CMSSMP22007 ; CERNEP2023282  
Measurement of the primary Lund jet plane density in protonproton collisions at $ \sqrt{s} = $ 13 TeV  
CMS Collaboration  
27 December 2023  
JHEP 05 (2024) 116  
Abstract: A measurement is presented of the primary Lund jet plane (LJP) density in inclusive jet production in protonproton collisions. The analysis uses 138 fb$ ^{1} $ of data collected by the CMS experiment at $ \sqrt{s} = $ 13 TeV. The LJP, a representation of the phase space of emissions inside jets, is constructed using iterative jet declustering. The transverse momentum $ k_{\mathrm{T}} $ and the splitting angle $ \Delta R $ of an emission relative to its emitter are measured at each step of the jet declustering process. The average density of emissions as function of $ \ln(k_{\mathrm{T}}/$GeV$)$ and $ \ln(R/\Delta R) $ is measured for jets with distance parameters $ R = $ 0.4 or 0.8, transverse momentum $ p_{\mathrm{T}} > $ 700 GeV, and rapidity $ y < $ 1.7. The jet substructure is measured using the chargedparticle tracks of the jet. The measured distributions, unfolded to the level of stable particles, are compared with theoretical predictions from simulations and with perturbative quantum chromodynamics calculations. Due to the ability of the LJP to factorize physical effects, these measurements can be used to improve different aspects of the physics modeling in event generators.  
Links: eprint arXiv:2312.16343 [hepex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; Physics Briefing ; CADI line (restricted) ; 
Figures  
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Figure 1:
Left: schematic diagram of the CambridgeAachen primary declustering tree of a jet. The black lines represent the branch that follows the harder subjet at each step of the declustering tree. The softer subjet at each node is used as a proxy for an emission in the primary LJP. Right: schematic diagram of the primary emissions of a jet in the LJP, which is filled from left to right corresponding to emissions ordered from large to small angles. The numbers represent the order of appearance in the declustering tree. The dashed diagonal line represents the kinematical limit. 
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Figure 1a:
Left: schematic diagram of the CambridgeAachen primary declustering tree of a jet. The black lines represent the branch that follows the harder subjet at each step of the declustering tree. The softer subjet at each node is used as a proxy for an emission in the primary LJP. Right: schematic diagram of the primary emissions of a jet in the LJP, which is filled from left to right corresponding to emissions ordered from large to small angles. The numbers represent the order of appearance in the declustering tree. The dashed diagonal line represents the kinematical limit. 
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Figure 1b:
Left: schematic diagram of the CambridgeAachen primary declustering tree of a jet. The black lines represent the branch that follows the harder subjet at each step of the declustering tree. The softer subjet at each node is used as a proxy for an emission in the primary LJP. Right: schematic diagram of the primary emissions of a jet in the LJP, which is filled from left to right corresponding to emissions ordered from large to small angles. The numbers represent the order of appearance in the declustering tree. The dashed diagonal line represents the kinematical limit. 
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Figure 2:
Schematic diagram of the mechanisms affecting different regions of the primary LJP in a given protonproton collision. Initialstate radiation (ISR), the underlying event (UE) activity, and multipleparton interactions (MPI) affect wideangle radiation at $ \Delta R \sim R $, close to the boundary of the jet. In an experimental context, pileup contributes to the same region as the UE. Hadronization affects the low $ \ln(k_{\mathrm{T}}/$GeV$)$ region (below $ k_{\mathrm{T}} \sim $ 1 GeV) at all angles. Soft and hard collinear parton splittings affect the rest of the LJP. The diagonal line represents the kinematical limit of the primary LJP, which corresponds to $ p_{\mathrm{T}}^{j_1} = p_{\mathrm{T}}^{j_2} $. 
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Figure 3:
Detectorlevel distributions of measured and MCsimulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3 for four different slices of the LJP, as indicated by the triangular diagrams in the plots. The lower panels in the plots show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. The comparison shows that neither HERWIG 7 CH3 nor PYTHIA8 CP5 are able to describe the data well in various regions of the LJP. The vertical bars represent the statistical uncertainties, which are smaller than the markers for most of the bins. 
