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| CMS-PAS-SMP-17-008 | ||
| Measurement of angular and momentum distributions in multijet and Z+2 jet final states in pp collisions at $\sqrt{s} =$ 8 and 13 TeV | ||
| CMS Collaboration | ||
| July 2020 | ||
| Abstract: We investigate collinear and wide-angle as well as soft and hard radiation in multijet and Z+2 jet events collected in pp collisions at the LHC. We measure the transverse momentum ratio of the two jets and the angular separation between them. The measurements use 19.8 fb$^{-1}$ and 2.29 fb$^{-1}$ of data collected by the CMS experiment at the center-of-mass energies of 8 and 13 TeV, respectively. The data are compared to theoretical predictions from event generators, including parton showers, multiparton interactions, and hadronization. We observe that the collinear and soft regions are in general well described by parton showers, while the regions of large angle separation are often better described by calculations using higher order QCD matrix elements. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, EPJC 81 (2021) 852. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
Four categories of parton radiation. (a) soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3) with a small angle radiation ($\Delta R_{23} < $ 1.0): small ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$, small $\Delta R_{23}$, (b) hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6) with a small angle radiation: large ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$, small $\Delta R_{23}$, (c) soft ${p_{\mathrm {T}}}$ radiation with a large angle radiation ($\Delta R_{23} > $ 1.0): small ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$, large $\Delta R_{23}$, (d) hard ${p_{\mathrm {T}}}$ radiation with a large angle radiation: large ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$, large $\Delta R_{23}$. |
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Figure 2:
Three jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0) |
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Figure 2-a:
Three jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0) |
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Figure 2-b:
Three jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0) |
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Figure 3:
Three jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
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Figure 3-a:
Three jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
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Figure 3-b:
Three jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
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Figure 4:
Three jet selection at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
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Figure 4-a:
Three jet selection at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
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Figure 4-b:
Three jet selection at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
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Figure 5:
Three jet selection at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 5-a:
Three jet selection at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 5-b:
Three jet selection at $\sqrt {s} = $ 13 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
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Figure 6:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
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Figure 6-a:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
png pdf |
Figure 6-b:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
png pdf |
Figure 7:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 7-a:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 7-b:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 8:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from PYTHIA 8 without PS and MPI: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
png pdf |
Figure 8-a:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from PYTHIA 8 without PS and MPI: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
png pdf |
Figure 8-b:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from PYTHIA 8 without PS and MPI: (left) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for small angle radiation ($\Delta R_{23} < $ 1.0), (right) ${p_{\mathrm{T3}} /p_{\mathrm{T2}}} $ for large angle radiation ($\Delta R_{23} > $ 1.0). |
