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| CMS-PAS-SMP-22-007 | ||
| Measurement of the primary Lund jet plane density in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 25 March 2023 | ||
| Abstract: A measurement of the primary Lund jet plane density in inclusive jet production in proton-proton collisions is presented. The analysis uses 138 fb$ ^{-1} $ of data collected by the CMS experiment at $ \sqrt{s} = $ 13 TeV. The Lund jet plane, a representation of the phase space of emissions inside jets, is extracted 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 in $ \ln(k_\mathrm{T}/\mathrm{GeV}) $ and $ \ln (R/\Delta R) $ is measured for jets with distance parameters $ R = $ 0.4 or 0.8 and transverse momentum $ p_\mathrm{T} > $ 700 GeV and rapidity $ |y| < $ 1.7. The jet substructure is extracted using the charged-particle tracks of the jet to achieve optimal momentum and angular resolution. The measured distributions are unfolded to the level of stable particles. The measurement is compared with theoretical predictions from state-of-the-art simulations. | ||
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Links:
CDS record (PDF) ;
Physics Briefing ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, Submitted to JHEP. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
(Left) Schematic diagram of the Cambridge/Aachen primary declustering tree of a jet. The emissions are angular ordered, as indicated with the numbers in the diagram. (Right) Schematic diagram of the primary emissions of a jet in the Lund jet plane. The Lund jet plane is filled from left to right, which corresponds to emissions ordered from large angles to small angles. The dashed line represents the kinematical limit. |
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Figure 1-a:
(Left) Schematic diagram of the Cambridge/Aachen primary declustering tree of a jet. The emissions are angular ordered, as indicated with the numbers in the diagram. (Right) Schematic diagram of the primary emissions of a jet in the Lund jet plane. The Lund jet plane is filled from left to right, which corresponds to emissions ordered from large angles to small angles. The dashed line represents the kinematical limit. |
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Figure 1-b:
(Left) Schematic diagram of the Cambridge/Aachen primary declustering tree of a jet. The emissions are angular ordered, as indicated with the numbers in the diagram. (Right) Schematic diagram of the primary emissions of a jet in the Lund jet plane. The Lund jet plane is filled from left to right, which corresponds to emissions ordered from large angles to small angles. The dashed line represents the kinematical limit. |
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Figure 2:
Schematic diagram of the physical effects affecting different regions of the primary Lund jet plane. Initial-state radiation (ISR) and the underlying event (UE) activity affect wide angle radiation. Hadronization affects the low $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $ region at all angles. Soft and hard collinear parton splittings affect the rest of the Lund jet plane. The diagonal line represents the kinematical limit of the primary Lund jet plane, which corresponds to $ p_{\mathrm{T}}^\mathrm{j1} = p_{\mathrm{T}}^\mathrm{j2} $. |
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Figure 3:
Detector-level distributions of data and Monte Carlo simulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3. The lower panels show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. |
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Figure 3-a:
Detector-level distributions of data and Monte Carlo simulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3. The lower panels show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. |
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Figure 3-b:
Detector-level distributions of data and Monte Carlo simulated events generated with PYTHIA8 CP5 and HERWIG 7 CH3. The lower panels show the ratio of the predictions with respect to the data. Only statistical uncertainties are included here. |
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Figure 4:
Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The right-hand side diagram represents the $ \eta $ and $ \phi $ coordinates of the emissions in the CMS coordinate system. The center of the particle-level 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 panel is associated to the same jet, and is filled with the primary emissions from the CA declustering from left to right (from large angles 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 4-a:
Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The right-hand side diagram represents the $ \eta $ and $ \phi $ coordinates of the emissions in the CMS coordinate system. The center of the particle-level 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 panel is associated to the same jet, and is filled with the primary emissions from the CA declustering from left to right (from large angles 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 4-b:
Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The right-hand side diagram represents the $ \eta $ and $ \phi $ coordinates of the emissions in the CMS coordinate system. The center of the particle-level 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 panel is associated to the same jet, and is filled with the primary emissions from the CA declustering from left to right (from large angles 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:
Detector-level (open symbols) and particle-level (closed symbols) distributions for the data and Monte Carlo simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in this plot. The lower panels show the ratio of the particle-level distributions relative to the respective detector-level distribution, which is used as a metric for the effective modifications of the Lund jet plane density due to the defector effects. The size of the corrections can be inferred from the ratio of the particle-level distributions to the detector-level distributions. |
