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| CMS-HIN-24-005 ; CERN-EP-2025-058 | ||
| Jet fragmentation function and groomed substructure of bottom quark jets in proton-proton collisions at 5.02 TeV | ||
| CMS Collaboration | ||
| 7 November 2025 | ||
| Submitted to J. High Energy Phys. | ||
| Abstract: A measurement of the substructure of bottom quark jets (b jets) in proton-proton (pp) collisions is presented. The measurement uses data collected in pp collisions at $ \sqrt{s} = $ 5.02 TeV recorded by the CMS experiment in 2017, corresponding to an integrated luminosity of 301 pb$^{-1}$. An algorithm to identify and cluster the charged decay daughters of b hadrons is developed for this analysis, which facilitates the exposure of the gluon radiation pattern of b jets using iterative Cambridge--Aachen declustering. The soft-drop-groomed jet radius, $ R_{\mathrm{g}} $, and momentum balance, $ z_{\mathrm{g}} $, of b quark jets are presented. These observables can be used to test perturbative quantum chromodynamics predictions that account for mass effects. Because the b hadron is partially reconstructed from its charged decay daughters, only charged particles are used for the jet substructure studies. In addition, a jet fragmentation function, $ z_{{\mathrm{b},\text{ch}}} $, is measured, which is defined as the distribution of the ratio of the transverse momentum ($ p_{\mathrm{T}} $) of the partially reconstructed b hadron with respect to the charged-particle component of the jet $ p_{\mathrm{T}} $. The substructure variable distributions are unfolded to the charged-particle level. The b jet substructure is compared to the substructure of jets in an inclusive jet sample that is dominated by light-quark and gluon jets in order to assess the role of the b quark mass. A strong suppression of emissions at small $ R_{\mathrm{g}} $ values is observed for b jets when compared to inclusive jets, consistent with the dead-cone effect. The measurement is also compared with theoretical predictions from Monte Carlo event generators. This is the first substructure measurement of b jets that clusters together the b hadron decay daughters. | ||
| Links: CDS record ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Left panel: A schematic diagram of two Cambridge--Aachen subjets, such as those found with the soft-drop grooming algorithm. The splitting angle $ \Delta R_{1,2} $ and the relative transverse momentum $ k_{\mathrm{T}} $ between the two subjets are annotated. Right panel: The Lund jet plane regions of bottom quark jets. The vertical axis is the logarithm of the relative transverse momentum $ k_{\mathrm{T}}/ $GeV of the softer subjet with respect to the harder subjet. The horizontal axis is the logarithm of the inverse of the opening angle between the softer and harder subjets, $ \Delta R_{1,2} $. The Lund jet plane is expected to be dominated by hadronization effects for $ k_{\mathrm{T}} $ below the GeV scale. Above the GeV scale, the Lund jet plane provides information on the parton showering description. Emissions are suppressed at small angles due to the dead-cone effect. The b hadron decays (not depicted) populate the same region. The blue shading, fading from left to right, represents the density of emissions in the primary Lund jet plane for b quark jets. |
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Figure 2:
The Lund jet plane of the soft-drop emissions of b quark jets at the particle-level of the PYTHIA8 CP5 simulation. The vertical axis is the logarithm of the $ k_{\mathrm{T}}/ $GeV of the emission, whereas the horizontal axis is the logarithm of $ R $/$ R_{\mathrm{g}} $, such that large-angle emissions populate the left-hand side of the diagrams and small-angle emissions populate the right-hand side. On the left-hand side, the SD algorithm is applied to the charged-particle jet constituents including the b hadron decay daughters. On the right-hand side, the b hadron charged decay daughters have been clustered together prior to the SD grooming, i.e.,, the charged component of the b hadron remains intact. The effect of the decays can be observed in the yellow hotspot at small angles and low $ k_{\mathrm{T}} $ on the left. |
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Figure 3:
The modification of the $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) distributions at the detector level without (violet dotted curve) and with (orange dashed-dotted curve) the partial reconstruction of the b hadron, compared to the particle-level distribution with the charged part of the generated b hadron intact (blue solid curve). The events are produced by the PYTHIA8 CP5 generator. |
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Figure 3-a:
The modification of the $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) distributions at the detector level without (violet dotted curve) and with (orange dashed-dotted curve) the partial reconstruction of the b hadron, compared to the particle-level distribution with the charged part of the generated b hadron intact (blue solid curve). The events are produced by the PYTHIA8 CP5 generator. |
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Figure 3-b:
The modification of the $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) distributions at the detector level without (violet dotted curve) and with (orange dashed-dotted curve) the partial reconstruction of the b hadron, compared to the particle-level distribution with the charged part of the generated b hadron intact (blue solid curve). The events are produced by the PYTHIA8 CP5 generator. |