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Figure 3a:
Detectorlevel distributions of measured and MCsimulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3 for four different slices of the LJP, as indicated by the triangular diagrams in the plots. The lower panels in the plots show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. The comparison shows that neither HERWIG 7 CH3 nor PYTHIA8 CP5 are able to describe the data well in various regions of the LJP. The vertical bars represent the statistical uncertainties, which are smaller than the markers for most of the bins. 
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Figure 3b:
Detectorlevel distributions of measured and MCsimulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3 for four different slices of the LJP, as indicated by the triangular diagrams in the plots. The lower panels in the plots show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. The comparison shows that neither HERWIG 7 CH3 nor PYTHIA8 CP5 are able to describe the data well in various regions of the LJP. The vertical bars represent the statistical uncertainties, which are smaller than the markers for most of the bins. 
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Figure 3c:
Detectorlevel distributions of measured and MCsimulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3 for four different slices of the LJP, as indicated by the triangular diagrams in the plots. The lower panels in the plots show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. The comparison shows that neither HERWIG 7 CH3 nor PYTHIA8 CP5 are able to describe the data well in various regions of the LJP. The vertical bars represent the statistical uncertainties, which are smaller than the markers for most of the bins. 
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Figure 3d:
Detectorlevel distributions of measured and MCsimulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3 for four different slices of the LJP, as indicated by the triangular diagrams in the plots. The lower panels in the plots show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. The comparison shows that neither HERWIG 7 CH3 nor PYTHIA8 CP5 are able to describe the data well in various regions of the LJP. The vertical bars represent the statistical uncertainties, which are smaller than the markers for most of the bins. 
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Figure 4:
Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The righthand side plot represents the $ \eta $ and $ \phi $ coordinates of the emissions in the CMS coordinate system to illustrate the geometrical matching used for the corrections in the measurement. The center of the particlelevel anti$ k_{\mathrm{T}} $ jet is represented by the solid circular marker. The circular line with radius $ R = $ 0.4 serves as a proxy for the anti$ k_{\mathrm{T}} $ distance parameter used to cluster the AK4 jet. The Lund plane on the left plot is associated with the same jet, and is filled with the primary emissions from the CA declustering from left to right (from large to small angles). The numbers in both plots represent the order of the emission of the primary CA tree declustering sequence. 
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Figure 4a:
Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The righthand side plot represents the $ \eta $ and $ \phi $ coordinates of the emissions in the CMS coordinate system to illustrate the geometrical matching used for the corrections in the measurement. The center of the particlelevel anti$ k_{\mathrm{T}} $ jet is represented by the solid circular marker. The circular line with radius $ R = $ 0.4 serves as a proxy for the anti$ k_{\mathrm{T}} $ distance parameter used to cluster the AK4 jet. The Lund plane on the left plot is associated with the same jet, and is filled with the primary emissions from the CA declustering from left to right (from large to small angles). The numbers in both plots represent the order of the emission of the primary CA tree declustering sequence. 
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Figure 4b:
Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The righthand side plot represents the $ \eta $ and $ \phi $ coordinates of the emissions in the CMS coordinate system to illustrate the geometrical matching used for the corrections in the measurement. The center of the particlelevel anti$ k_{\mathrm{T}} $ jet is represented by the solid circular marker. The circular line with radius $ R = $ 0.4 serves as a proxy for the anti$ k_{\mathrm{T}} $ distance parameter used to cluster the AK4 jet. The Lund plane on the left plot is associated with the same jet, and is filled with the primary emissions from the CA declustering from left to right (from large to small angles). The numbers in both plots represent the order of the emission of the primary CA tree declustering sequence. 
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Figure 5:
Detectorlevel (open symbols) and particlelevel (closed symbols) distributions for the data and MC simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in these plots, which are smaller than the markers for most of the bins. The lower panels in the plot show the ratio of the particlelevel to the respective detectorlevel distributions, which is used as a metric for the effective modifications of the LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particlelevel to the detectorlevel distributions, which are larger closer to the kinematical edge of the LJP. 
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Figure 5a:
Detectorlevel (open symbols) and particlelevel (closed symbols) distributions for the data and MC simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in these plots, which are smaller than the markers for most of the bins. The lower panels in the plot show the ratio of the particlelevel to the respective detectorlevel distributions, which is used as a metric for the effective modifications of the LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particlelevel to the detectorlevel distributions, which are larger closer to the kinematical edge of the LJP. 
