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Measurement of the $\lvert V_\mathrm{cb}\rvert$ element of the CKM matrix using $\mathrm{t\bar{t}}$ events in pp collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at 13 TeV collected by the CMS experiment, this paper presents a measurement of the CKM matrix element $|V_{cb}|$ derived from the branching fraction of the rare W $\to$ cb decay in top quark pair events, yielding a value of $4.59^{+0.44}_{-0.48} \text{(stat)} ^{0.64}_{-0.76} \text{(syst)} \times 10^{-2}$ that offers a complementary, nonperturbative-QCD-independent determination at the electroweak scale.

Original author: CMS Collaboration

Published 2026-11-03

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CC BY 4.0

Original author: CMS Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

The universe is built from a handful of fundamental particles that interact through forces, but the rules governing how these particles change from one type to another are written in a specific mathematical table known as the Cabibbo–Kobayashi–Maskawa matrix. This table acts as a rulebook for the weak nuclear force, dictating the probability that a heavy quark will transform into a lighter one. One entry in this table, representing the transformation of a bottom quark into a charm quark, has long been a source of intense scrutiny. Physicists have measured this value using two different methods: one by watching heavy particles decay in a way that requires complex theoretical calculations to interpret, and another by observing similar decays that rely on different calculations. For years, these two methods have disagreed with each other by a margin that suggests something might be missing from our current understanding of physics. To resolve this tension, scientists needed a third way to measure this value, one that did not rely on the same complicated calculations that had caused the disagreement in the first place.

Researchers at the Large Hadron Collider have now provided this independent measurement by observing the decay of top quarks, the heaviest known elementary particles. When two protons collide at high speeds, they occasionally produce a pair of top quarks. These particles are so unstable that they vanish almost instantly, transforming into a W boson and a bottom quark. The W boson then decays further, sometimes turning into a pair of quarks. In the vast majority of cases, the W boson decays into the most common pair of quarks, but very rarely, it decays into a bottom quark and a charm quark. This rare event is the key to the measurement. Because the top quark decays so quickly, the W boson it produces is essentially "on-shell," meaning it behaves exactly as predicted by the standard model without the messy complications of the internal structure of larger particles. This allows physicists to measure the transformation probability directly, free from the theoretical uncertainties that plagued previous attempts.

The CMS experiment, a massive detector designed to capture the debris of these collisions, analyzed data corresponding to an integrated luminosity of 138 fb⁻¹ collected from proton-proton collisions. The team focused on a specific signature where one of the W bosons from the top quark pair decays into a single electron or muon, while the other decays into two jets of particles. To find the rare signal where the hadronic W boson produced a bottom and a charm quark, the researchers had to distinguish it from the overwhelming background of events where the W boson produced the much more common pairs of up and down quarks, or charm and strange quarks. They used a sophisticated computer algorithm trained to recognize the unique "flavor" of the particles involved. This algorithm looked at the tracks left by the particles and the energy they deposited, specifically searching for the tell-tale signs of a bottom quark and a charm quark appearing together in the debris of the W boson decay.

After sifting through the data, the researchers found a signal consistent with the rare decay. They calculated the value of the matrix element to be 0.0459, with an uncertainty range that accounts for both statistical fluctuations and systematic errors in the measurement. This result is consistent within uncertainties with both the inclusive and exclusive determinations obtained from the two previous methods, suggesting that the discrepancy might be resolved once more precise data is available, or that the current measurements are consistent within their margins of error. The measurement is not yet precise enough to definitively declare a winner among the competing theories, but it provides a crucial, independent check that does not depend on the same theoretical inputs as the others. By confirming that the decay of a W boson at the energy scale of the top quark follows the expected patterns, the study reinforces the standard model while offering a new path to investigate the subtle differences that might hint at new physics. The work demonstrates that even in a sea of common events, rare processes can be isolated and measured with enough precision to test the fundamental laws of nature.

Technical Summary: Measurement of the |Vcb| Element of the CKM Matrix using tt Events

Problem and Motivation
The precise determination of the Cabibbo–Kobayashi–Maskawa (CKM) matrix element $|V_{cb}|$ is a critical test of the Standard Model (SM). Currently, $|V_{cb}|$ is determined primarily through semileptonic $B$ meson decays, utilizing two distinct approaches: inclusive measurements relying on the heavy-quark expansion, and exclusive measurements depending on hadronic form factors constrained by lattice QCD. Despite significant advances, a persistent discrepancy exceeding three standard deviations exists between the values obtained from these two methods, a tension known as the " $|V_{cb}|$ puzzle."

