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| CMS-PAS-HIN-24-005 | ||
| Jet fragmentation function and groomed substructure of bottom quark jets in proton-proton collisions at 5.02 TeV | ||
| CMS Collaboration | ||
| 6 September 2024 | ||
| Abstract: A measurement of the substructure of bottom quark jets (b jets) in proton-proton (pp) collisions is presented. The measurement uses 301 pb$ ^{-1} $ of data collected in pp collisions by the CMS experiment at $ \sqrt{s} = $ 5.02 TeV. An algorithm to identify and cluster the decay charged-particle 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 clustering. The soft drop groomed jet radius $ R_{\mathrm{g}} $ and the groomed momentum balance $ z_{\mathrm{g}} $ of b quark jets are presented. The $ z_{\mathrm{g}} $ and $ R_{\mathrm{g}} $ observables can be used to test perturbative quantum chromodynamics predictions based on the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi parton splitting functions that account for mass effects. Because the b hadron is partially reconstructed using charged particles, only charged particles are used for the jet substructure. In addition, a jet fragmentation function is measured, which is the ratio of the transverse momentum $ p_{\mathrm{T}} $ of the partially reconstructed b hadron with respect to the charged component of the jet $ p_{\mathrm{T}} $. The substructure 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 the b hadron decay daughters. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Left: 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: Lund jet plane regions of bottom quark jets. The vertical axis is the logarithm of the relative transverse momentum $ k_{\mathrm{T}} $ of the softer subjet with respect to the harder subjet. The horizontal axis is the logarithm 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, depicted in blue. The b hadron decays (not depicted) populate the same region. The shading 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 simulation (PYTHIA8 CP5). The vertical axis is the logarithm of the $ k_{\mathrm{T}} $ 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. Left panel: the Lund plane with the b hadron charged decay daughters present and treated at the same level as the other hadrons in the CA declustering, where the effect of the decays can be observed in the yellow hotspot at small angles and low $ k_{\mathrm{T}} $. Right panel: with the b hadron charged decay daughters clustered together, i.e., the charged component of the b hadron remains intact. |
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Figure 2-a:
The Lund jet plane of the soft drop emissions of b quark jets at the particle level simulation (PYTHIA8 CP5). The vertical axis is the logarithm of the $ k_{\mathrm{T}} $ 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. Left panel: the Lund plane with the b hadron charged decay daughters present and treated at the same level as the other hadrons in the CA declustering, where the effect of the decays can be observed in the yellow hotspot at small angles and low $ k_{\mathrm{T}} $. Right panel: with the b hadron charged decay daughters clustered together, i.e., the charged component of the b hadron remains intact. |
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Figure 2-b:
The Lund jet plane of the soft drop emissions of b quark jets at the particle level simulation (PYTHIA8 CP5). The vertical axis is the logarithm of the $ k_{\mathrm{T}} $ 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. Left panel: the Lund plane with the b hadron charged decay daughters present and treated at the same level as the other hadrons in the CA declustering, where the effect of the decays can be observed in the yellow hotspot at small angles and low $ k_{\mathrm{T}} $. Right panel: with the b hadron charged decay daughters clustered together, i.e., the charged component of the b hadron remains intact. |
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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 and 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 and 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 and 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,ch}} $ 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 from the top to the bottom of the stacked histogram, with the fractions acquired from the fit. The ratio between the data and the fit values is also presented. |
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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,ch}} $ 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 from the top to the bottom of the stacked histogram, with the fractions acquired from the fit. The ratio between the data and the fit values is also presented. |
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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,ch}} $ 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 from the top to the bottom of the stacked histogram, with the fractions acquired from the fit. The ratio between the data and the fit values is also presented. |
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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,ch}} $ 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 from the top to the bottom of the stacked histogram, with the fractions acquired from the fit. The ratio between the data and the fit values is also presented. |
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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 (Top panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, bottom panel: $ z_{\mathrm{b,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 (Top panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, bottom panel: $ z_{\mathrm{b,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 (Top panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, bottom panel: $ z_{\mathrm{b,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 (Top panel: $ R_{\mathrm{g}} $, middle panel: $ z_{\mathrm{g}} $, bottom panel: $ z_{\mathrm{b,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 stable-particle level for inclusive jets. The gray band represents the systematic uncertainties added in quadrature, while the vertical bars represent the statistical uncertainty. A comparison with PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators is presented. |
