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 | ||

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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These preliminary results are superseded in this paper, EPJC 81 (2021) 852.The superseded preliminary plots can be found here. |

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). |

png pdf |
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). |

png pdf |
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). |

png pdf |
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). |

png pdf |
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). |

png pdf |
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. |

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Compact Muon Solenoid LHC, CERN |