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Figure 4:
Examples of the fit of the partially reconstructed b hadron mass to double-b, single-b, and light+c jet templates coming from PYTHIA8 CP5. From left to right, the distributions in selected $ R_{\mathrm{g}} $, $ z_{\mathrm{g}} $, and $ z_{{\mathrm{b},\text{ch}}} $ bins are presented. The black points represent the data counts, while the violet, blue, and orange filled curves represent the double-b, single-b, and light+c jet templates, with the fractions acquired from the fit. The ratio between the data and the fit values is presented in the lower panels. |
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Figure 4-a:
Examples of the fit of the partially reconstructed b hadron mass to double-b, single-b, and light+c jet templates coming from PYTHIA8 CP5. From left to right, the distributions in selected $ R_{\mathrm{g}} $, $ z_{\mathrm{g}} $, and $ z_{{\mathrm{b},\text{ch}}} $ bins are presented. The black points represent the data counts, while the violet, blue, and orange filled curves represent the double-b, single-b, and light+c jet templates, with the fractions acquired from the fit. The ratio between the data and the fit values is presented in the lower panels. |
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Figure 4-b:
Examples of the fit of the partially reconstructed b hadron mass to double-b, single-b, and light+c jet templates coming from PYTHIA8 CP5. From left to right, the distributions in selected $ R_{\mathrm{g}} $, $ z_{\mathrm{g}} $, and $ z_{{\mathrm{b},\text{ch}}} $ bins are presented. The black points represent the data counts, while the violet, blue, and orange filled curves represent the double-b, single-b, and light+c jet templates, with the fractions acquired from the fit. The ratio between the data and the fit values is presented in the lower panels. |
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Figure 4-c:
Examples of the fit of the partially reconstructed b hadron mass to double-b, single-b, and light+c jet templates coming from PYTHIA8 CP5. From left to right, the distributions in selected $ R_{\mathrm{g}} $, $ z_{\mathrm{g}} $, and $ z_{{\mathrm{b},\text{ch}}} $ bins are presented. The black points represent the data counts, while the violet, blue, and orange filled curves represent the double-b, single-b, and light+c jet templates, with the fractions acquired from the fit. The ratio between the data and the fit values is presented in the lower panels. |
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Figure 5:
The breakdown of systematic uncertainties for inclusive jets (upper panel: $ R_{\mathrm{g}} $, lower panel: $ z_{\mathrm{g}} $). The statistical uncertainty is also shown in gray shaded boxes. |
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Figure 5-a:
The breakdown of systematic uncertainties for inclusive jets (upper panel: $ R_{\mathrm{g}} $, lower panel: $ z_{\mathrm{g}} $). The statistical uncertainty is also shown in gray shaded boxes. |
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Figure 5-b:
The breakdown of systematic uncertainties for inclusive jets (upper panel: $ R_{\mathrm{g}} $, lower panel: $ z_{\mathrm{g}} $). The statistical uncertainty is also shown in gray shaded boxes. |
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Figure 6:
The breakdown of systematic uncertainties for b jets (upper panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, lower panel: $ z_{{\mathrm{b},\text{ch}}} $). The statistical uncertainty is also shown in gray shaded boxes. |
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Figure 6-a:
The breakdown of systematic uncertainties for b jets (upper panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, lower panel: $ z_{{\mathrm{b},\text{ch}}} $). The statistical uncertainty is also shown in gray shaded boxes. |
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Figure 6-b:
The breakdown of systematic uncertainties for b jets (upper panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, lower panel: $ z_{{\mathrm{b},\text{ch}}} $). The statistical uncertainty is also shown in gray shaded boxes. |
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Figure 6-c:
The breakdown of systematic uncertainties for b jets (upper panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, lower panel: $ z_{{\mathrm{b},\text{ch}}} $). The statistical uncertainty is also shown in gray shaded boxes. |
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Figure 7:
Distributions of groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the charged-particle level for inclusive jets. The gray band represents the systematic uncertainties added in quadrature, while the vertical bars represent the statistical uncertainty. Distributions coming from the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators are also presented. The ratio of the MC simulations to the data is presented in the lower panels. |
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Figure 7-a:
Distributions of groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the charged-particle level for inclusive jets. The gray band represents the systematic uncertainties added in quadrature, while the vertical bars represent the statistical uncertainty. Distributions coming from the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators are also presented. The ratio of the MC simulations to the data is presented in the lower panels. |