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Figure 5b:
Detectorlevel (open symbols) and particlelevel (closed symbols) distributions for the data and MC simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in these plots, which are smaller than the markers for most of the bins. The lower panels in the plot show the ratio of the particlelevel to the respective detectorlevel distributions, which is used as a metric for the effective modifications of the LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particlelevel to the detectorlevel distributions, which are larger closer to the kinematical edge of the LJP. 
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Figure 5c:
Detectorlevel (open symbols) and particlelevel (closed symbols) distributions for the data and MC simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in these plots, which are smaller than the markers for most of the bins. The lower panels in the plot show the ratio of the particlelevel to the respective detectorlevel distributions, which is used as a metric for the effective modifications of the LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particlelevel to the detectorlevel distributions, which are larger closer to the kinematical edge of the LJP. 
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Figure 5d:
Detectorlevel (open symbols) and particlelevel (closed symbols) distributions for the data and MC simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in these plots, which are smaller than the markers for most of the bins. The lower panels in the plot show the ratio of the particlelevel to the respective detectorlevel distributions, which is used as a metric for the effective modifications of the LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particlelevel to the detectorlevel distributions, which are larger closer to the kinematical edge of the LJP. 
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Figure 6:
Different components of the systematic uncertainties for AK4 jets for two different vertical slices of the LJP density. The upper plot is for large angles 0.205 $ < \Delta R < $ 0.287, and the lower plot is for small angles 0.039 $ < \Delta R < $ 0.054. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band. 
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Figure 6a:
Different components of the systematic uncertainties for AK4 jets for two different vertical slices of the LJP density. The upper plot is for large angles 0.205 $ < \Delta R < $ 0.287, and the lower plot is for small angles 0.039 $ < \Delta R < $ 0.054. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band. 
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Figure 6b:
Different components of the systematic uncertainties for AK4 jets for two different vertical slices of the LJP density. The upper plot is for large angles 0.205 $ < \Delta R < $ 0.287, and the lower plot is for small angles 0.039 $ < \Delta R < $ 0.054. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band. 
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Figure 7:
Different components of the systematic uncertainties for AK4 jets for different horizontal slices of the LJP density. The upper plot is for low $ k_{\mathrm{T}} $ of 1.09 $ < k_{\mathrm{T}} < $ 1.79 GeV, and the lower plot is for higher $ k_{\mathrm{T}} $ of 8.03 $ < k_{\mathrm{T}} < $ 13.25 GeV. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band. 
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Figure 7a:
Different components of the systematic uncertainties for AK4 jets for different horizontal slices of the LJP density. The upper plot is for low $ k_{\mathrm{T}} $ of 1.09 $ < k_{\mathrm{T}} < $ 1.79 GeV, and the lower plot is for higher $ k_{\mathrm{T}} $ of 8.03 $ < k_{\mathrm{T}} < $ 13.25 GeV. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band. 
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Figure 7b:
Different components of the systematic uncertainties for AK4 jets for different horizontal slices of the LJP density. The upper plot is for low $ k_{\mathrm{T}} $ of 1.09 $ < k_{\mathrm{T}} < $ 1.79 GeV, and the lower plot is for higher $ k_{\mathrm{T}} $ of 8.03 $ < k_{\mathrm{T}} < $ 13.25 GeV. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band. 
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Figure 8:
Twodimensional distributions of the primary LJP densities corrected to particle level for AK4 jets (upper plot) and AK8 jets (lower plot). The diagonal line in both plots represents the kinematical limit of the emissions for a jet with $ p_{\mathrm{T}}^\text{jet} = $ 700 GeV. 
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Figure 8a:
Twodimensional distributions of the primary LJP densities corrected to particle level for AK4 jets (upper plot) and AK8 jets (lower plot). The diagonal line in both plots represents the kinematical limit of the emissions for a jet with $ p_{\mathrm{T}}^\text{jet} = $ 700 GeV. 
