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Compact Muon Solenoid
LHC, CERN

CMS-GEN-19-001 ; CERN-EP-2020-182
Development and validation of HERWIG 7 tunes from CMS underlying-event measurements
Eur. Phys. J. C 81 (2021) 312
Abstract: This paper presents a new set of parameters ("tunes'') for the underlying-event model of the HERWIG 7 event generator. These parameters control the description of multiple-parton interactions (MPI) and colour reconnection in HERWIG 7, and are obtained from a fit to minimum-bias data collected by the CMS experiment at $\sqrt{s}=$ 0.9, 7, and 13 TeV. The tunes are based on the NNPDF 3.1 next-to-next-to-leading-order parton distribution function (PDF) set for the parton shower, and either a leading-order or next-to-next-to-leading-order PDF set for the simulation of MPI and the beam remnants. Predictions utilizing the tunes are produced for event shape observables in electron-positron collisions, and for minimum-bias, inclusive jet, top quark pair, and Z and W boson events in proton-proton collisions, and are compared with data. Each of the new tunes describes the data at a reasonable level, and the tunes using a leading-order PDF for the simulation of MPI provide the best description of the data.
Figures & Tables Summary References CMS Publications
Figures

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Figure 1:
Illustration of the different $\phi $ regions, with respect to the leading object in an event, used to probe the properties of the UE in measurements.

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Figure 2:
The normalized ${{\mathrm {d} N_{\mathrm{CH}}/\mathrm {d} \eta}}$ of charged hadrons as a function of $\eta $ [27]. CMS MB data are compared with SoftTune and the CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 3:
The normalized ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (upper) and ${N_{\mathrm{CH}}}$ (lower) density distributions in the transMin (left) and transMax (right) regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 3-a:
The normalized ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 3-b:
The normalized ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 3-c:
The normalized ${N_{\mathrm{CH}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 3-d:
The normalized ${N_{\mathrm{CH}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 4:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (upper) and ${N_{\mathrm{CH}}}$ (lower) density distributions in the transMin (left) and transMax (right) regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [23]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 4-a:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [23]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 4-b:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [23]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 4-c:
The ${N_{\mathrm{CH}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [23]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 4-d:
The ${N_{\mathrm{CH}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [23]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 5:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the transverse regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track jet, ${{p_{\mathrm {T}}} ^{\mathrm {jet}}}$ [25]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 5-a:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transverse regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track jet, ${{p_{\mathrm {T}}} ^{\mathrm {jet}}}$ [25]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 5-b:
The ${N_{\mathrm{CH}}}$ density distributions in the transverse regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track jet, ${{p_{\mathrm {T}}} ^{\mathrm {jet}}}$ [25]. CMS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 6:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (upper) and ${N_{\mathrm{CH}}}$ (lower) density distributions in the transMin (left) and transMax (right) regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [31]. CDF MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 6-a:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [31]. CDF MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 6-b:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [31]. CDF MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 6-c:
The ${N_{\mathrm{CH}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [31]. CDF MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 6-d:
The ${N_{\mathrm{CH}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [31]. CDF MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 7:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (upper) and ${N_{\mathrm{CH}}}$ (lower) density distributions in the transMin (left) and transMax (right) regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH1 and CH3 tunes, and from PYTHIA 8, with the CP1 and CP5 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 7-a:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH1 and CH3 tunes, and from PYTHIA 8, with the CP1 and CP5 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 7-b:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH1 and CH3 tunes, and from PYTHIA 8, with the CP1 and CP5 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 7-c:
The ${N_{\mathrm{CH}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH1 and CH3 tunes, and from PYTHIA 8, with the CP1 and CP5 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 7-d:
The ${N_{\mathrm{CH}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH1 and CH3 tunes, and from PYTHIA 8, with the CP1 and CP5 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 8:
The normalized ${{\mathrm {d} N_{\mathrm{CH}}/\mathrm {d} \eta}}$ of charged hadrons as a function of $\eta $ [27]. CMS MB data are compared with the predictions from HERWIG 7, with the CH1 and CH3 tunes, and from PYTHIA 8, with the CP1 and CP5 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 9:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (upper) and ${N_{\mathrm{CH}}}$ (lower) density distributions in the transMin (left) and transMax (right) regions, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties. The grey-shaded band corresponds to the envelope of the "up'' and "down'' variations of the CH3 tune.

