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CMS-GEN-17-002 ; CERN-EP-2022-005
CMS PYTHIA 8 colour reconnection tunes based on underlying-event data
Eur. Phys. J. C 83 (2023) 571
Abstract: New sets of parameter tunes for two of the colour reconnection models, quantum chromodynamics-inspired and gluon-move, implemented in the PYTHIA 8 event generator, are obtained based on the default CMS PYTHIA 8 underlying-event tune, CP5. Measurements sensitive to the underlying event performed by the CMS experiment at centre-of-mass energies $ \sqrt{s}= $ 7 and 13 TeV, and by the CDF experiment at 1.96 TeV are used to constrain the parameters of colour reconnection models and multiple-parton interactions simultaneously. The new colour reconnection tunes are compared with various measurements at 1.96, 7, 8, and 13 TeV including measurements of the underlying-event, strange-particle multiplicities, jet substructure observables, jet shapes, and colour flow in top quark pair ( $ \mathrm{t} \overline{\mathrm{t}} $) events. The new tunes are also used to estimate the uncertainty related to colour reconnection modelling in the top quark mass measurement using the decay products of $ \mathrm{t} \overline{\mathrm{t}} $ events in the semileptonic channel at 13 TeV.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Rules for colour flow for quark-gluon vertices. Figure is taken from Ref. [5]. Quark-gluon vertices are shown in black with Feynman diagrams and colour connection lines are shown with coloured lines.

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Figure 2:
The schematic description of the result of a typical hadron-hadron collision. The ``toward'' region contains the ``toward-side'' jet, whereas the ``away'' region may contain an ``away-side'' jet.

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Figure 3:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5, CP5-``QCD-inspired'', and CP5-``gluon-move'' using their default parameter settings in Refs. [14,9], are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data where the model uncertainty is also included. The comparisons show that the models do not describe the data and need to be retuned.

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Figure 3-a:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5, CP5-``QCD-inspired'', and CP5-``gluon-move'' using their default parameter settings in Refs. [14,9], are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data where the model uncertainty is also included. The comparisons show that the models do not describe the data and need to be retuned.

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Figure 3-b:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5, CP5-``QCD-inspired'', and CP5-``gluon-move'' using their default parameter settings in Refs. [14,9], are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data where the model uncertainty is also included. The comparisons show that the models do not describe the data and need to be retuned.

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Figure 3-c:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5, CP5-``QCD-inspired'', and CP5-``gluon-move'' using their default parameter settings in Refs. [14,9], are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data where the model uncertainty is also included. The comparisons show that the models do not describe the data and need to be retuned.

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Figure 3-d:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5, CP5-``QCD-inspired'', and CP5-``gluon-move'' using their default parameter settings in Refs. [14,9], are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data where the model uncertainty is also included. The comparisons show that the models do not describe the data and need to be retuned.

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Figure 4:
The pseudorapidity of charged hadrons, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured in $ |\eta| < $ 2 by the CMS experiment at $ \sqrt{s}= $ 13 TeV [23]. The predictions of the tunes CP5, CP5-``QCD-inspired'', and CP5-``gluon-move'' using their default parameter settings in Refs. [14,9], are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data where model uncertainty is also included. The comparisons show that the models need to be retuned in order to have a better agreement with the data.

