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| CMS-SMP-25-008 ; CERN-EP-2026-232 | ||
| Evidence for the dead-cone effect in bottom quark initiated jets produced in proton-proton collisions at $ \sqrt{s} = $ 13 TeV | ||
| CMS Collaboration | ||
| 29 August 2026 | ||
| Submitted to Physical Review Letters | ||
| Abstract: The suppression of collinear gluon emissions from a massive quark, or the ``dead-cone effect,'' is the primary manifestation of quark mass effects in parton showers. A proton-proton collision data set recorded by the CMS experiment at $ \sqrt{s}= $ 13 TeV with an integrated luminosity of 59.8 fb$ ^{-1} $ is analyzed. A differential measurement is presented of the emission density of bottom quark jets, studied as a function of the angular separation between iteratively declustered subjets. The measurement is performed in bottom quark initiated jets with transverse momenta between 40 and 200 GeV originating from top quark pair production. Compared to data, a parton shower Monte Carlo model that includes the dead-cone effect is favored, while a model without the dead-cone effect is disfavored with a significance of 4.3 standard deviations. | ||
| Links: e-print arXiv:2608.29412 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; | ||
| Figures | |
png pdf |
Figure 1:
An illustration of the iterative declustering of a b quark jet to construct the Lund jet plane (LJP). The upper diagram shows the showering of a b quark (pointing arrow) ordered in descending angular separation between the b quark and the gluon radiation (curly line). The pink cones along the direction of the emitters represent the dead cones. The lower diagram shows the corresponding LJP, where each colored point corresponds to a declustering step in the upper diagram and the pink block indicates the region sensitive to the dead cone. |
png pdf |
Figure 1-a:
An illustration of the iterative declustering of a b quark jet to construct the Lund jet plane (LJP). The upper diagram shows the showering of a b quark (pointing arrow) ordered in descending angular separation between the b quark and the gluon radiation (curly line). The pink cones along the direction of the emitters represent the dead cones. The lower diagram shows the corresponding LJP, where each colored point corresponds to a declustering step in the upper diagram and the pink block indicates the region sensitive to the dead cone. |
png pdf |
Figure 1-b:
An illustration of the iterative declustering of a b quark jet to construct the Lund jet plane (LJP). The upper diagram shows the showering of a b quark (pointing arrow) ordered in descending angular separation between the b quark and the gluon radiation (curly line). The pink cones along the direction of the emitters represent the dead cones. The lower diagram shows the corresponding LJP, where each colored point corresponds to a declustering step in the upper diagram and the pink block indicates the region sensitive to the dead cone. |
png pdf |
Figure 2:
(Upper) Ratio of the emission density distribution between the b quark jets selected using either the DEEPJET b tagger or the T&P method to the b quark jets selected using generator-level information. (Lower) The detector-level and generator-level emission density distributions for b quark jets with 40 $ < p_{\mathrm{T}} < $ 80 GeV in the POWHEG +PYTHIA\ $ \mathrm{t} \overline{\mathrm{t}} $ sample are shown with and without the partial b hadron reconstruction, either with generator-level information or with the transformer encoder. The statistical uncertainties are too small to be visible in either panel. |
png pdf |
Figure 2-a:
(Upper) Ratio of the emission density distribution between the b quark jets selected using either the DEEPJET b tagger or the T&P method to the b quark jets selected using generator-level information. (Lower) The detector-level and generator-level emission density distributions for b quark jets with 40 $ < p_{\mathrm{T}} < $ 80 GeV in the POWHEG +PYTHIA\ $ \mathrm{t} \overline{\mathrm{t}} $ sample are shown with and without the partial b hadron reconstruction, either with generator-level information or with the transformer encoder. The statistical uncertainties are too small to be visible in either panel. |
png pdf |
Figure 2-b:
