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Left: schematic diagram of the Cambridge--Aachen 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.

Left: schematic diagram of the Cambridge--Aachen 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.

Schematic diagram of the mechanisms affecting different regions of the primary LJP in a given proton-proton collision. Initial-state radiation (ISR), the underlying event (UE) activity, and multiple-parton interactions (MPI) affect wide-angle radiation at $\DeltaR \sim R$, close to the boundary of the jet. In an experimental context, pileup contributes to the same region as the UE. Hadronization affects the low \lnkT region (below $\kt \sim 1\GeV$) 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 $\pt^{j_1} = \pt^{j_2}$.

Detector-level distributions of measured and MC-simulated events generated with \PYTHIA{8} CP5 and \HERWIG{7} CH3 for four different slices of the charged-particle 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 \PYTHIA{8} 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.

Detector-level distributions of measured and MC-simulated events generated with \PYTHIA{8} CP5 and \HERWIG{7} CH3 for four different slices of the charged-particle 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 \PYTHIA{8} 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.

Detector-level distributions of measured and MC-simulated events generated with \PYTHIA{8} CP5 and \HERWIG{7} CH3 for four different slices of the charged-particle 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 \PYTHIA{8} 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.

Detector-level distributions of measured and MC-simulated events generated with \PYTHIA{8} CP5 and \HERWIG{7} CH3 for four different slices of the charged-particle 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 \PYTHIA{8} 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.

Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The right-hand 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 particle-level anti-\kt jet is represented by the solid circular marker. The circular line with radius $R = 0.4$ serves as a proxy for the anti-\kt 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.

Event displays of a simulated AK4 jet at detector level (solid triangles) and particle level (open triangles). The right-hand 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 particle-level anti-\kt jet is represented by the solid circular marker. The circular line with radius $R = 0.4$ serves as a proxy for the anti-\kt 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.

Detector-level (open symbols) and particle-level (closed symbols) distributions for the data and MC simulated events of \PYTHIA{8} 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 particle-level to the respective detector-level distributions, which is used as a metric for the effective modifications of the charged-particle LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particle-level to the detector-level distributions, which are larger closer to the kinematical edge of the LJP.

Detector-level (open symbols) and particle-level (closed symbols) distributions for the data and MC simulated events of \PYTHIA{8} 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 particle-level to the respective detector-level distributions, which is used as a metric for the effective modifications of the charged-particle LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particle-level to the detector-level distributions, which are larger closer to the kinematical edge of the LJP.

Detector-level (open symbols) and particle-level (closed symbols) distributions for the data and MC simulated events of \PYTHIA{8} 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 particle-level to the respective detector-level distributions, which is used as a metric for the effective modifications of the charged-particle LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particle-level to the detector-level distributions, which are larger closer to the kinematical edge of the LJP.

Detector-level (open symbols) and particle-level (closed symbols) distributions for the data and MC simulated events of \PYTHIA{8} 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 particle-level to the respective detector-level distributions, which is used as a metric for the effective modifications of the charged-particle LJP density because of the detector effects. The size of the corrections can be inferred from the ratio of the particle-level to the detector-level distributions, which are larger closer to the kinematical edge of the LJP.

Different components of the systematic uncertainties for AK4 jets for two different vertical slices of the charged-particle LJP density. The upper plot is for large angles $0.205 < \DeltaR < 0.287$, and the lower plot is for small angles $0.039 < \DeltaR < 0.054$. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band.

Different components of the systematic uncertainties for AK4 jets for two different vertical slices of the charged-particle LJP density. The upper plot is for large angles $0.205 < \DeltaR < 0.287$, and the lower plot is for small angles $0.039 < \DeltaR < 0.054$. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band.

Different components of the systematic uncertainties for AK4 jets for different horizontal slices of the charged-particle LJP density. The upper plot is for low \kt of $1.09 < \kt < 1.79\GeV$, and the lower plot is for higher \kt of $8.03 < \kt < 13.25\GeV$. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band.

Different components of the systematic uncertainties for AK4 jets for different horizontal slices of the charged-particle LJP density. The upper plot is for low \kt of $1.09 < \kt < 1.79\GeV$, and the lower plot is for higher \kt of $8.03 < \kt < 13.25\GeV$. The total experimental uncertainty is represented by the filled area. The statistical uncertainties in the data are represented by the hashed band.

Two-dimensional distributions of the charged-particle 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 $\pt^\text{jet} = 700\GeV$.

Two-dimensional distributions of the charged-particle 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 $\pt^\text{jet} = 700\GeV$.