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Figure 8b:
Twodimensional distributions of the primary LJP densities corrected to particle level for AK4 jets (upper plot) and AK8 jets (lower plot). The diagonal line in both plots represents the kinematical limit of the emissions for a jet with $ p_{\mathrm{T}}^\text{jet} = $ 700 GeV. 
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Figure 9:
Four slices of the primary LJP density of AK4 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot contains low$ k_{\mathrm{T}} $ splittings, whereas the lowerright plot contains high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 9a:
Four slices of the primary LJP density of AK4 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot contains low$ k_{\mathrm{T}} $ splittings, whereas the lowerright plot contains high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 9b:
Four slices of the primary LJP density of AK4 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot contains low$ k_{\mathrm{T}} $ splittings, whereas the lowerright plot contains high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 9c:
Four slices of the primary LJP density of AK4 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot contains low$ k_{\mathrm{T}} $ splittings, whereas the lowerright plot contains high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 9d:
Four slices of the primary LJP density of AK4 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot contains low$ k_{\mathrm{T}} $ splittings, whereas the lowerright plot contains high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 10:
Four slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 10a:
Four slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 10b:
Four slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 10c:
Four slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 10d:
Four slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8 CP5 and HERWIG 7 CH3. Variations of the ISR and FSR scales for PYTHIA8 CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
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Figure 11:
Four different slices of the primary LJP density of AK8 jets compared with predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
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Figure 11a:
Four different slices of the primary LJP density of AK8 jets compared with predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
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Figure 11b:
Four different slices of the primary LJP density of AK8 jets compared with predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 11c:
Four different slices of the primary LJP density of AK8 jets compared with predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 11d:
Four different slices of the primary LJP density of AK8 jets compared with predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
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Figure 12:
Four different slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8+ VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA 2. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 12a:
Four different slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8+ VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA 2. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 12b:
Four different slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8+ VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA 2. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 12c:
Four different slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8+ VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA 2. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 12d:
Four different slices of the primary LJP density of AK8 jets compared with predictions by PYTHIA8+ VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA 2. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/$GeV$)$: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 13:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angularordered shower of HERWIG 7. Each recoil scheme achieves a different degree of logarithmic accuracy, up to NLL for certain observables, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 13a:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angularordered shower of HERWIG 7. Each recoil scheme achieves a different degree of logarithmic accuracy, up to NLL for certain observables, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 13b:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angularordered shower of HERWIG 7. Each recoil scheme achieves a different degree of logarithmic accuracy, up to NLL for certain observables, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 13c:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angularordered shower of HERWIG 7. Each recoil scheme achieves a different degree of logarithmic accuracy, up to NLL for certain observables, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 13d:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angularordered shower of HERWIG 7. Each recoil scheme achieves a different degree of logarithmic accuracy, up to NLL for certain observables, as described in the text. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 14:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($ k_{\mathrm{T}}^\text{FSR\,cutoff} $) in PYTHIA8 with the Monash tune. The larger $ k_{\mathrm{T}}^\text{FSR\,cutoff} $ value yields a better agreement with the data at low $ k_{\mathrm{T}} $. The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 14a:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($ k_{\mathrm{T}}^\text{FSR\,cutoff} $) in PYTHIA8 with the Monash tune. The larger $ k_{\mathrm{T}}^\text{FSR\,cutoff} $ value yields a better agreement with the data at low $ k_{\mathrm{T}} $. The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 14b:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($ k_{\mathrm{T}}^\text{FSR\,cutoff} $) in PYTHIA8 with the Monash tune. The larger $ k_{\mathrm{T}}^\text{FSR\,cutoff} $ value yields a better agreement with the data at low $ k_{\mathrm{T}} $. The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 14c:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($ k_{\mathrm{T}}^\text{FSR\,cutoff} $) in PYTHIA8 with the Monash tune. The larger $ k_{\mathrm{T}}^\text{FSR\,cutoff} $ value yields a better agreement with the data at low $ k_{\mathrm{T}} $. The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 14d:
Four different slices of the primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($ k_{\mathrm{T}}^\text{FSR\,cutoff} $) in PYTHIA8 with the Monash tune. The larger $ k_{\mathrm{T}}^\text{FSR\,cutoff} $ value yields a better agreement with the data at low $ k_{\mathrm{T}} $. The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. Statistical uncertainties in data and MCsimulated events are represented by vertical bars, which are smaller than the markers in most of the bins. 