png pdf |
Figure 9:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from PYTHIA 8 without PS and MPI: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 9-a:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from PYTHIA 8 without PS and MPI: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
png pdf |
Figure 9-b:
Z+2-jet selection at $\sqrt {s} = $ 8 TeV and comparison to theoretical predictions from PYTHIA 8 without PS and MPI: (left) $\Delta R_{23}$ for soft ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} < $ 0.3), (right) $\Delta R_{23}$ for hard ${p_{\mathrm {T}}}$ radiation ($ {p_{\mathrm {T3}} /p_{\mathrm {T2}}} > $ 0.6). |
| Tables | |
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Table 1:
Monte Carlo event generators, parton densities, and underlying event tunes used for comparison with measurements. |
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Table 2:
Summary of the phase space selection for the three-jet and Z+2-jet event selection. The anti-$ {k_{\mathrm {T}}}$ jet algorithm distance parameter is $R_{\rm jet} = $ 0.5 for $\sqrt {s} = $ 8 TeV and $R_{\rm jet}=$ 0.4 for $\sqrt {s} = $ 13 TeV. |
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Table 3:
Systematic uncertainties of the measurements (in %). |
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Table 4:
Event classification according to the radiation type |
| Summary |
|
Two kinematic variables are introduced to measure the radiation pattern in multijet events: the transverse momentum ratio of the two jets and the angular separation between them. The variable ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ is used as a measure to distinguish between the soft and the hard ${p_{\mathrm{T}}}$ radiations, $\Delta R_{23}$ classifies events into small and large angle radiation types. Events with three or more energetic jets as well as Z+jet events are selected, and collision data collected at $\sqrt{s} = $ 8 TeV corresponding to an integrated luminosity of 19.8 fb$^{-1}$ are used. Multjet events at $\sqrt{s} = $ 13 TeV corresponding to an integrated luminosity of 2.29 fb$^{-1}$ are also analysed. No significant dependence of the differential cross sections on the center-of-mass energy is observed. In conclusion, wide-angle radiation (large $\delta R$) and hard radiation (large ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$) are well described by the ME calculations (LO4jets+PS), while the PS approaches (LO2jets+PS\ and NLO2jets+PS) fail to describe the wide-angle and hard radiation regions. The collinear region (small $\delta R$) is nicely described by PS calculations (LO2jets+PS\ and NLO2jets+PS) while the ME calculations (LO4jets+PS) show clear deviations from data. In the soft region (small ${p_{\mathrm{T3}} / p_{\mathrm{T2}}}$) the PS approaches describe the measurement also in the wide-angle region (whole range in $\delta R$), while for large ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ higher-order ME contributions are needed in the multijet measurement. The shapes of Z+jet distributions are reasonably well described by all of the tested generators. However, we observe the underestimation of $j_3$ emission for the high ${p_{\mathrm{T3}} /p_{\mathrm{T2}}}$ range both in collinear and wide-angle regions for all of the models used. This measurement illustrates how well the collinear, soft and wide-angle, hard regions are described by different approaches and clearly indicates advantages of different approaches. The different kinematic regions and the different initial state flavor composition could be the reason why the multijet measurements are less well described by theoretical predictions compared to the Z+jet measurements. However, the measurements reported here do not allow for a final conclusion and new dedicated measurements would be needed. Nevertheless, the measurement also illustrates that the tested methods of merging ME with PS calculations are not yet optimal to describe the full phase space region. |
| References | ||||
| 1 | CMS Collaboration | Probing Color Coherence Effects in pp Collisions at $ \sqrt{s}= $ 7 TeV | EPJC 74 (2014) 2901 | CMS-SMP-12-010 1311.5815 |
| 2 | CDF Collaboration | Evidence for color coherence in $ \rm{p\bar{p}} $ collisions at $ \sqrt{s} = $ 1.8 TeV | PRD 50 (1994) 5562 | |