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Figure 7-a:
Distributions of groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the stable-particle level for inclusive jets. The gray band represents the systematic uncertainties added in quadrature, while the vertical bars represent the statistical uncertainty. A comparison with PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators is presented. |
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Figure 7-b:
Distributions of groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the stable-particle level for inclusive jets. The gray band represents the systematic uncertainties added in quadrature, while the vertical bars represent the statistical uncertainty. A comparison with PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators is presented. |
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Figure 8:
Distributions of the groomed substructure observables $ R_{\mathrm{g}} $ (left) and $ z_{\mathrm{g}} $ (right) corrected to the particle level for b jets. A comparison with PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators is presented. |
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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 particle level for b jets. A comparison with PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators is presented. |
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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 particle level for b jets. A comparison with PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators is presented. |
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Figure 9:
The distribution of the charged momentum fraction $ z_{\mathrm{b,ch}} $ of the partially reconstructed b hadron corrected to the particle level. A comparison with PYTHIA8 CP5 and HERWIG 7 CH3 MC event generators is presented. |
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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, with the exception of those related to flavor. |
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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, with the exception of those related to flavor. |
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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, with the exception of those related to flavor. |
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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. |
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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. |
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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. |
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Figure 12:
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 13:
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 13-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 13-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 note presented a measurement of the substructure of bottom quark jets (b jets) and of inclusive jets in proton-proton (pp) collisions at $ \sqrt{s} = $ 5.02 TeV using data corresponding to an integrated luminosity of 301 $\,\text{pb}^{-1}$ collected in 2017 with the CMS experiment. We analyzed the substructure of jets initially clustered with the anti-$ k_{\mathrm{T}} $ algorithm with the distance parameter $ R = $ 0.4 having transverse momentum 100 $ < p_{\mathrm{T}} < $ 120 GeV and pseudorapidity $ |\eta| < $ 2. The charged-particle constituents of the jets are used for the substructure. The groomed jet radius $ R_{\mathrm{g}} $, groomed momentum fraction $ z_{\mathrm{g}} $, and the jet fragmentation function $ z_{\mathrm{b,ch}} $ are measured and corrected to the particle level. Such 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 at an equal footing as the hadrons that are produced from the transition from partons to hadrons. To better understand the gluon-radiation pattern from b jets, the b hadron decay daughters need to be handled in a careful way experimentally. This measurement uses an algorithm to identify and cluster the b hadron decay charged-particle daughters of b-tagged jets in a generic way, which allows for a cleaner interpretation of the measured substructure distributions in terms of the parton showering description. The contributions from gluon, light quark, charm quark jets, and gluon splitting ($ \mathrm{g} \to \mathrm{b} \bar{\mathrm{b}} $) are subtracted from the measured distributions. 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 at the detector-level, which is applied as a bin-by-bin substructure- and jet $ p_{\mathrm{T}} $-dependent correction after the unfolding correction for bin-to-bin migration effects. The particle-level distributions have uncertainties of the order of 5% and up to 20%, dominated by the physics model uncertainty in most of the bins ( HERWIG 7 CH3 compared with PYTHIA8 CP5). The groomed-jet radius and groomed momentum fraction of b jets is well described by PYTHIA8 CP5 and HERWIG 7 CH3 simulations. The jet fragmentation function, on the other hand, is described better by PYTHIA8 CP5 at high values of $ z \approx $ 1 (i.e., for cases where the b hadron carries a substantial amount of the jet $ p_{\mathrm{T}} $). The $ z \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,ch}} $ can be used simultaneously to constrain nonperturbative and perturbative aspects of b jet substructure. When comparing to inclusive jets, we find large differences, not covered by the systematic uncertainties, for $ R_{\mathrm{g}} $. 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 groomed momentum balance $ z_{\mathrm{g}} $ than the inclusive jet reference, indicating that the b quark carries a greater amount of momentum when emitting gluons. The measurement shows that the distributions that remove soft- and wide-angle radiation are well described by the PYTHIA8 CP5 and HERWIG 7 CH3 event generators for b jets. For the jet fragmentation function, PYTHIA8 CP5 describes the data better than HERWIG 7 CH3. Although both HERWIG 7 CH3 and PYTHIA8 CP5 describe the $ R_{\mathrm{g}} $ and $ z_{\mathrm{g}} $ distributions well for b jets, PYTHIA8 CP5 does not have a good description of the inclusive jet substructure. |
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