This paper addresses the need for an independent determination of $|V_{cb}|$ that does not rely on the nonperturbative quantum chromodynamics (QCD) inputs inherent to $B$ meson decay measurements. The proposed approach extracts $|V_{cb}|$ from the branching fraction of the rare hadronic decay $W \to cb$ within top quark pair ( $t\bar{t}$ ) events. This method probes $|V_{cb}|$ at the electroweak scale (order $m_W$ ), distinct from the characteristic scale of $B$ decays (order $m_b/2$ ), and avoids modeling low- $q^2$ hadronic form factors or meson bound-state dynamics.

Methodology
The analysis utilizes proton-proton collision data at $\sqrt{s} = 13$ TeV collected by the CMS experiment, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The study targets the lepton+jets final state of $t\bar{t}$ events, where one $W$ boson decays leptonically (providing a trigger and background suppression) and the other decays hadronically (providing the signal probe).

Event Selection and Reconstruction: Events are selected requiring at least four jets (with $p_T > 25$ GeV), at least two $b$ -tagged jets, and exactly one isolated lepton. A two-step Boosted Decision Tree (BDT) strategy, based on XGBoost, is employed to reconstruct the $t\bar{t}$ system. The first BDT selects the overall jet-parton configuration, while the second resolves the up-down assignment of the jets from the hadronic $W$ decay. Crucially, the B scores of the jets assigned to the $W$ decay are intentionally omitted from the first BDT to prevent the preferential assignment of jets from additional heavy-flavor (HF) radiation as $W$ decay products.
Signal Discrimination: To isolate the rare $W \to cb$ signal from dominant backgrounds ( $W \to ud$ and $W \to cs$ ), a deep neural network discriminant ( $D_{W \to cb}$ ) based on the TabNet architecture is constructed. This classifier is trained to distinguish seven event classes defined by the hadronic $W$ decay mode, the presence of additional HF jets, and the success of the jet-parton matching. The input features include the DEEPJET $b$ -tagging scores of the $W$ -daughter jets, reconstruction fidelity metrics ( $D_{reco}$ ), and kinematic variables.
Background Constraints: A dedicated dilepton control region (DL CR), enriched in $t\bar{t} + \text{HF}$ events, is introduced to constrain the modeling of additional HF radiation. A simultaneous binned maximum likelihood fit is performed across the single-lepton (SL) signal region and the DL CR, sharing nuisance parameters to constrain the $t\bar{t} + \text{HF}$ background normalization and composition directly from data.
Theoretical Modeling: The nominal analysis uses a dedicated next-to-leading-order (NLO) prediction in the four-flavor scheme (4FS) for $t\bar{t} + b\bar{b}$ production, where additional $b$ quarks are included at the matrix element level. CKM unitarity constraints are applied during the fit, dynamically rescaling the $W \to cs$ and $W \to cd$ background contributions as the $|V_{cb}|$ signal strength varies.

Key Contributions

Novel Extraction Strategy: This work presents the most sensitive direct measurement of $|V_{cb}|$ to date using $t\bar{t}$ events, employing a multivariate analysis that leverages heavy-flavor jet properties and kinematic reconstruction to isolate the $W \to cb$ signal.
Advanced Machine Learning: The implementation of the TabNet algorithm for signal extraction and a two-stage BDT for $t\bar{t}$ reconstruction demonstrates improved sensitivity over previous proposals that relied on simpler discriminants.
Data-Driven Background Control: The use of a simultaneous fit with a dilepton control region effectively constrains the significant systematic uncertainties associated with the modeling of $t\bar{t}$ events with additional heavy-flavor jets.
Model Independence: The measurement provides a determination of $|V_{cb}|$ at the electroweak scale, independent of the heavy-quark expansion and lattice QCD inputs required for $B$ meson decay analyses.

Results
The measured signal strength is $r = |V_{cb}|^2 / |V_{cb}^{\text{PDG}}|^2 = 1.27^{+0.46}_{-0.44}$ . This corresponds to a measured value of:
$|V_{cb}| = [4.59^{+0.44}_{-0.48} (\text{stat})^{+0.64}_{-0.76} (\text{syst})] \times 10^{-2}$

The precision of the measurement is primarily limited by the theoretical modeling of $t\bar{t}$ production with additional heavy-flavor jets and flavor-tagging uncertainties. The result is consistent within uncertainties with both the inclusive and exclusive determinations from semileptonic $B$ meson decays. An alternative fit using the five-flavor scheme (5FS) for $t\bar{t}$ production yields a compatible result ( $r_{5FS} = 1.08^{+0.42}_{-0.41}$ ), with no significant tension observed between the two modeling descriptions.

Significance
The paper claims that while the current precision is lower than that of $B$ meson decay measurements, this result provides a crucial complementary determination of $|V_{cb}|$ at the electroweak scale. By relying on distinct theoretical and experimental inputs, this measurement offers an independent check on the $|V_{cb}|$ puzzle. The author states that the established strategy could assist future studies in probing the long-standing discrepancy between inclusive and exclusive $|V_{cb}|$ determinations.

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