png pdf 
Figure 15:
Measured LJP distribution for AK8 jets, compared with the leadingorder perturbativeQCD asymptotic prediction in the soft and collinear limit. The grey boxes represent the total experimental uncertainty from the measured data. For the prediction, an effective color factor of $ C_{\mathrm{R}}^{\text{eff}} = 0.59 C_{\mathrm{F}}+0.41 C_{\mathrm{A}} \approx $ 2 is assumed, as described in the text. The strong coupling $ \alpha_\mathrm{S} $ evolves with $ k_{\mathrm{T}} $ using the oneloop $ \beta $ function with $ \alpha_\mathrm{S} (m_\mathrm{Z}) = $ 0.118. The theoretical uncertainty band is calculated with variations of the renormalization scale up and down by factors of 2. The discontinuity is due to the change of the number of active flavors when $ k_{\mathrm{T}} $ reaches the mass of the bottom quark, which is assumed to be 4.2 GeV. 
png pdf 
Figure 16:
Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez [10]. The calculations include allorders resummation at nexttoleading logarithmic (NLL) accuracy matched to a nexttoleading order (NLO) fixedorder calculation, and supplemented with nonperturbative (NP) corrections, as described in the text. The band around the theory prediction represents the uncertainty from variations of the renormalization scale uncertainty in the perturbative calculation as well as uncertainties in the NP corrections. The gray band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
png pdf 
Figure 16a:
Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez [10]. The calculations include allorders resummation at nexttoleading logarithmic (NLL) accuracy matched to a nexttoleading order (NLO) fixedorder calculation, and supplemented with nonperturbative (NP) corrections, as described in the text. The band around the theory prediction represents the uncertainty from variations of the renormalization scale uncertainty in the perturbative calculation as well as uncertainties in the NP corrections. The gray band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
png pdf 
Figure 16b:
Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez [10]. The calculations include allorders resummation at nexttoleading logarithmic (NLL) accuracy matched to a nexttoleading order (NLO) fixedorder calculation, and supplemented with nonperturbative (NP) corrections, as described in the text. The band around the theory prediction represents the uncertainty from variations of the renormalization scale uncertainty in the perturbative calculation as well as uncertainties in the NP corrections. The gray band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
png pdf 
Figure 16c:
Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez [10]. The calculations include allorders resummation at nexttoleading logarithmic (NLL) accuracy matched to a nexttoleading order (NLO) fixedorder calculation, and supplemented with nonperturbative (NP) corrections, as described in the text. The band around the theory prediction represents the uncertainty from variations of the renormalization scale uncertainty in the perturbative calculation as well as uncertainties in the NP corrections. The gray band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
png pdf 
Figure 16d:
Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez [10]. The calculations include allorders resummation at nexttoleading logarithmic (NLL) accuracy matched to a nexttoleading order (NLO) fixedorder calculation, and supplemented with nonperturbative (NP) corrections, as described in the text. The band around the theory prediction represents the uncertainty from variations of the renormalization scale uncertainty in the perturbative calculation as well as uncertainties in the NP corrections. The gray band represents the total experimental uncertainty. The upper two plots correspond to vertical slices of the LJP for fixed $ \ln(R/\Delta R) $ (large angles on upperleft, small angles on upperright). The lower two plots correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lowerleft plot corresponds to low$ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lowerright plot corresponds to high$ k_{\mathrm{T}} $ splittings, which populate mostly wideangle radiation. 
