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| CMS-SMP-22-004 ; CERN-EP-2025-192 | ||
| Measurement of event shape variables using charged particles inside jets in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 19 February 2026 | ||
| Submitted to the Journal of High Energy Physics | ||
| Abstract: Event shape variables, constructed from the four-momenta of the final-state objects in an event, are sensitive to the predictions of quantum chromodynamics in multijet production. A measurement of five event shape variables is presented, using proton-proton collision data collected at a centre-of-mass energy of 13 TeV with the CMS detector during 2016--2018, corresponding to an integrated luminosity of 138 fb$ ^{-1} $. The variables are evaluated using the charged particles inside jets. After correcting for detector effects, their distributions are compared with the results from the predictions from a number of models for multijet production. Overall, there is general agreement between several theoretical predictions and the data. | ||
| Links: e-print arXiv:2602.17509 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
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Figure 1-a:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
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Figure 1-b:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
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Figure 1-c:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
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Figure 1-d:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
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Figure 1-e:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
png pdf |
Figure 1-f:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
png pdf |
Figure 1-g:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
png pdf |
Figure 1-h:
Normalized unfolded distributions of the complement of transverse thrust ($ \tau_{\mathrm{\perp}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+ PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. For each plot the inner grey band and the yellow band represent the statistical and total uncertainties and the lower panel shows the ratio of simulation to data. The error bars corresponding to PYTHIA 8 (in red) and MG5+PYTHIA 8 (in blue) represent their respective variations of the renormalization and factorization scales. |
png pdf |
Figure 2:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 2-a:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 2-b:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 2-c:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 2-d:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 2-e:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 2-f:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 2-g:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 2-h:
Normalized unfolded distributions of the third jet resolution parameter ($ Y_{\mathrm{23}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 3:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 3-a:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 3-b:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 3-c:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 3-d:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 3-e:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 3-f:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 3-g:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 3-h:
Normalized unfolded distributions of total jet broadening ($ B_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 4:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 4-a:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 4-b:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 4-c:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 4-d:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 4-e:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 4-f:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 4-g:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 4-h:
Normalized unfolded distributions of total jet mass ($ \rho_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
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Figure 5:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-a:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-b:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-c:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-d:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-e:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-f:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-g:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
png pdf |
Figure 5-h:
Normalized unfolded distributions of total transverse jet mass ($ \rho^{{\mathrm T}}_{\mathrm{tot}} $) compared with the predictions of PYTHIA 8 (CP5 tune) (red, solid), HERWIG 7 (CH3 tune) (green, dash-dotted) and MG5+PYTHIA 8 (blue, dotted) for different $ {H_{\mathrm{T,2}}} $ ranges. Notations as in Fig. 1. |
| Tables | |
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Table 1:
The $ {H_{\mathrm{T,2}}} $ threshold values, and trigger turn-on points, for the 2016, 2017, and 2018 data sets. |
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Table 2:
Average of the relative uncertainties in the normalized unfolded distributions of the five ESVs. |
| Summary |
| In this study the charged particles inside jets have been used to evaluate five event shape variables. The complement of transverse thrust, total jet mass, third jet resolution parameter, total jet broadening, and total transverse jet mass are studied for different ranges of $ {H_{\mathrm{T,2}}} $, the average $ p_{\mathrm{T}} $ of the leading and the second leading jets in an event. Data from proton-proton collisions at $ \sqrt{s} = $ 13 TeV, collected during 2016--2018, have been used for the study. For each event shape variable, detector effects are corrected using a two-dimensional unfolding procedure in which each ESV is unfolded simultaneously with $ {H_{\mathrm{T,2}}} $. Detailed comparisons of the leading-order predictions of PYTHIA 8 (CP5 tune), MadGraph-5_aMC@NLO+PYTHIA 8 (CP5 tune), and HERWIG 7 (CH3 tune) with data have been made, covering a large phase space. With the increase in the energy of the parton-parton scattering, the agreement improves for PYTHIA 8, remains unchanged for HERWIG 7, and worsens for MadGraph-5_aMC@NLO+PYTHIA 8. Overall, the results indicate that our understanding of the energy flow in an event at different energy scales needs improvement. |
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