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Figure 9-a:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties. The grey-shaded band corresponds to the envelope of the "up'' and "down'' variations of the CH3 tune.

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Figure 9-b:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties. The grey-shaded band corresponds to the envelope of the "up'' and "down'' variations of the CH3 tune.

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Figure 9-c:
The ${N_{\mathrm{CH}}}$ density distributions in the transMin region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties. The grey-shaded band corresponds to the envelope of the "up'' and "down'' variations of the CH3 tune.

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Figure 9-d:
The ${N_{\mathrm{CH}}}$ density distributions in the transMax region, as a function of the ${p_{\mathrm {T}}}$ of the leading track, ${{p_{\mathrm {T}}} ^{\mathrm {max}}}$ [24]. CMS MB data are compared with the predictions from HERWIG 7, with the CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties. The grey-shaded band corresponds to the envelope of the "up'' and "down'' variations of the CH3 tune.

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Figure 10:
The normalized ${{\mathrm {d} N_{\mathrm{CH}}/\mathrm {d} \eta}}$ of charged hadrons as a function of $\eta $ [27]. CMS MB data are compared with the predictions from HERWIG 7, with the CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties. The grey-shaded band corresponds to the envelope of the "up'' and "down'' variations of the CH3 tune.

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Figure 11:
Normalized differential cross sections for $\mathrm{e^{-}} \mathrm{e^{+}}$ [32] as a function of the variables $T$ (upper left), ${T_{\mathrm {major}}}$ (upper right), $O$ (lower left), and $S$ (lower right) for ALEPH data at $ {\sqrt {s}} = $ 91.2 GeV. ALEPH data are compared with the predictions from HERWIG 7 using the SoftTune and CH tunes. The coloured band in the ratios of the different predictions from simulation to the data represents the total experimental uncertainty in the data.

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Figure 11-a:
Normalized differential cross sections for $\mathrm{e^{-}} \mathrm{e^{+}}$ [32] as a function of the variable $T$ for ALEPH data at $ {\sqrt {s}} = $ 91.2 GeV. ALEPH data are compared with the predictions from HERWIG 7 using the SoftTune and CH tunes. The coloured band in the ratios of the different predictions from simulation to the data represents the total experimental uncertainty in the data.

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Figure 11-b:
Normalized differential cross sections for $\mathrm{e^{-}} \mathrm{e^{+}}$ [32] as a function of the variable ${T_{\mathrm {major}}}$ for ALEPH data at $ {\sqrt {s}} = $ 91.2 GeV. ALEPH data are compared with the predictions from HERWIG 7 using the SoftTune and CH tunes. The coloured band in the ratios of the different predictions from simulation to the data represents the total experimental uncertainty in the data.

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Figure 11-c:
Normalized differential cross sections for $\mathrm{e^{-}} \mathrm{e^{+}}$ [32] as a function of the variable $O$ for ALEPH data at $ {\sqrt {s}} = $ 91.2 GeV. ALEPH data are compared with the predictions from HERWIG 7 using the SoftTune and CH tunes. The coloured band in the ratios of the different predictions from simulation to the data represents the total experimental uncertainty in the data.

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Figure 11-d:
Normalized differential cross sections for $\mathrm{e^{-}} \mathrm{e^{+}}$ [32] as a function of the variable $S$ for ALEPH data at $ {\sqrt {s}} = $ 91.2 GeV. ALEPH data are compared with the predictions from HERWIG 7 using the SoftTune and CH tunes. The coloured band in the ratios of the different predictions from simulation to the data represents the total experimental uncertainty in the data.