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Figure 5:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 5-a:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 5-b:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 5-c:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 5-d:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 6:
The pseudorapidity of charged hadrons, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [22]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 7:
The mean charged-particle average transverse momentum as functions of charged-particle multiplicity in the transMAX (left) and transMIN (right) regions, measured by the ATLAS experiment at $ \sqrt{s}= $ 13 TeV [18]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 7-a:
The mean charged-particle average transverse momentum as functions of charged-particle multiplicity in the transMAX (left) and transMIN (right) regions, measured by the ATLAS experiment at $ \sqrt{s}= $ 13 TeV [18]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 7-b:
The mean charged-particle average transverse momentum as functions of charged-particle multiplicity in the transMAX (left) and transMIN (right) regions, measured by the ATLAS experiment at $ \sqrt{s}= $ 13 TeV [18]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 8:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [19]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 8-a:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [19]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 8-b:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [19]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 8-c:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [19]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 8-d:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ (right) densities in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [19]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 9:
The charged-particle (upper left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (upper right) in the transverse region, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, and average transverse momentum in the transverse region as functions of the leading charged particle $ p_{\mathrm{T}} $ (lower left) and of the charged particle multiplicity (lower right), measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [20]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 9-a:
The charged-particle (upper left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (upper right) in the transverse region, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, and average transverse momentum in the transverse region as functions of the leading charged particle $ p_{\mathrm{T}} $ (lower left) and of the charged particle multiplicity (lower right), measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [20]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 9-b:
The charged-particle (upper left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (upper right) in the transverse region, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, and average transverse momentum in the transverse region as functions of the leading charged particle $ p_{\mathrm{T}} $ (lower left) and of the charged particle multiplicity (lower right), measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [20]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 9-c:
The charged-particle (upper left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (upper right) in the transverse region, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, and average transverse momentum in the transverse region as functions of the leading charged particle $ p_{\mathrm{T}} $ (lower left) and of the charged particle multiplicity (lower right), measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [20]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 9-d:
The charged-particle (upper left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (upper right) in the transverse region, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, and average transverse momentum in the transverse region as functions of the leading charged particle $ p_{\mathrm{T}} $ (lower left) and of the charged particle multiplicity (lower right), measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [20]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 10:
The pseudorapidity of charged particles, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, with at least one charged particle in $ |\eta| < $ 2.4, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [31]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 11:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CDF experiment at $ \sqrt{s}= $ 1.96 TeV [21]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 11-a:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CDF experiment at $ \sqrt{s}= $ 1.96 TeV [21]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 11-b:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CDF experiment at $ \sqrt{s}= $ 1.96 TeV [21]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 11-c:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CDF experiment at $ \sqrt{s}= $ 1.96 TeV [21]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 11-d:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions, as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CDF experiment at $ \sqrt{s}= $ 1.96 TeV [21]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 12:
The energy density as a function of pseudorapidity, in two different selections, in MB events (left) and in events with a presence of a hard dijet system (right), measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [34]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 12-a:
The energy density as a function of pseudorapidity, in two different selections, in MB events (left) and in events with a presence of a hard dijet system (right), measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [34]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 12-b:
The energy density as a function of pseudorapidity, in two different selections, in MB events (left) and in events with a presence of a hard dijet system (right), measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [34]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 13:
The pseudorapidity of charged particles, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured by the CMS and TOTEM collaborations at $ \sqrt{s}= $ 8 TeV [32] (left) and measured by the TOTEM collaboration at $ \sqrt{s}= $ 7 TeV [33] (right). The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data. For the CMS-TOTEM measurement, at least one charged particle with $ p_{\mathrm{T}} > $ 0 is required in 5.3 $ < \eta < $ 6.5 or $ -$6.5 $ < \eta < $ $-$5.3. For the TOTEM measurement, at least one charged particle with $ p_{\mathrm{T}} > $ 40 MeV is required in 5.3 $ < |\eta| < $ 6.4.

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Figure 13-a:
The pseudorapidity of charged particles, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured by the CMS and TOTEM collaborations at $ \sqrt{s}= $ 8 TeV [32] (left) and measured by the TOTEM collaboration at $ \sqrt{s}= $ 7 TeV [33] (right). The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data. For the CMS-TOTEM measurement, at least one charged particle with $ p_{\mathrm{T}} > $ 0 is required in 5.3 $ < \eta < $ 6.5 or $ -$6.5 $ < \eta < $ $-$5.3. For the TOTEM measurement, at least one charged particle with $ p_{\mathrm{T}} > $ 40 MeV is required in 5.3 $ < |\eta| < $ 6.4.

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Figure 13-b:
The pseudorapidity of charged particles, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured by the CMS and TOTEM collaborations at $ \sqrt{s}= $ 8 TeV [32] (left) and measured by the TOTEM collaboration at $ \sqrt{s}= $ 7 TeV [33] (right). The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data. For the CMS-TOTEM measurement, at least one charged particle with $ p_{\mathrm{T}} > $ 0 is required in 5.3 $ < \eta < $ 6.5 or $ -$6.5 $ < \eta < $ $-$5.3. For the TOTEM measurement, at least one charged particle with $ p_{\mathrm{T}} > $ 40 MeV is required in 5.3 $ < |\eta| < $ 6.4.