| 3 | D0 Collaboration | Color coherent radiation in multijet events from $ \rm{p\bar{p}} $ collisions at $ \sqrt{s} = $ 1.8 TeV | PLB 414 (1997) 419 | hep-ex/9706012 |
| 4 | S. Catani, F. Krauss, R. Kuhn, and B. R. Webber | QCD matrix elements + parton showers | JHEP 11 (2001) 063 | hep-ph/0109231 |
| 5 | A. Buckley et al. | General-purpose event generators for LHC physics | PR 504 (2011) 145 | 1101.2599 |
| 6 | M. Bengtsson and T. Sjostrand | Coherent parton showers versus matrix elements-implications of PETRA/PEP data | PLB 185 (1987) 435 | |
| 7 | S. Mrenna and P. Richardson | Matching matrix elements and parton showers with HERWIG and PYTHIA | JHEP 05 (2004) 040 | hep-ph/0312274 |
| 8 | CMS Collaboration | The CMS experiment at the CERN LHC | JINST 03 (2008) S08004 | CMS-00-001 |
| 9 | T. Sjostrand et al. | An introduction to pythia 8.2 | CPC 191 (2015) 159 | 1410.3012 |
| 10 | NNPDF Collaboration | Parton distributions with QED corrections | NPB 877 (2013) 290 | 1308.0598 |
| 11 | NNPDF Collaboration | Unbiased global determination of parton distributions and their uncertainties at NNLO and at LO | NPB 855 (2012) 153 | 1107.2652 |
| 12 | CMS Collaboration | Event generator tunes obtained from underlying event and multiparton scattering measurements | EPJC 76 (2016) 155 | CMS-GEN-14-001 1512.00815 |
| 13 | B. Andersson | The Lund model | Camb. Monogr. Part. Phys. NP Cosmol. 7 (1997) 1 | |
| 14 | J. Alwall et al. | The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations | JHEP 07 (2014) 079 | 1405.0301 |
| 15 | J. Alwall et al. | Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions | EPJC 53 (2008) 473 | 0706.2569 |
| 16 | P. Nason | A new method for combining NLO QCD with shower Monte Carlo algorithms | JHEP 11 (2004) 040 | hep-ph/0409146 |
| 17 | S. Frixione, P. Nason, and C. Oleari | Matching NLO QCD computations with Parton Shower simulations: the POWHEG method | JHEP 11 (2007) 070 | 0709.2092 |
| 18 | S. Alioli, P. Nason, C. Oleari, and E. Re | A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX | JHEP 06 (2010) 043 | 1002.2581 |
| 19 | H.-L. Lai et al. | New parton distributions for collider physics | PRD 82 (2010) 074024 | 1007.2241 |
| 20 | S. Alioli et al. | Jet pair production in POWHEG | JHEP 04 (2011) 081 | 1012.3380 |
| 21 | T. Gleisberg et al. | Event generation with SHERPA 1.1 | JHEP 02 (2009) 007 | 0811.4622 |
| 22 | NNPDF Collaboration | Parton distributions for the LHC Run II | JHEP 04 (2015) 040 | 1410.8849 |
| 23 | CMS Collaboration | Particle-flow reconstruction and global event description with the CMS detector | JINST 12 (2017) P10003 | CMS-PRF-14-001 1706.04965 |
| 24 | M. Cacciari, G. P. Salam, and G. Soyez | The anti-$ {k_{\mathrm{T}}} $ jet clustering algorithm | JHEP 04 (2008) 063 | 0802.1189 |
| 25 | M. Cacciari, G. P. Salam, and G. Soyez | FastJet user manual | EPJC 72 (2012) 1896 | 1111.6097 |
| 26 | CMS Collaboration | Pileup removal algorithms | CMS-PAS-JME-14-001 | CMS-PAS-JME-14-001 |
| 27 | CMS Collaboration | The CMS trigger system | JINST 12 (2017) P01020 | CMS-TRG-12-001 1609.02366 |
| 28 | CMS Collaboration | Measurement and QCD analysis of double-differential inclusive jet cross sections in pp collisions at $ \sqrt{s}= $ 8 TeV and cross section ratios to 2.76 and 7 TeV | JHEP 03 (2017) 156 | CMS-SMP-14-001 1609.05331 |
| 29 | CMS Collaboration | Measurement of the double-differential inclusive jet cross section in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | EPJC 76 (2016) 451 | CMS-SMP-15-007 1605.04436 |
| 30 | GEANT4 Collaboration | GEANT4--a simulation toolkit | NIMA 506 (2003) 250 | |
| 31 | G. D'Agostini | A multidimensional unfolding method based on bayes theorem | NIMA 362 (1995) 487 | |
| 32 | T. Adye | Unfolding algorithms and tests using RooUnfold | in PHYSTAT 2011, p. 313 CERN, Geneva | 1105.1160 |
| 33 | A. Hocker and V. Kartvelishvili | SVD approach to data unfolding | NIMA 372 (1996) 469 | hep-ph/9509307 |
| 34 | CMS Collaboration | Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV | JINST 12 (2017) P02014 | CMS-JME-13-004 1607.03663 |
| 35 | J. Butterworth et al. | PDF4LHC recommendations for LHC Run II | JPG 43 (2016) 023001 | 1510.03865 |
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Compact Muon Solenoid LHC, CERN |
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