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Figure 12:
The differential cross sections are shown as functions of: the ${p_{\mathrm {T}}}$ (upper left) and rapidity (upper right) of the hadronically decaying top quark; the invariant mass of the ${\mathrm{t} \mathrm{\bar{t}}}$ system (lower left); the additional jet multiplicity (lower right) [38]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 12-a:
The differential cross sections are shown as a function of the ${p_{\mathrm {T}}}$ [38]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 12-b:
The differential cross sections are shown as a function of rapidity of the hadronically decaying top quark [38]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 12-c:
The differential cross sections are shown as a function of the invariant mass of the ${\mathrm{t} \mathrm{\bar{t}}}$ system [38]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 12-d:
The differential cross sections are shown as a function of the additional jet multiplicity [38]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 13:
The differential cross sections are shown as functions of ${H_{\mathrm {T}}}$ (left) and ${{p_{\mathrm {T}}} ^\text {miss}}$ (right) [41]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 13-a:
The differential cross sections are shown as a function of ${H_{\mathrm {T}}}$ [41]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 13-b:
The differential cross sections are shown as a function of ${{p_{\mathrm {T}}} ^\text {miss}}$ [41]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 14:
The normalized jet substructure observables in single-lepton events: the charged-particle multiplicity (upper left); the eccentricity (upper right); the groomed momentum fraction (lower left); and the angle between the groomed subjects (lower right) [42]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 14-a:
The normalized jet substructure charged-particle multiplicity observable in single-lepton events [42]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 14-b:
The normalized jet substructure eccentricity observable in single-lepton events [42]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 14-c:
The normalized jet substructure groomed momentum fraction observable in single-lepton events [42]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 14-d:
The normalized jet substructure angle between the groomed subjects observable in single-lepton events [42]. CMS ${\mathrm{t} \mathrm{\bar{t}}}$ data are compared with the predictions from POWHEG + HERWIG 7, with the SoftTune, CH1, CH2, and CH3 tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 15:
The differential jet shape ${\rho (\mathrm {r})}$ (upper left and right) and the second moment of the jet transverse width $< \delta R^2 >$ in inclusive jet events [43]. CMS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 15-a:
The differential jet shape ${\rho (\mathrm {r})}$ (upper left and right) and the second moment of the jet transverse width $< \delta R^2 >$ in inclusive jet events [43]. CMS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 15-b:
The differential jet shape ${\rho (\mathrm {r})}$ (upper left and right) and the second moment of the jet transverse width $< \delta R^2 >$ in inclusive jet events [43]. CMS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 15-c:
The differential jet shape ${\rho (\mathrm {r})}$ (upper left and right) and the second moment of the jet transverse width $< \delta R^2 >$ in inclusive jet events [43]. CMS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 16:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the transverse region, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The transverse region is defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 16-a:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the transverse region, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The transverse region is defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 16-b:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the transverse region, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The transverse region is defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 17:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the toward (upper), and away (lower) regions, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The toward and away regions are defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 17-a:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the toward (upper), and away (lower) regions, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The toward and away regions are defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 17-b:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the toward (upper), and away (lower) regions, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The toward and away regions are defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 17-c:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the toward (upper), and away (lower) regions, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The toward and away regions are defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 17-d:
The ${{p_{\mathrm {T}}} ^{\mathrm {sum}}}$ (left) and ${N_{\mathrm{CH}}}$ (right) density distributions in the toward (upper), and away (lower) regions, as a function of the ${p_{\mathrm {T}}}$ of the two muons, ${{p_{\mathrm {T}}} (\mu \mu)}$ [45]. The toward and away regions are defined with respect to ${{p_{\mathrm {T}}} (\mu \mu)}$, where the two muons are required to have an invariant mass close the the mass of the Z boson. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 18:
The exclusive jet multiplicity in Z (left) and W (right) boson events, measured by CMS at $ {\sqrt {s}} = $ 13 TeV [46,47]. CMS Z boson and W boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 18-a:
The exclusive jet multiplicity in Z (left) and W (right) boson events, measured by CMS at $ {\sqrt {s}} = $ 13 TeV [46,47]. CMS Z boson and W boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 18-b:
The exclusive jet multiplicity in Z (left) and W (right) boson events, measured by CMS at $ {\sqrt {s}} = $ 13 TeV [46,47]. CMS Z boson and W boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 19:
Differential cross sections as a function of ${{p_{\mathrm {T}}} (\mathrm{Z})}$ (upper left), ${{p_{\mathrm {T}}} ^{\mathrm {bal}}}$ (upper right), and JZB (lower) [46]. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 19-a:
Differential cross sections as a function of ${{p_{\mathrm {T}}} (\mathrm{Z})}$ (upper left), ${{p_{\mathrm {T}}} ^{\mathrm {bal}}}$ (upper right), and JZB (lower) [46]. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 19-b:
Differential cross sections as a function of ${{p_{\mathrm {T}}} (\mathrm{Z})}$ (upper left), ${{p_{\mathrm {T}}} ^{\mathrm {bal}}}$ (upper right), and JZB (lower) [46]. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 19-c:
Differential cross sections as a function of ${{p_{\mathrm {T}}} (\mathrm{Z})}$ (upper left), ${{p_{\mathrm {T}}} ^{\mathrm {bal}}}$ (upper right), and JZB (lower) [46]. CMS Z boson data are compared with the predictions from MadGraph 5\_aMC@NLO + HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 20:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 20-a:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 20-b:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 20-c:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 20-d:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 21:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 21-a:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 21-b:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 21-c:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 21-d:
Normalized plots [48] for the pseudorapidity of charged particles for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left), for charged particles with $ {p_{\mathrm {T}}} > $ 500 MeV. The figure on the upper right shows a similar distribution for $ {N_{\mathrm{CH}}} \ge $ 2, and the lower right for $ {N_{\mathrm{CH}}} \ge $ 20, where the charged particles have $ {p_{\mathrm {T}}} > $ 100 MeV. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 22:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 22-a:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 22-b:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 22-c:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 22-d:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 23:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 23-a:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 23-b:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 23-c:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 23-d:
Normalized plots [48] for the charged-particle ${p_{\mathrm {T}}}$ for $ {N_{\mathrm{CH}}} \ge $ 1 (upper left), $ {N_{\mathrm{CH}}} \ge $ 2 (upper right), and $ {N_{\mathrm{CH}}} \ge $ 6 (lower left). The mean charged-particle ${p_{\mathrm {T}}}$ as a function of the charged-particle multiplicity is also shown (lower right). ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 24:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 2.5. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 24-a:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 2.5. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 24-b:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 2.5. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 24-c:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 2.5. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 25:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 0.8. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 25-a:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 0.8. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 25-b:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 0.8. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 25-c:
Normalized plots [49] for the pseudorapidity of charged particles (upper left), charged-particle ${p_{\mathrm {T}}}$ distribution (upper left), and the mean charged-particle ${p_{\mathrm {T}}}$ distribution as a function of the charged-particle multiplicity (lower), all for $ {| \eta |} < $ 0.8. ATLAS MB data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 26:
The ATLAS data at $ {\sqrt {s}} = $ 7 TeV on the ${F(z)}$ and ${f({p_{\mathrm {T}}} ^{\mathrm {rel}}})$ distributions [17]. ATLAS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 26-a:
The ATLAS data at $ {\sqrt {s}} = $ 7 TeV on the ${F(z)}$ and ${f({p_{\mathrm {T}}} ^{\mathrm {rel}}})$ distributions [17]. ATLAS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 26-b:
The ATLAS data at $ {\sqrt {s}} = $ 7 TeV on the ${F(z)}$ and ${f({p_{\mathrm {T}}} ^{\mathrm {rel}}})$ distributions [17]. ATLAS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 26-c:
The ATLAS data at $ {\sqrt {s}} = $ 7 TeV on the ${F(z)}$ and ${f({p_{\mathrm {T}}} ^{\mathrm {rel}}})$ distributions [17]. ATLAS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.