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Figure 14:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 14-a:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 14-b:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 15:
Ratios of particle yields, $ \text{p}/\pi $, as a function of transverse momentum in mininum-bias events, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [39]. The predictions of the CP5 and CP5-CR tunes are compared with CMS data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 16:
Average charged-hadron multiplicity, as a function of the jet $ p_{\mathrm{T}} $, for jets with rapidity $ |y| < $ 1, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [27]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 17:
Distributions of $ F(z) $ for 25 $ < p_{\mathrm{T}}^{\text{jet}} < $ 40 GeV (left) and 400 $ < p_{\mathrm{T}}^{\text{jet}} < $ 500 GeV (right) for jets with pseudorapidity $ |\eta_\text{jet}| < $ 1.2, measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [28]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 17-a:
Distributions of $ F(z) $ for 25 $ < p_{\mathrm{T}}^{\text{jet}} < $ 40 GeV (left) and 400 $ < p_{\mathrm{T}}^{\text{jet}} < $ 500 GeV (right) for jets with pseudorapidity $ |\eta_\text{jet}| < $ 1.2, measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [28]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 17-b:
Distributions of $ F(z) $ for 25 $ < p_{\mathrm{T}}^{\text{jet}} < $ 40 GeV (left) and 400 $ < p_{\mathrm{T}}^{\text{jet}} < $ 500 GeV (right) for jets with pseudorapidity $ |\eta_\text{jet}| < $ 1.2, measured by the ATLAS experiment at $ \sqrt{s}= $ 7 TeV [28]. The predictions of the CP5 and CP5-CR tunes are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 18:
Number of charged particles and $ p_{\mathrm{T}} $ flow in the transverse region of DY events, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV in bins of Z boson $ p_{\mathrm{T}} $ [44]. The plots show the predictions of PYTHIA 8 with the CP5 and CP5-CR tunes, as well as MadGraph-5_aMC@NLO with the CP5 tune compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 18-a:
Number of charged particles and $ p_{\mathrm{T}} $ flow in the transverse region of DY events, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV in bins of Z boson $ p_{\mathrm{T}} $ [44]. The plots show the predictions of PYTHIA 8 with the CP5 and CP5-CR tunes, as well as MadGraph-5_aMC@NLO with the CP5 tune compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 18-b:
Number of charged particles and $ p_{\mathrm{T}} $ flow in the transverse region of DY events, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV in bins of Z boson $ p_{\mathrm{T}} $ [44]. The plots show the predictions of PYTHIA 8 with the CP5 and CP5-CR tunes, as well as MadGraph-5_aMC@NLO with the CP5 tune compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 19:
Distributions of the particle multiplicity in gluon jets (left) and the angle $ \Delta R_g $ between two groomed subjets in inclusive jets (right) measured by the CMS experiment in $ {\mathrm{t}\overline{\mathrm{t}}} $ events at $ \sqrt{s}= $ 13 TeV [53]. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 19-a:
Distributions of the particle multiplicity in gluon jets (left) and the angle $ \Delta R_g $ between two groomed subjets in inclusive jets (right) measured by the CMS experiment in $ {\mathrm{t}\overline{\mathrm{t}}} $ events at $ \sqrt{s}= $ 13 TeV [53]. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 19-b:
Distributions of the particle multiplicity in gluon jets (left) and the angle $ \Delta R_g $ between two groomed subjets in inclusive jets (right) measured by the CMS experiment in $ {\mathrm{t}\overline{\mathrm{t}}} $ events at $ \sqrt{s}= $ 13 TeV [53]. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 20:
Normalised $ \mathrm{t} \overline{\mathrm{t}} $ differential cross section for the pull angle between jets from the W boson in top quark decays, calculated from the charged constituents of the jets, measured by the ATLAS experiment using $ \sqrt{s}= $ 8 TeV data [58] to investigate colour flow. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure 21:
The invariant mass of hadronically decaying top quark candidates for different tune configurations. The coloured band and vertical bars represent the statistical uncertainty in the predictions.

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Figure A1:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure A1-a:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure A1-b:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure A1-c:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure A1-d:
The strange particle production, $ \Lambda $ baryons (left) and $ \mathrm{K^0_S} $ mesons (right), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure A2:
Ratios of particle yields, $ p/\pi $, as a function of transverse momentum in MB events, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [39]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure A2-a:
Ratios of particle yields, $ p/\pi $, as a function of transverse momentum in MB events, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [39]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure A2-b:
Ratios of particle yields, $ p/\pi $, as a function of transverse momentum in MB events, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [39]. The predictions of the CP1 and CP1-CR tunes (upper) and CP2 and CP2-CR tunes (lower) are compared with data. The coloured band and error bars on the data points represent the total experimental uncertainty in the data.

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Figure B1:
Sample histograms showing the range of variation available on the observable histograms are given for CP5-CR1.

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Figure B1-a:
Sample histograms showing the range of variation available on the observable histograms are given for CP5-CR1.

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Figure B1-b:
Sample histograms showing the range of variation available on the observable histograms are given for CP5-CR1.