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Figure 5-a:
Detector-level (open symbols) and particle-level (closed symbols) distributions for the data and Monte Carlo simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in this plot. The lower panels show the ratio of the particle-level distributions relative to the respective detector-level distribution, which is used as a metric for the effective modifications of the Lund jet plane density due to the defector effects. The size of the corrections can be inferred from the ratio of the particle-level distributions to the detector-level distributions. |
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Figure 5-b:
Detector-level (open symbols) and particle-level (closed symbols) distributions for the data and Monte Carlo simulated events of PYTHIA8 CP5. Only statistical uncertainties are included in this plot. The lower panels show the ratio of the particle-level distributions relative to the respective detector-level distribution, which is used as a metric for the effective modifications of the Lund jet plane density due to the defector effects. The size of the corrections can be inferred from the ratio of the particle-level distributions to the detector-level distributions. |
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Figure 6:
Different components of the systematic uncertainties for AK4 jets for different slices of the Lund jet plane density. The upper panel is for large angles, while the lower panel is for small angles. The total experimental uncertainty is represented by the filled area. The statistical uncertainties are represented by the hashed band. |
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Figure 6-a:
Different components of the systematic uncertainties for AK4 jets for different slices of the Lund jet plane density. The upper panel is for large angles, while the lower panel is for small angles. The total experimental uncertainty is represented by the filled area. The statistical uncertainties are represented by the hashed band. |
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Figure 6-b:
Different components of the systematic uncertainties for AK4 jets for different slices of the Lund jet plane density. The upper panel is for large angles, while the lower panel is for small angles. The total experimental uncertainty is represented by the filled area. The statistical uncertainties are represented by the hashed band. |
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Figure 7:
Two-dimensional distributions of the primary Lund jet plane densities corrected to particle level for AK4 jets (upper panel) and AK8 jets (lower panel). 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 7-a:
Two-dimensional distributions of the primary Lund jet plane densities corrected to particle level for AK4 jets (upper panel) and AK8 jets (lower panel). 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 7-b:
Two-dimensional distributions of the primary Lund jet plane densities corrected to particle level for AK4 jets (upper panel) and AK8 jets (lower panel). 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 8:
Four slices of the primary Lund jet plane density of AK4 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel contains low $ k_{\mathrm{T}} $ splittings, whereas the lower right panel contains high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 8-a:
Four slices of the primary Lund jet plane density of AK4 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel contains low $ k_{\mathrm{T}} $ splittings, whereas the lower right panel contains high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 8-b:
Four slices of the primary Lund jet plane density of AK4 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel contains low $ k_{\mathrm{T}} $ splittings, whereas the lower right panel contains high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 8-c:
Four slices of the primary Lund jet plane density of AK4 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel contains low $ k_{\mathrm{T}} $ splittings, whereas the lower right panel contains high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 8-d:
Four slices of the primary Lund jet plane density of AK4 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel contains low $ k_{\mathrm{T}} $ splittings, whereas the lower right panel contains high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 9:
Four slices of the primary Lund jet plane density of AK8 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 9-a:
Four slices of the primary Lund jet plane density of AK8 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 9-b:
Four slices of the primary Lund jet plane density of AK8 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 9-c:
Four slices of the primary Lund jet plane density of AK8 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 9-d:
Four slices of the primary Lund jet plane density of AK8 jets compared to 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 panels correspond to vertical slices for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 10:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 10-a:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 10-b:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 10-c:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 10-d:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions generated with PYTHIA8 using tunes CP2, CP5, Monash, and CUEP8M1. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 11:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions by PYTHIA8 + VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 11-a:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions by PYTHIA8 + VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 11-b:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions by PYTHIA8 + VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
