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| CMS-PAS-TOP-26-001 | ||
| Measurement of the $ \vert V_{\mathrm{cb}}\vert $ element of the CKM matrix from top quark pair events in proton-proton collisions at $ \sqrt{s}= $ 13 TeV | ||
| CMS Collaboration | ||
| 2026-07-30 | ||
| Abstract: A measurement of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element $ \vert V_{\mathrm{cb}}\vert $ is presented using top quark pair events produced in proton-proton collisions at $ \sqrt{s}= $ 13 TeV. The data correspond to an integrated luminosity of 138 fb$ ^{-1} $ collected by the CMS experiment at the LHC. The measurement targets the lepton+jets final state, where one W boson decays leptonically and the other hadronically. The value of $ \vert V_{\mathrm{cb}}\vert $ is extracted from the branching fraction of the $ \mathrm{W}{\rightarrow}\mathrm{cb} $ decay. To identify this rare signal amid the dominant $ \mathrm{W}{\rightarrow}\mathrm{ud} $ and $ \mathrm{W}{\rightarrow}\mathrm{cs} $ backgrounds, a multivariate discriminator based primarily on the b jet tagging information of the jets assigned to the hadronic W boson decay is used. The measured value is $ \vert V_{\mathrm{cb}}\vert=4.59 ^{+0.44}_{-0.48} $ (stat) $ ^{+0.64}_{-0.76} $ (syst) $ \times10^{-2} $. This result represents the most precise measurement of $ \vert V_{\mathrm{cb}}\vert $ from on-shell W boson decays at a hadron collider, providing a complementary determination at the electroweak scale that is independent of the nonperturbative QCD inputs used in measurements based on semileptonic B-hadron decays. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
Distributions of the $ \mathcal{D}_{\mathrm{reco}} $ evaluated on simulated lepton+jets $ \mathrm{t} \overline{\mathrm{t}} $ events, categorized by the hadronic W boson decay mode: $ \mathrm{W}{\to}\mathrm{u}\mathrm{d} (\mathrm{u}\mathrm{s}) $ (left), $ \mathrm{W}{\to}\mathrm{c}\mathrm{s} (\mathrm{c}\mathrm{d}) $ (center), and the signal $ \mathrm{W}{\to}\mathrm{c}\mathrm{b} $ (right). The stacked histograms represent the categorization of the selected jet-parton assignments based on generator-level truth information, as defined in the text. |
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Figure 2:
Feature importance for the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminant as determined by the TabNet model during training. |
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Figure 3:
Receiver operating characteristic (ROC) curves evaluating the binary classification performance of the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminant. The curves demonstrate the separation power of the correctly matched $ \mathrm{W}{\to}\mathrm{c}\mathrm{b} $ signal against various topologies, which are explicitly categorized by the hadronic W boson decay mode and the additional heavy-flavor jet content. The definitions of the signal and background classes, including the matching requirement, are given in Table 2. |
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Figure 4:
Distributions of the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator for simulated events, categorized by the hadronic W boson decay mode: $ \mathrm{W}{\to}\mathrm{u}\mathrm{d} (\mathrm{u}\mathrm{s}) $ (left), $ \mathrm{W}{\to}\mathrm{c}\mathrm{s} (\mathrm{c}\mathrm{d}) $ (center), and $ \mathrm{W}{\to}\mathrm{c}\mathrm{b} $ (right). The stacked histograms represent the categorization of the jet-parton assignments, following the identical definitions established in figure 1. |
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Figure 5:
Pre-fit distributions in the single-lepton region of the $ B $ scores of the $ j_{D}^{W} $ (upper left) and $ j_{U}^{W} $ (upper right) candidates, the $ \mathcal{D}_{\mathrm{reco}} $ discriminator (middle left), the reconstructed hadronic top quark mass (middle right), the $ \min m_{\mathrm{b}\mathrm{b}} $ observable (lower left), and the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator (lower right). The signal contribution is overlaid and is not included in the stacked background prediction. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include statistical and systematic components before the likelihood fit. |
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Figure 5-a:
Pre-fit distributions in the single-lepton region of the $ B $ scores of the $ j_{D}^{W} $ (upper left) and $ j_{U}^{W} $ (upper right) candidates, the $ \mathcal{D}_{\mathrm{reco}} $ discriminator (middle left), the reconstructed hadronic top quark mass (middle right), the $ \min m_{\mathrm{b}\mathrm{b}} $ observable (lower left), and the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator (lower right). The signal contribution is overlaid and is not included in the stacked background prediction. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include statistical and systematic components before the likelihood fit. |
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Figure 5-b:
Pre-fit distributions in the single-lepton region of the $ B $ scores of the $ j_{D}^{W} $ (upper left) and $ j_{U}^{W} $ (upper right) candidates, the $ \mathcal{D}_{\mathrm{reco}} $ discriminator (middle left), the reconstructed hadronic top quark mass (middle right), the $ \min m_{\mathrm{b}\mathrm{b}} $ observable (lower left), and the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator (lower right). The signal contribution is overlaid and is not included in the stacked background prediction. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include statistical and systematic components before the likelihood fit. |
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Figure 5-c:
Pre-fit distributions in the single-lepton region of the $ B $ scores of the $ j_{D}^{W} $ (upper left) and $ j_{U}^{W} $ (upper right) candidates, the $ \mathcal{D}_{\mathrm{reco}} $ discriminator (middle left), the reconstructed hadronic top quark mass (middle right), the $ \min m_{\mathrm{b}\mathrm{b}} $ observable (lower left), and the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator (lower right). The signal contribution is overlaid and is not included in the stacked background prediction. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include statistical and systematic components before the likelihood fit. |
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Figure 5-d:
Pre-fit distributions in the single-lepton region of the $ B $ scores of the $ j_{D}^{W} $ (upper left) and $ j_{U}^{W} $ (upper right) candidates, the $ \mathcal{D}_{\mathrm{reco}} $ discriminator (middle left), the reconstructed hadronic top quark mass (middle right), the $ \min m_{\mathrm{b}\mathrm{b}} $ observable (lower left), and the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator (lower right). The signal contribution is overlaid and is not included in the stacked background prediction. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include statistical and systematic components before the likelihood fit. |
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Figure 5-e:
Pre-fit distributions in the single-lepton region of the $ B $ scores of the $ j_{D}^{W} $ (upper left) and $ j_{U}^{W} $ (upper right) candidates, the $ \mathcal{D}_{\mathrm{reco}} $ discriminator (middle left), the reconstructed hadronic top quark mass (middle right), the $ \min m_{\mathrm{b}\mathrm{b}} $ observable (lower left), and the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator (lower right). The signal contribution is overlaid and is not included in the stacked background prediction. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include statistical and systematic components before the likelihood fit. |
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Figure 5-f:
Pre-fit distributions in the single-lepton region of the $ B $ scores of the $ j_{D}^{W} $ (upper left) and $ j_{U}^{W} $ (upper right) candidates, the $ \mathcal{D}_{\mathrm{reco}} $ discriminator (middle left), the reconstructed hadronic top quark mass (middle right), the $ \min m_{\mathrm{b}\mathrm{b}} $ observable (lower left), and the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator (lower right). The signal contribution is overlaid and is not included in the stacked background prediction. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include statistical and systematic components before the likelihood fit. |
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Figure 6:
Pre-fit distribution of the unrolled 2D $ B $ template in the dilepton control region. The $ \mathrm{t} \overline{\mathrm{t}} $ contributions are grouped by the flavor content of additional jets; the detailed generator-level categories are defined in section 3. The uncertainty band includes statistical and systematic components before the likelihood fit. |
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Figure 7:
Post-fit distributions of the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminator in the single-lepton region. For visual clarity, $ {\mathrm{t}\overline{\mathrm{t}}} {+}\text{HF} $ contributions are included in the $ \mathrm{t} \overline{\mathrm{t}} $ categories labeled by the hadronic W boson decay mode and in the $ \mathrm{t} \overline{\mathrm{t}} $ dilepton category. The uncertainty bands include both statistical and systematic components. |
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Figure 8:
Post-fit distributions of the unrolled 2D $ B $ template in the dilepton control region. The $ \mathrm{t} \overline{\mathrm{t}} $ contributions are grouped by the flavor content of additional jets; the detailed generator-level categories are defined in section 3. The uncertainty bands include both statistical and systematic components. |
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Figure 9:
Profile likelihood scan as a function of $ |V_{\mathrm{c}\mathrm{b}}| $. The horizontal lines at $ -2\Delta ln \mathcal{L} = 1 $ and 4 indicate the 68% and 95% confidence intervals, respectively. |
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Figure 10:
Bootstrap compatibility test of the POI values obtained with the 4FS and 5FS fits. The left panel shows the paired $ ( r_\mathrm{4FS} , r_\mathrm{5FS} ) $ distribution, and the right panel shows the distribution of $ Delta r = r_\mathrm{4FS} - r_\mathrm{5FS} $. |
| Tables | |
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Table 1:
Summary of event selection. |
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Table 2:
Definition of the seven training classes for the $ \mathcal{D}_{\mathrm{W}{\to}\mathrm{c}\mathrm{b}} $ discriminant. The events are categorized into seven distinct classes based on the decay mode of the hadronic W boson, the presence and flavor of additional heavy-flavor jets, and the success of the jet-parton matching during the $ \mathrm{t} \overline{\mathrm{t}} $ reconstruction. Classes 1 and 2 constitute the targeted signal process, while Classes 3 through 7 represent the various background topologies. The additional b-flavored jet class comprises the $ {\mathrm{t}\overline{\mathrm{t}}} {+}\mathrm{b} $, $ {\mathrm{t}\overline{\mathrm{t}}} {+}2\mathrm{b} $, and $ {\mathrm{t}\overline{\mathrm{t}}} {+}\mathrm{b}\mathrm{b} $ generator-level categories, whereas the additional c-flavored jet class comprises the $ {\mathrm{t}\overline{\mathrm{t}}} {+}\mathrm{c} $ and $ {\mathrm{t}\overline{\mathrm{t}}} {+}\mathrm{c}\overline{\mathrm{c}} $ generator-level categories. |
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Table 3:
Leading contributions to the uncertainty in the fitted signal strength $(r)$. Each contribution is evaluated from profile-likelihood scans by fixing the corresponding group of nuisance parameters. Because correlations between different nuisance-parameter groups cannot be uniquely assigned in this procedure, the individual contributions are not expected to add in quadrature to the total uncertainty. |
| Summary |
| A measurement of the magnitude of the Cabibbo--Kobayashi--Maskawa (CKM) matrix element $ |V_{\mathrm{c}\mathrm{b}}| $ is presented using top-quark pair ( $ \mathrm{t} \overline{\mathrm{t}} $) events in the lepton+jets final state produced in proton-proton collisions at $ \sqrt{s} = $ 13 TeV. The data correspond to an integrated luminosity of 138 fb$ ^{-1} $ collected by the CMS experiment. The analysis exploits the hadronic decay of the W boson in $ \mathrm{t} \overline{\mathrm{t}} $ events to determine $ |V_{\mathrm{c}\mathrm{b}}| $ at the electroweak scale, without relying on the nonperturbative QCD inputs required in semileptonic b-flavored hadron decay measurements. The $ \mathrm{t} \overline{\mathrm{t}} $ system is reconstructed using a boosted decision tree algorithm, and a dedicated discriminator is constructed to separate the $ \mathrm{W}{\to}\mathrm{c}\mathrm{b} $ signal from the dominant $ \mathrm{t} \overline{\mathrm{t}} $ backgrounds using flavor-tagging and kinematic information. A simultaneous binned maximum-likelihood fit is applied to the signal region and control regions to extract the signal strength. Backgrounds from $ \mathrm{t} \overline{\mathrm{t}} $ production with additional heavy-flavor jets are constrained in the fit, with the nominal modeling of the additional-b component based on a dedicated NLO $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{b}\overline{\mathrm{b}} $ prediction (4FS). An alternative fit using the inclusive $ \mathrm{t} \overline{\mathrm{t}} $ prediction at NLO in QCD (5FS) is found to be compatible with the nominal result within the sensitivity of the analysis. The measured signal strength is $ r = 1.20^{+0.44}_{-0.42} $, corresponding to \[ |V_{\mathrm{c}\mathrm{b}}| = 4.59^{+0.44}_{-0.48} (\mathrm{stat}) ^{+0.64}_{-0.76} (\mathrm{syst}) \times 10^-2. \] The uncertainties include both statistical and systematic contributions and are dominated by the modeling of $ \mathrm{t} \overline{\mathrm{t}} $ production with additional heavy-flavor jets and by flavor-tagging uncertainties. The measured value is consistent within uncertainties with both the inclusive and exclusive determinations from semileptonic $ {\mathrm{B}} $ meson decays [9]. Although its precision is currently lower than that of those determinations, it provides a theoretically complementary probe of $ |V_{\mathrm{c}\mathrm{b}}| $ through the decay of an on-shell W boson at the electroweak scale. This result represents the most sensitive hadron-collider constraint to date on $ |V_{\mathrm{c}\mathrm{b}}| $ from W boson decays. Future measurements will benefit from the increased luminosity and the enhanced heavy-flavor tagging performance expected in CMS Run 3. Furthermore, extending the phase space to include the boosted regime offers a promising complementary avenue, where specialized boosted-jet tagging techniques can help suppress backgrounds and reduce systematic uncertainties [62]. The synergy between the resolved-channel strategy established in this work and future boosted-regime analyses holds the potential to reach the precision required to shed light on the long-standing discrepancy between inclusive and exclusive determinations of $ |V_{\mathrm{c}\mathrm{b}}| $. |
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