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Figure B1-c:
Sample histograms showing the range of variation available on the observable histograms are given for CP5-CR1.

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Figure B1-d:
Sample histograms showing the range of variation available on the observable histograms are given for CP5-CR1.

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Figure B2:
The pseudorapidity of charged hadrons, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [22]. The prediction of the CP5-CR1 tune is compared with data. The coloured band represents the tune uncertainties.

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Figure B3:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR1 are compared with data. The coloured band represents the tune uncertainties.

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Figure B3-a:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR1 are compared with data. The coloured band represents the tune uncertainties.

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Figure B3-b:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR1 are compared with data. The coloured band represents the tune uncertainties.

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Figure B3-c:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR1 are compared with data. The coloured band represents the tune uncertainties.

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Figure B3-d:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR1 are compared with data. The coloured band represents the tune uncertainties.

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Figure B4:
The pseudorapidity of charged hadrons, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [22]. The prediction of the CP5-CR2 tune is compared with data. The coloured band represents the tune uncertainties.

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Figure B5:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR2 are compared with data. The coloured band represents the tune uncertainties.

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Figure B5-a:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR2 are compared with data. The coloured band represents the tune uncertainties.

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Figure B5-b:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR2 are compared with data. The coloured band represents the tune uncertainties.

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Figure B5-c:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR2 are compared with data. The coloured band represents the tune uncertainties.

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Figure B5-d:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The predictions of the tunes CP5-CR2 are compared with data. The coloured band represents the tune uncertainties.

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Figure C1:
The pseudorapidity of charged hadrons, $ \mathrm{d}N_{\mathrm{ch}}/\mathrm{d}\eta $, measured in $ |\eta| < $ 2 by the CMS experiment at $ \sqrt{s}= $ 13 TeV [23]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to this observable.

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Figure C2:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.

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Figure C2-a:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.

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Figure C2-b:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.

png pdf
Figure C2-c:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.

png pdf
Figure C2-d:
The charged-particle (left) and $ p_{\mathrm{T}}^{\text{sum}} $ densities (right) in the transMIN (upper) and transMAX (lower) regions as functions of the $ p_{\mathrm{T}} $ of the leading charged particle, $ p_{\mathrm{T}}^{\text{max}} $, measured by the CMS experiment at $ \sqrt{s}= $ 13 TeV [17]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.

png pdf
Figure C3:
The strange particle production, $ \Lambda $ baryons (upper) and $ \mathrm{K^0_S} $ mesons (lower), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.

png pdf
Figure C3-a:
The strange particle production, $ \Lambda $ baryons (upper) and $ \mathrm{K^0_S} $ mesons (lower), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.

png pdf
Figure C3-b:
The strange particle production, $ \Lambda $ baryons (upper) and $ \mathrm{K^0_S} $ mesons (lower), as a function of rapidity, measured by the CMS experiment at $ \sqrt{s}= $ 7 TeV [16]. The red line shows the prediction of CP5-``QCD-inspired,'' where the default value of the ColourReconnection:junctionCorrection parameter is 1.2. The predictions shown with the blue and green lines use 4.0 and 0.05 for the ColourReconnection:junctionCorrection parameter, respectively. These comparisons demonstrate the sensitivity of the ColourReconnection:junctionCorrection parameter to these observables.
Tables

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Table 1:
List of input RIVET routines, centre-of-mass energy values, $ \eta $ ranges, names of distributions, fit ranges, and relative importance of the distributions used in the fits to derive the tunes CP5-CR1 and CP5-CR2.

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Table 2:
The MPI and CR parameter ranges used in the tuning procedure.

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Table 3:
The parameters obtained in the fits of the CP5-CR1 and CP5-CR2 tunes, compared with that of the CP5 tune. The upper part of the table displays the fixed input parameters of the tune, whereas the lower part shows the fitted tune parameters. The number of degrees of freedom ($ N_\mathrm{dof} $) and the goodness of fit divided by $ N_\mathrm{dof} $ are also shown.

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Table 4:
The $ \chi^2 $ values and the numbers of degrees of freedom ($ N_\mathrm{dof} $) for the comparison of $ \mathrm{t} \overline{\mathrm{t}} $ data with the predictions of the different PYTHIA 8 tunes, for the distributions of the charged-particle multiplicity $ \lambda_0^0 $, the angle between the groomed subjets $ \Delta R_g $ at $ \sqrt{s} $ = 13 TeV [53], and the pull angle measured in the ATLAS analysis of the colour flow at 8 TeV [58]. The FSR up and down entries denote variations of the renormalisation scale in the $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $ by factors of 0.5 and 2, respectively.