png pdf |
Figure 11-c:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions by PYTHIA8 + VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 11-d:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions by PYTHIA8 + VINCIA, PYTHIA8+ DIRE, HERWIG 7 with dipole shower, and SHERPA. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ \ln(k_{\mathrm{T}}/\,\text{GeV}) $: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 12:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions based on different choices of the recoil scheme of the angular ordered shower of HERWIG 7. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 12-a:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions based on different choices of the recoil scheme of the angular ordered shower of HERWIG 7. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
png pdf |
Figure 12-b:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions based on different choices of the recoil scheme of the angular ordered shower of HERWIG 7. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
png pdf |
Figure 12-c:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions based on different choices of the recoil scheme of the angular ordered shower of HERWIG 7. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
png pdf |
Figure 12-d:
Four different slices of the primary Lund jet plane density of AK8 jets compared to predictions based on different choices of the recoil scheme of the angular ordered shower of HERWIG 7. The band represents the total experimental uncertainty. The upper two panels correspond to vertical slices of the Lund jet plane for fixed $ \ln(R/\Delta R) $ (large angles on upper left, small angles on upper right). The lower two panels correspond to two different horizontal slices for fixed $ k_{\mathrm{T}} $ interval: the lower left panel corresponds to low $ k_{\mathrm{T}} $ splittings and spans the full range in $ \ln(R/\Delta R) $, whereas the lower right panel corresponds to high-$ k_{\mathrm{T}} $ splittings, which populate mostly wide-angle radiation. |
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Figure 13:
Measured Lund jet plane distribution for AK8 jets, compared to the leading-order pQCD asymptotic prediction in the soft and collinear limit. An effective color factor of $ C_\mathrm{R}^\mathrm{eff} = $ 0.59 $C_\mathrm{F} + $ 0.41 $C_\mathrm{A} $ is assumed, as described in the text. The strong coupling $ \alpha_\mathrm{S} $ evolves with $ k_{\mathrm{T}} $ using the one-loop $ \beta $ function with $ \alpha_\mathrm{S} (m_\mathrm{Z}) = $ 0.116. The theoretical uncertainty band is calculated with variations of the renormalization scale 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. |
| Summary |
| In this note, we have presented a measurement of the primary Lund jet plane density in inclusive jet production in proton-proton (pp) collisions at 13 TeV using 138 fb$ ^{-1} $ of data collected with the CMS experiment. The primary Lund jet plane, a two-dimensional representation of the phase space of emissions inside the jet, is extracted using iterative Cambridge/Aachen jet declustering. The jet substructure is extracted using the charged-particle constituents of anti-$ k_{\mathrm{T}} $ jets with transverse momentum $ p_{\mathrm{T}} > $ 700 GeV and jet rapidity $ |y| < $ 1.7 with distance parameters of $ R = $ 0.4 or 0.8. The average density of emissions is measured as a function of the logarithm of the relative transverse momentum $ k_{\mathrm{T}} $ and the distance $ \Delta R $, and is fully corrected to stable particle level. The corrected distributions have an experimental uncertainty of 2--20%. The dependence on the parton shower and hadronization model is the dominant systematic uncertainty in the bulk of the Lund jet plane. Tracking inefficiencies become more important close to the kinematical edge of the Lund jet plane. The PYTHIA8 CP5 predictions systematically overestimate the Lund jet plane density at small $ k_{\mathrm{T}} $, which is the region dominated by hadronization. By choosing a smaller value of the renormalization scale in the evolution of the final-state radiation (FSR) shower, a better agreement of the PYTHIA8 CP5 tune is found in the perturbative region. The latter corresponds to effectively choosing a larger value of the strong coupling at the mass of the Z boson for FSR, $ \alpha_\mathrm{S}^\text{FSR}(m_\mathrm{Z}) $, which has been observed in other jet substructure measurements [72]. The HERWIG 7 predictions with the dot-product preserving recoil scheme, together with a veto on the virtuality of the partons at the end of the cascade, has the best global agreement with the data among the generators tested in the measurement. Predictions based on SHERPA, which has a dipole shower and cluster fragmentation model, is in agreement with the data in the bulk of the Lund jet plane, within 5--10%. The predictions from PYTHIA8 using the VINCIA and DIRE showers are generally in agreement with the data in the bulk of the Lund jet plane within 1--10% percent; they overestimate the density of emissions at low $ k_{\mathrm{T}} $ by 15--20%, as is the case for the standard shower of PYTHIA8. Finally, the PYTHIA8 predictions based on the Monash and CUEP8M1 tunes have in general a better agreement with the data than the predictions based on the CP tunes. For the most part, these differences are due to the different values of $ \alpha_\mathrm{S} $ used for FSR in the PYTHIA8 tunes tested in this measurement. These observations are qualitatively consistent with those made in a previous measurement of generalized angularities in Z+jets and dijet events at 13 TeV [75]. Since the measurement is corrected to particle level, it can be used as an input to improve the description from event generators and for future developments of parton showers with corrections beyond leading-logarithmic accuracy. |
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