(Upper) Ratio of the emission density distribution between the b quark jets selected using either the DEEPJET b tagger or the T&P method to the b quark jets selected using generator-level information. (Lower) The detector-level and generator-level emission density distributions for b quark jets with 40 $ < p_{\mathrm{T}} < $ 80 GeV in the POWHEG +PYTHIA\ $ \mathrm{t} \overline{\mathrm{t}} $ sample are shown with and without the partial b hadron reconstruction, either with generator-level information or with the transformer encoder. The statistical uncertainties are too small to be visible in either panel. |
png pdf |
Figure 2-c:
(Upper) Ratio of the emission density distribution between the b quark jets selected using either the DEEPJET b tagger or the T&P method to the b quark jets selected using generator-level information. (Lower) The detector-level and generator-level emission density distributions for b quark jets with 40 $ < p_{\mathrm{T}} < $ 80 GeV in the POWHEG +PYTHIA\ $ \mathrm{t} \overline{\mathrm{t}} $ sample are shown with and without the partial b hadron reconstruction, either with generator-level information or with the transformer encoder. The statistical uncertainties are too small to be visible in either panel. |
png pdf |
Figure 2-d:
(Upper) Ratio of the emission density distribution between the b quark jets selected using either the DEEPJET b tagger or the T&P method to the b quark jets selected using generator-level information. (Lower) The detector-level and generator-level emission density distributions for b quark jets with 40 $ < p_{\mathrm{T}} < $ 80 GeV in the POWHEG +PYTHIA\ $ \mathrm{t} \overline{\mathrm{t}} $ sample are shown with and without the partial b hadron reconstruction, either with generator-level information or with the transformer encoder. The statistical uncertainties are too small to be visible in either panel. |
png pdf |
Figure 3:
The measured emission density per $ {\ln(R/{\Delta R})} $ for b quark jets with (upper) 40 $ < p_{\mathrm{T}} < $ 80 GeV and (lower) 80 $ < p_{\mathrm{T}} < $ 200 GeV, with vertical error bars representing the total uncertainties. Data are compared with the generator-level distributions from different MC samples. The middle panels show the ratio of the data to the MC predictions with a dashed line at one for reference. The total uncertainties of the data are shown as the gray band. The lower panels show the breakdown of the data uncertainties into various sources. |
png pdf |
Figure 3-a:
The measured emission density per $ {\ln(R/{\Delta R})} $ for b quark jets with (upper) 40 $ < p_{\mathrm{T}} < $ 80 GeV and (lower) 80 $ < p_{\mathrm{T}} < $ 200 GeV, with vertical error bars representing the total uncertainties. Data are compared with the generator-level distributions from different MC samples. The middle panels show the ratio of the data to the MC predictions with a dashed line at one for reference. The total uncertainties of the data are shown as the gray band. The lower panels show the breakdown of the data uncertainties into various sources. |
png pdf |
Figure 3-b:
The measured emission density per $ {\ln(R/{\Delta R})} $ for b quark jets with (upper) 40 $ < p_{\mathrm{T}} < $ 80 GeV and (lower) 80 $ < p_{\mathrm{T}} < $ 200 GeV, with vertical error bars representing the total uncertainties. Data are compared with the generator-level distributions from different MC samples. The middle panels show the ratio of the data to the MC predictions with a dashed line at one for reference. The total uncertainties of the data are shown as the gray band. The lower panels show the breakdown of the data uncertainties into various sources. |
png pdf |
Figure 3-c:
The measured emission density per $ {\ln(R/{\Delta R})} $ for b quark jets with (upper) 40 $ < p_{\mathrm{T}} < $ 80 GeV and (lower) 80 $ < p_{\mathrm{T}} < $ 200 GeV, with vertical error bars representing the total uncertainties. Data are compared with the generator-level distributions from different MC samples. The middle panels show the ratio of the data to the MC predictions with a dashed line at one for reference. The total uncertainties of the data are shown as the gray band. The lower panels show the breakdown of the data uncertainties into various sources. |
png pdf |
Figure 3-d:
The measured emission density per $ {\ln(R/{\Delta R})} $ for b quark jets with (upper) 40 $ < p_{\mathrm{T}} < $ 80 GeV and (lower) 80 $ < p_{\mathrm{T}} < $ 200 GeV, with vertical error bars representing the total uncertainties. Data are compared with the generator-level distributions from different MC samples. The middle panels show the ratio of the data to the MC predictions with a dashed line at one for reference. The total uncertainties of the data are shown as the gray band. The lower panels show the breakdown of the data uncertainties into various sources. |