Summary 
We have presented a measurement of the primary Lund jet plane (LJP) density in inclusive jet production in protonproton collisions at $ \sqrt{s} = $ 13 TeV using data, corresponding to an integrated luminosity of 138 fb$ ^{1} $, collected in Run 2 (20162018) with the CMS experiment. The LJP is a twodimensional representation of the phase space of emissions inside a jet constructed using iterative CambridgeAachen declustering. The logarithm of the relative transverse momentum $ k_{\mathrm{T}} $ of the emission and the logarithm of the opening angle of the branching $ \Delta R $ are used for the vertical and horizontal axes of the LJP. We analyzed the substructure of jets initially clustered with the anti$ k_{\mathrm{T}} $ algorithm with transverse momentum $ p_{\mathrm{T}} > $ 700 GeV and rapidity $ y < $ 1.7 clustered with distance parameters $ R = $ 0.4 or 0.8. The smaller $ R = $ 0.4 is the standard $ R $ for Run 2 analyses. The larger $ R = $ 0.8, used for the first time in a measurement of the primary LJP density, enables the exploration of a broader kinematical region of the LJP that is inaccessible with the $ R = $ 0.4 parameter value, particularly for wideangle, hard radiation. Clustering effects associated with the initial anti$ k_{\mathrm{T}} $ clustering have a less strong effect in the collinear region with the larger $ R $ value; hence the angular region where the emission density plateaus is wider for $ R = $ 0.8 jets. The corrected distributions have an experimental uncertainty in a range of 27% in the region away from the kinematical LJP edge and about 1525% close to the LJP edge. We compared the corrected primary LJP density with various particlelevel predictions from Monte Carlo (MC) simulated events. The predictions use different implementations of parton showers as well as different models for the underlyingevent (UE) activity, beambeam remnants, hadronization, and color reconnection effects. The aforementioned mechanisms can be effectively factorized in the primary LJP density, which allows for strong constraints in terms of the substructure of jets. At leadinglogarithmic (LL) accuracy, the primary LJP density is proportional to the strong coupling $ \alpha_\mathrm{S}(k_{\mathrm{T}}) $, so it can be used to tune the value of $ \alpha_\mathrm{S} $ evaluated at the Z boson mass used for finalstate radiation (FSR) in MC event generators, $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $. Predictions generated with the CP5 tune of the PYTHIA8 generator underestimate the measured density of emissions in the perturbative region ($ k_{\mathrm{T}} > $ 5 GeV) by about 15% because of the small value of $ \alpha_\mathrm{S}^\mathrm{FSR}(m_\mathrm{Z}) $ used for this tune. Other PYTHIA8 tunes or parton shower options tested in the measurement are in better agreement with the data. The predictions generated with the angularordered shower of the HERWIG 7.2.0 generator are in better agreement with the data than those generated with its alternative dipole shower. The data were also compared with different recoil schemes of the angularordered shower of HERWIG 7, which allow the parton shower to reach up to nexttoLL (NLL) accuracy for certain global observables. The HERWIG 7 predictions with the dotproduct preserving recoil scheme, together with a veto on highvirtuality partons, have the best global agreement with the data among the generators tested in the measurement. The low$ k_{\mathrm{T}} $ region is dominated by hadronization effects in a wide range of $ \Delta R $ values, with additional contributions from the UE at large $ \Delta R \approx R $. The predictions based on cluster fragmentation models, such as those generated with HERWIG 7 or SHERPA 2 generators, are in better agreement with the data at low $ k_{\mathrm{T}} $ for a wide range of $ \Delta R $ values than those of PYTHIA8. The PYTHIA8 predictions, where hadronization is described with the Lund string fragmentation model, overestimate the LJP density by about 1520% for $ k_{\mathrm{T}} $ at the GeV scale for a wide range of $ \Delta R $ values. One possibility to improve the description of the low $ k_{\mathrm{T}} $ region is to include the FSR cutoff $ k_{\mathrm{T}} $ as a free parameter in future event generator tuning; a larger FSR cutoff $ k_{\mathrm{T}} $ value decreases the density of emissions at low $ k_{\mathrm{T}} $ in the LJP without affecting the high$ k_{\mathrm{T}} $ region that is dominated by the parton shower. Finally, the data are also compared with a perturbative QCD calculation with a resummation at NLL accuracy, which is matched to a fixedorder nexttoleading order calculation [10]. To compare with the measured LJP at hadron level, nonperturbative corrections are supplemented to the calculation. The predictions are in agreement with the data within the theoretical and experimental uncertainties. For collinear emissions, the data can be qualitatively described with the running of $ \alpha_\mathrm{S} $ with $ k_{\mathrm{T}} $. These measurements highlight the different aspects of the physics modeling of event generators that should be improved, ranging from the modeling of hadronization and up to the logarithmic accuracy of parton showering algorithms. 
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