Four slices of the charged-particle primary LJP density of AK4 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot contains low-\kt splittings, whereas the lower-right plot contains high-\kt splittings, which populate mostly wide-angle radiation.

Four slices of the charged-particle primary LJP density of AK4 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot contains low-\kt splittings, whereas the lower-right plot contains high-\kt splittings, which populate mostly wide-angle radiation.

Four slices of the charged-particle primary LJP density of AK4 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot contains low-\kt splittings, whereas the lower-right plot contains high-\kt splittings, which populate mostly wide-angle radiation.

Four slices of the charged-particle primary LJP density of AK4 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot contains low-\kt splittings, whereas the lower-right plot contains high-\kt splittings, which populate mostly wide-angle radiation.

Four slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.

Four slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.

Four slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.

Four slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8} CP5 and \HERWIG{7} CH3. Variations of the ISR and FSR scales for \PYTHIA{8} CP5 predictions are shown as well. The band represents the total experimental uncertainty. The upper two plots correspond to vertical slices for fixed \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions generated with \PYTHIA{8} using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of \alpSFSR, 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions generated with \PYTHIA{8} using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of \alpSFSR, 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions generated with \PYTHIA{8} using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of \alpSFSR, 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions generated with \PYTHIA{8} using tunes CP2, CP5, Monash, and CUEP8M1. The most important difference between the tunes is the value of \alpSFSR, 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8}+\VINCIA, \PYTHIA{8}+\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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8}+\VINCIA, \PYTHIA{8}+\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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8}+\VINCIA, \PYTHIA{8}+\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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions by \PYTHIA{8}+\VINCIA, \PYTHIA{8}+\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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \lnkT: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the of the charged-particle primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angular-ordered 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the of the charged-particle primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angular-ordered 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the of the charged-particle primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angular-ordered 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the of the charged-particle primary LJP density of AK8 jets compared with predictions based on different choices of the recoil scheme of the angular-ordered 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($\ktFSRcutoff$) in \PYTHIA{8} with the Monash tune. The larger $\ktFSRcutoff$ value yields a better agreement with the data at low \kt. The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($\ktFSRcutoff$) in \PYTHIA{8} with the Monash tune. The larger $\ktFSRcutoff$ value yields a better agreement with the data at low \kt. The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($\ktFSRcutoff$) in \PYTHIA{8} with the Monash tune. The larger $\ktFSRcutoff$ value yields a better agreement with the data at low \kt. The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Four different slices of the charged-particle primary LJP density of AK8 jets compared with predictions based on different values of the transverse momentum cutoff used for FSR ($\ktFSRcutoff$) in \PYTHIA{8} with the Monash tune. The larger $\ktFSRcutoff$ value yields a better agreement with the data at low \kt. The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation. Statistical uncertainties in data and MC-simulated events are represented by vertical bars, which are smaller than the markers in most of the bins.

Measured LJP distribution for AK8 jets, compared with the leading-order perturbative-QCD 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 $\CReff~=~0.59 ~\CF+0.41~\CA \approx 2$ is assumed, as described in the text. The strong coupling \alpS evolves with \kt using the one-loop $\beta$ function with $\alpS (m_\PZ) = 0.118$. 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 \kt reaches the mass of the bottom quark, which is assumed to be 4.2\GeV.

Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez~\cite{Lifson:2020gua}. The calculations include all-orders resummation at next-to-leading logarithmic (NLL) accuracy matched to a next-to-leading order (NLO) fixed-order 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.

Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez~\cite{Lifson:2020gua}. The calculations include all-orders resummation at next-to-leading logarithmic (NLL) accuracy matched to a next-to-leading order (NLO) fixed-order 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.

Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez~\cite{Lifson:2020gua}. The calculations include all-orders resummation at next-to-leading logarithmic (NLL) accuracy matched to a next-to-leading order (NLO) fixed-order 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.

Four different slices of the primary LJP density of AK8 jets compared with perturbation theory calculations by A. Lifson, G. P. Salam, G. Soyez~\cite{Lifson:2020gua}. The calculations include all-orders resummation at next-to-leading logarithmic (NLL) accuracy matched to a next-to-leading order (NLO) fixed-order 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 \lnDeltaR (large angles on upper-left, small angles on upper-right). The lower two plots correspond to two different horizontal slices for fixed \kt interval: the lower-left plot corresponds to low-\kt splittings and spans the full range in \lnDeltaR, whereas the lower-right plot corresponds to high-\kt splittings, which populate mostly wide-angle radiation.