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Figure 7-b:
Distributions of groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the charged-particle level for inclusive jets. The gray band represents the systematic uncertainties added in quadrature, while the vertical bars represent the statistical uncertainty. Distributions coming from the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators are also presented. The ratio of the MC simulations to the data is presented in the lower panels. |
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Figure 8:
Distributions of the groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the charged-particle level for b jets. Distributions coming from the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators are also presented. The ratio of the MC simulations to the data is presented in the lower panels. |
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Figure 8-a:
Distributions of the groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the charged-particle level for b jets. Distributions coming from the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators are also presented. The ratio of the MC simulations to the data is presented in the lower panels. |
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Figure 8-b:
Distributions of the groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the charged-particle level for b jets. Distributions coming from the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators are also presented. The ratio of the MC simulations to the data is presented in the lower panels. |
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Figure 9:
The distribution of the jet fragmentation function $ z_{{\mathrm{b},\text{ch}}} $ corrected to the charged-particle level. Distributions coming from the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators are also presented. The ratio of the MC simulations to the data is presented in the lower panel. |
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Figure 10:
A comparison of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and inclusive jets. Most sources of systematic uncertainty are considered fully correlated in the ratio, which is presented in the lower panels, with the exception of those related to flavor and the response matrix. |
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Figure 10-a:
A comparison of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and inclusive jets. Most sources of systematic uncertainty are considered fully correlated in the ratio, which is presented in the lower panels, with the exception of those related to flavor and the response matrix. |
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Figure 10-b:
A comparison of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and inclusive jets. Most sources of systematic uncertainty are considered fully correlated in the ratio, which is presented in the lower panels, with the exception of those related to flavor and the response matrix. |
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Figure 11:
The ratio of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and inclusive jets compared to the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators. Most sources of systematic uncertainty are considered fully correlated in the ratio, with the exception of those related to flavor and the response matrix. The ratio of the MC simulations to the data is presented in the lower panels. |
png pdf |
Figure 11-a:
The ratio of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and inclusive jets compared to the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators. Most sources of systematic uncertainty are considered fully correlated in the ratio, with the exception of those related to flavor and the response matrix. The ratio of the MC simulations to the data is presented in the lower panels. |
png pdf |
Figure 11-b:
The ratio of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and inclusive jets compared to the PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators. Most sources of systematic uncertainty are considered fully correlated in the ratio, with the exception of those related to flavor and the response matrix. The ratio of the MC simulations to the data is presented in the lower panels. |
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Figure 12:
The ratio of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and light-quark (dashed red line) or inclusive jets (solid blue line) at the particle level of the PYTHIA8 CP5 event generator. |
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Figure 12-a:
The ratio of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and light-quark (dashed red line) or inclusive jets (solid blue line) at the particle level of the PYTHIA8 CP5 event generator. |
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Figure 12-b:
The ratio of the groomed observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) between b and light-quark (dashed red line) or inclusive jets (solid blue line) at the particle level of the PYTHIA8 CP5 event generator. |
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Figure 13:
The background rejection rate versus the signal efficiency for the b hadron decay product identification. The model is a gradient boosted decision tree with 11 input variables related to tracking and secondary vertex information. ``Background'' refers to charged particles coming from the primary interaction, while ``signal'' signifies charged particles resulting from a b hadron decay. Dashed lines are drawn at 1 for each axis. The intersection of those lines is the optimal performance of a classifier. |