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Table 5:
The top quark mass ($ m_{\mathrm{t}} $) and W mass ($ m_{\mathrm{W}} $) extracted by a fit to the predictions of the different PYTHIA 8 tunes, along with the differences from the nominal $ m_{\mathrm{t}} $ value ($ \Delta m_{\mathrm{t}} $), $ m_{\mathrm{W}} $ value ($ \Delta m_{\mathrm{W}} $), and $ \Delta m_{\mathrm{t}}^\text{hyb} $ which represents an estimation of the $ m_{\mathrm{t}} $ uncertainty considering the shift in $ m_{\mathrm{W}} $ included with a weight of 0.5. The uncertainties in the $ m_{\mathrm{t}} $ and $ m_{\mathrm{W}} $ values correspond to the uncertainty in the fitted $ m_{\mathrm{t}} $ and $ m_{\mathrm{W}} $.

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Table A1:
List of input RIVET routines, centre-of-mass energy values, $ \eta $ ranges, names of distributions, fit ranges, and relative importance of the distributions used in the fits to derive the tunes CP1-CR1 and CP1-CR2.

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Table A2:
List of input RIVET routines, centre-of-mass energy values, $ \eta $ ranges, names of distributions, fit ranges, and relative importance of the distributions used in the fits to derive the tunes CP2-CR1 and CP2-CR2.

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Table A3:
The parameters obtained in the fits of the CP1-CR1 and CP1-CR2 tunes, compared with the ones of the tune CP1. The upper part of the table displays the fixed input parameters of the tune, while the lower part shows the fitted tune parameters. The number of degrees of freedom ($ N_\mathrm{dof} $) and the goodness of fit divided by the number of degrees of freedom are also shown.

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Table A4:
The parameters obtained in the fits of the CP2-CR1 and CP2-CR2 tunes, compared with the ones of the tune CP2. The upper part of the table displays the fixed input parameters of the tune, while the lower part shows the fitted tune parameters. The number of degrees of freedom ($ N_\mathrm{dof} $) and the goodness of fit divided by the number of degrees of freedom are also shown.

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Table B1:
Parameters of the ``up'' and ``down'' variations of the CP5-CR1 tune.

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Table B2:
Parameters of the ``up'' and ``down'' variations of the CP5-CR2 tune.

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Table C1:
The values of the parameters obtained in the fits of the CP5-CR1-v2.
Summary
New sets of parameters for two of the colour reconnection (CR) models implemented in the PYTHIA 8 event generator, QCD-inspired and gluon-move, are obtained, based on the default CMS PYTHIA 8 tune CP5. Measurements sensitive to underlying-event (UE) contributions performed at hadron-colliders at $ \sqrt{s}= $ 1.96, 7, and 13 TeV are used to constrain the parameters for the CR and for the multiple-parton interactions simultaneously. Various measurements at 1.96, 7, 8, and 13 TeV are used to evaluate the performance of the new tunes. The central values predicted by the new CR tunes for the UE and minimum-bias events describe the data significantly better than the CR models with their default parameters before tuning. The predictions of the new tunes achieve a reasonable agreement in many UE observables, including the ones measured at forward pseudorapidities. However, the models after tuning do not generally perform better than the CP5 tune for the observables presented in this study. Although the new CR tunes presented in this work are not intended to improve the description of the measurements of strange particle multiplicities for $ \Lambda $ baryons and $ \mathrm{K^0_S} $ mesons, we test the new tunes against them. We find that the new CR models, when tuned using only measurements that are sensitive to the UE, do not provide a better description of the distribution of strange particle production as a function of rapidity for $ \Lambda $ baryons. However, we observe that all CP5 tunes, irrespective of the CR model, describe particle production for $ \mathrm{K^0_S} $ as a function of rapidity well. Including these observables in the fits, along with the latest measurements of baryon/meson production, could be beneficial for future tune derivations. The predictions of the new tunes for jet shapes and colour flow measurements done with top quark pair events are also compared with data. All tunes give similar predictions, but none of the tunes describe the jet shape distributions well. Some differences are also observed with respect to the colour flow data, which is particularly sensitive to the early resonance decay option in the CR models. The differences between the predictions using the different tunes observed here indicate that the inclusion of observables, such as the jet pull angle and other jet substructure observables, could be beneficial in tuning studies. A study of the uncertainty in the top quark mass measurement due to CR effects is also presented. The new CR tunes will play a role in the evaluation of systematic uncertainties associated with the modelling of colour reconnection.
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Compact Muon Solenoid
LHC, CERN