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Figure 26-d:
The ATLAS data at $ {\sqrt {s}} = $ 7 TeV on the ${F(z)}$ and ${f({p_{\mathrm {T}}} ^{\mathrm {rel}}})$ distributions [17]. ATLAS inclusive jet data are compared with the predictions from HERWIG 7, with the SoftTune and CH tunes. The coloured band in the ratio plot represents the total experimental uncertainty in the data. The vertical bars on the points for the different predictions represent the statistical uncertainties.
Tables

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Table 1:
Parameters considered in the tuning, and their allowed ranges in the fit.

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Table 2:
Value of the parameters for the SoftTune [12,3], CH1, CH2, and CH3 tunes.

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Table 3:
Parameters of the central, "up'', and "down'' variations of the CH3 tune.
Summary
Three new tunes for the multiple-parton interaction (MPI) model of the HERWIG 7 (version 7.1.4) generator have been derived from minimum-bias (MB) data collected by the CMS experiment. All of the CH ("CMS HERWIG'') tunes, CH1, CH2, and CH3, are based on the next-to-next-to-leading-order (NNLO) NNPDF 3.1 PDF set for the simulation of the parton shower (PS) in HERWIG 7; the value of the strong coupling at a scale equal to the Z boson mass is ${\alpha_S}(m_{\mathrm{Z}})=$ 0.118 with a two-loop evolution of ${\alpha_S}$. The configuration of the tunes differs in the PDF used for the simulation of MPI and beam remnants. The tune CH1 uses the same NNLO PDF set for these aspects of the HERWIG 7 simulation, whereas CH2 and CH3 use leading-order (LO) versions of the PDF set. The tune CH2 is based on an LO PDF set that was derived assuming ${\alpha_S}(m_{\mathrm{Z}})=$ 0.118, and CH3 on an LO PDF set assuming ${\alpha_S}(m_{\mathrm{Z}})=$ 0.130.

The parameters of the MPI model were optimized for each tune with the PROFESSOR framework to describe the underlying event (UE) in MB data collected by CMS. The predictions using the tune CH2 or CH3 provide a better description of the data than those using CH1 or SoftTune. Furthermore, the differences in the predictions of CH2 and CH3 are observed to be small. The configuration of PDF sets in the tune CH3, where the LO PDF used for the simulation of MPI, was derived with a value of ${\alpha_S}(m_{\mathrm{Z}})$ typically associated with LO PDF sets, is the preferred choice over CH2. Two alternative tunes representing the uncertainties in the fitted parameters of CH3 are also derived, based on the tuning procedure provided by PROFESSOR.

Predictions using the three CH tunes are compared with a range of data beyond MB events: event shape data from LEP; proton-proton data enriched in top quark pairs, Z bosons and W bosons; and inclusive jet data. This validated the performance of HERWIG 7 using these tunes against a wide range of data sets sensitive to various aspects of the modelling by HERWIG 7, and in particular the modelling of the UE. The event shape observables measured at LEP, which are sensitive to the modelling of final-state radiation, are well described by HERWIG 7 with the new tunes. Predictions using the new tunes are also shown to describe the UE in events containing Z bosons, demonstrating the universality of the UE modelling in HERWIG 7. The kinematics of top quark events, and the modelling of jets in $\mathrm{t\bar{t}}$, Z boson, W boson, and inclusive jet data are also well described by predictions using the new tunes. In general, predictions with the new CH tunes derived in this paper provide a better description of measured observables than those using SoftTune, the default tune available in HERWIG 7.
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