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Figure 14:
The migration matrices of $ R_{\mathrm{g}} $ for b jets. The particle level corresponds to clustered b hadron decay products. In the left panel, the decay products are present during the iterative declustering at the detector level, while in the right panel, the decay products have been identified using the gradient boosted decision tree and they have been clustered together into the partially reconstructed b hadron and replaced in the jet constituents. |
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Figure 14-a:
The migration matrices of $ R_{\mathrm{g}} $ for b jets. The particle level corresponds to clustered b hadron decay products. In the left panel, the decay products are present during the iterative declustering at the detector level, while in the right panel, the decay products have been identified using the gradient boosted decision tree and they have been clustered together into the partially reconstructed b hadron and replaced in the jet constituents. |
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Figure 14-b:
The migration matrices of $ R_{\mathrm{g}} $ for b jets. The particle level corresponds to clustered b hadron decay products. In the left panel, the decay products are present during the iterative declustering at the detector level, while in the right panel, the decay products have been identified using the gradient boosted decision tree and they have been clustered together into the partially reconstructed b hadron and replaced in the jet constituents. |
| Summary |
| This paper presents measurements of the substructure of bottom quark jets (b jets) and of inclusive jets in proton-proton collisions at $ \sqrt{s} = $ 5.02 TeV using data corresponding to an integrated luminosity of 301 pb$^{-1}$ collected in 2017 with the CMS experiment. The jets considered were initially clustered with the anti-$ k_{\mathrm{T}} $ algorithm using a distance parameter of $ R = $ 0.4, and had transverse momentum 100 $ < p_{\mathrm{T}} < $ 120 GeV and pseudorapidity $ |\eta| < $ 2. The substructure observables are calculated using the charged-particle constituents of the jets. The groomed jet radius $ R_{\mathrm{g}} $, groomed momentum balance $ z_{\mathrm{g}} $, and the jet fragmentation function $ z_{{\mathrm{b},\text{ch}}} $ are measured and corrected to the charged-particle level. Corrections include background subtraction, migration effects, and efficiency corrections. A challenge in the interpretation of previous b jet substructure measurements is that the b hadron decay daughters are clustered in the jet on an equal footing with the hadrons that are produced from the transition from partons to hadrons. To better understand the gluon radiation pattern of b jets, the b hadron decay daughters need to be handled in a careful way experimentally. This measurement uses a novel algorithm to identify and cluster the b hadron charged decay daughters of b-tagged jets in a generic way, which allows for a cleaner interpretation of the measured substructure variable distributions in terms of the parton showering description. The contributions from gluon, light-quark, charm quark jets, and jets originating from gluon splitting ($ \mathrm{g} \to \mathrm{b} \overline{\mathrm{b}} $) are subtracted from the measurements. The distributions are unfolded to the charged-particle level using unregularized unfolding. The correction to the charged-particle level accounts also for the removal of the particle-level biases that arise from the usage of b tagging. The charged-particle-level distributions have uncertainties of the order of 5% and reaching up to 20% in certain bins. The dominant systematic uncertainty is related to the physics model (PYTHIA8 CP5 or HERWIG 7 CH3) used in extraction of the corrections. The groomed momentum balance distributions of inclusive jets and b jets are well described by both PYTHIA8 CP5 and HERWIG 7 CH3. The description of the groomed jet radius, however, depends on the jet flavor and the physics model. The HERWIG 7 CH3 prediction agrees well with the data in the case of inclusive jets, while a bigger discrepancy is observed for b jets. The PYTHIA8 CP5 generator fails to describe either distribution. The jet fragmentation function, on the other hand, is described better by PYTHIA8 CP5 at high values of $ z_{{\mathrm{b},\text{ch}}} $, i.e.,, for cases where the b hadron carries a substantial amount of the jet $ p_{\mathrm{T}} $. The $ z_{{\mathrm{b},\text{ch}}} \approx $ 1 region corresponds to b jets without splittings that satisfy the soft-drop condition. Therefore, $ z_{\mathrm{g}} $, $ R_{\mathrm{g}} $, and $ z_{{\mathrm{b},\text{ch}}} $ can be used simultaneously to constrain nonperturbative and perturbative aspects of b jet substructure. The $ R_{\mathrm{g}} $ distribution for b jets is found to differ significantly from that of inclusive jets. The suppression at small $ R_{\mathrm{g}} $ for b jets is consistent with the expectations of the dead-cone effect. The b jets also have a more asymmetric $ z_{\mathrm{g}} $ distribution than the inclusive jet reference, indicating that the b quark carries a greater amount of momentum when emitting gluons. The identified b quark dead cone may serve as a control region for isolated medium-induced radiation in Pb-Pb collisions in a future measurement. |
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