1,2} < $ 170$^{\text{o}}$ (middle), 170 $ < \Delta\phi_{1,2} < $ 180$^{\text{o}}$ (right). The data are compared with NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. The shaded bands show the uncertainty from a variation of the renormalization and factorization scales. The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend. |
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Figure 10:
Transverse momenta of the four leading jets, with the yellow band representing the total experimental uncertainty. The data are compared with LO (PYTHIA 8) and NLO (MG5_aMC+Py8 ) predictions. The red band in the NLO prediction represents the renormalization and factorization scale uncertainty. |
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Figure 11:
Transverse momentum distributions of the four leading jets. The transverse momentum of the leading and subleading (third and fourth leading) $ p_{\mathrm{T}} $ jets from left to right is shown in the upper (lower) figure. The data are compared with LO predictions of PYTHIA 8, HERWIG++, MADGRAPH+PY8 and MADGRAPH+CA3. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. |
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Figure 11-a:
The transverse momentum of the leading (left) and subleading (right) leading $ p_{\mathrm{T}} $ jets is shown. The data are compared with LO predictions of PYTHIA 8, HERWIG++, MADGRAPH+PY8 and MADGRAPH+CA3. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. |
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Figure 11-b:
The transverse momentum of the third (left) and fourth (right) leading $ p_{\mathrm{T}} $ jets is shown. The data are compared with LO predictions of PYTHIA 8, HERWIG++, MADGRAPH+PY8 and MADGRAPH+CA3. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. |
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Figure 12:
Transverse momentum distributions of the four leading jets. The transverse momentum of the leading and subleading (third and fourth leading) $ p_{\mathrm{T}} $ jets from left to right is shown in the upper (lower) figure. The data are compared with NLO predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The vertical error bars correspond to the statistical uncertainty, and the yellow band to total uncertainty of the measurement. The bands show the uncertainty from a variation of the renormalization and factorization scales. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. |
png pdf |
Figure 12-a:
he transverse momentum of the leading (left) and subleading (right) leading $ p_{\mathrm{T}} $ jets is shown. The data are compared with NLO predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The vertical error bars correspond to the statistical uncertainty, and the yellow band to total uncertainty of the measurement. The bands show the uncertainty from a variation of the renormalization and factorization scales. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. |
png pdf |
Figure 12-b:
The transverse momentum of the third (left) and fourth (right) leading $ p_{\mathrm{T}} $ jets is shown. The data are compared with NLO predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The vertical error bars correspond to the statistical uncertainty, and the yellow band to total uncertainty of the measurement. The bands show the uncertainty from a variation of the renormalization and factorization scales. The predictions are normalized to the measured dijet cross section using the scaling factors shown in the legend. |
| Tables | |
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Table 1:
Description of the simulated samples used in the analysis. |
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Table 2:
The integrated luminosity for each trigger sample considered in this analysis with the $ p_{\mathrm{T}} $ thresholds for HLT (PF) reconstruction. |
| Summary |
| A study of multijet events has been performed in proton-proton collisions at a center-of-mass energy of 13 TeV using data collected with the CMS detector corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The measurements are performed by selecting a dijet system containing a jet with $ p_{\mathrm{T}} > $ 200 GeV and a subleading jet with $ p_{\mathrm{T}} > $ 100 GeV within $ |y| < $ 2.5. For the first time, the jet multiplicity in bins of the leading jet $ p_{\mathrm{T}} $ and the azimuthal angle difference between the two leading jets, $ \Delta\phi_{1,2} $, is measured. The jet multiplicity distributions show that even in the back-to-back region of the dijet system, up to seven jets are measurable. The differential production cross sections are measured for the highest $ p_{\mathrm{T}} $ jets up to the TeV scale. The measurement of the differential cross section as a function of the jet $ p_{\mathrm{T}} $ for the four highest $ p_{\mathrm{T}} $ jets is an important reference for standard model multijet cross section calculations, and especially for the simulations including parton showers for higher jet multiplicity. The measured multiplicity distribution of jets with $ p_{\mathrm{T}} > $ 50 GeV and $ |y| < $ 2.5 is not well described by the leading order MADGRAPH+PYTHIA 8 simulation. However, in the back-to-back region HERWIG++ and MADGRAPH+CASCADE3 provide a better description of the shape of the jet multiplicity. The measured differential cross section as a function of the transverse momentum of the four leading $ p_{\mathrm{T}} $ jets is not described by any of the LO predictions either in normalization or in shape. However, MADGRAPH+CASCADE3 describes the shape of the distribution better than MADGRAPH+PYTHIA 8. The predictions using dijet NLO matrix elements, MG5_AMC+PYTHIA 8(jj) and MG5_AMC+CASCADE3(jj) describe the lower multiplicity regions, as well as the transverse momenta of the leading jets, reasonably well. The three-jet NLO calculation MG5_AMC+CASCADE3(jjj) describes very well the cross section of the third and fourth jets. The measurements presented here provide stringent tests of theoretical predictions in the perturbative high-$ p_{\mathrm{T}} $ and high-jet multiplicity regions. Although the higher jet multiplicities are not described with either parton shower approach, it is interesting that the lower jet multiplicity cross section is described satisfactorily with NLO dijet calculations supplemented with PB -TMDs and TMD parton shower with fewer tunable parameters than in the case with conventional parton showers. The measured observables and its statistical correlations are provided in HEPData [41] as tabulated results. |
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