png pdf |
Figure 4:
Architecture of the transformer encoder trained to identify b hadron decay products in jets. Input to the network are three-dimensional arrays that represent the number of jets, the number of constituents in a jet, and the number of features. The first feed forward (FF1) block is a single-layered dense network that expands the feature dimension to 128. This is followed by the multihead attention (MHA) block with four heads, and another FF block (FF2) with two layers. Both blocks keep 128 hidden dimensions. Skip connections and layer normalizations (Add & norm) are added in between the MHA and FF1, and after FF2. The MHA, FF2, and Add & norm blocks are repeated together for four different times. The final block is a single-layered FF (FF3) that contracts the final output to two-dimensional arrays representing a sequence of probabilities for each constituent in a jet to be a b hadron decay product or not. |
png pdf |
Figure 4-a:
Architecture of the transformer encoder trained to identify b hadron decay products in jets. Input to the network are three-dimensional arrays that represent the number of jets, the number of constituents in a jet, and the number of features. The first feed forward (FF1) block is a single-layered dense network that expands the feature dimension to 128. This is followed by the multihead attention (MHA) block with four heads, and another FF block (FF2) with two layers. Both blocks keep 128 hidden dimensions. Skip connections and layer normalizations (Add & norm) are added in between the MHA and FF1, and after FF2. The MHA, FF2, and Add & norm blocks are repeated together for four different times. The final block is a single-layered FF (FF3) that contracts the final output to two-dimensional arrays representing a sequence of probabilities for each constituent in a jet to be a b hadron decay product or not. |
png pdf |
Figure 4-b:
Architecture of the transformer encoder trained to identify b hadron decay products in jets. Input to the network are three-dimensional arrays that represent the number of jets, the number of constituents in a jet, and the number of features. The first feed forward (FF1) block is a single-layered dense network that expands the feature dimension to 128. This is followed by the multihead attention (MHA) block with four heads, and another FF block (FF2) with two layers. Both blocks keep 128 hidden dimensions. Skip connections and layer normalizations (Add & norm) are added in between the MHA and FF1, and after FF2. The MHA, FF2, and Add & norm blocks are repeated together for four different times. The final block is a single-layered FF (FF3) that contracts the final output to two-dimensional arrays representing a sequence of probabilities for each constituent in a jet to be a b hadron decay product or not. |
| Tables | |
png pdf |
Table 1:
Performance of the TFE to identify b hadron decay products in jets in the training, testing, and validation sets of the POWHEG +PYTHIA dileptonic $ \mathrm{t} \overline{\mathrm{t}} $ sample. |
| Summary |
| In summary, a measurement of the emission density distribution in bottom quark initiated jets (b jets) from top quark pair events in proton-proton collisions at $\sqrt{s}=13$ TeV with the CMS detector has been presented. A sample of b jets with minimized flavor tagging biases is selected with a tag-and-probe method. A transformer encoder is trained to partially reconstruct b hadrons in jets and preserve an uncontaminated angle-ordered emission history, reconstructed on the Lund jet plane [36][37]. A new experimental benchmark is provided to compare with analytical quantum chromodynamics predictions including the effect of quark masses [26][51] and for parton shower model development [50]. A suppression of collinear emissions relative to a light-quark simulation is shown by the measured emission density distribution. Compared to data, a parton shower Monte Carlo model that includes the dead-cone effect is favored, while a model without the dead-cone effect is disfavored with a significance of 4.3 standard deviations. |
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