Measurement of the $|V_{cb}|$ element of the CKM matrix in $t\bar{t}$ decays with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, this paper presents the first measurement of the CKM matrix element $|V_{cb}|$ from on-shell $W$-boson decays in top quark pairs, yielding a value of $(50^{+11}_{-14})\times10^{-3}$ that is consistent with existing low-energy determinations while probing a novel high-momentum-transfer physical regime.

The Gist

The Big Picture: Catching a Ghost in a Giant Factory

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle factory. Inside, it smashes protons together at nearly the speed of light, creating a chaotic explosion of new particles. Among the debris, the experimenters are looking for a specific, rare event: the creation and immediate death of a Top Quark.

The Top Quark is the "heavyweight champion" of the particle world. It's so heavy and unstable that it dies almost instantly, before it can even form a stable atom. When it dies, it usually splits into a Bottom Quark and a W Boson (a carrier of the weak force).

The W Boson is like a busy delivery truck. It doesn't stay still; it immediately drops off its cargo. Usually, it drops off a "light" package (like an Up or Down quark). But sometimes, very rarely, it drops off a "heavy" package: a Charm quark and a Bottom quark.

The goal of this paper is to count exactly how often the W Boson drops off that specific "Charm + Bottom" package. Why? Because this frequency is controlled by a fundamental number in the universe called $|V_{cb}|$.

The Problem: The "B-Factory" vs. The "Top-Factory"

For decades, physicists have tried to measure this number ($|V_{cb}|$) by studying B-mesons (particles containing Bottom quarks) in old, low-energy experiments. Think of this like trying to understand how a car engine works by watching a car drive slowly through a quiet neighborhood. You get a good look, but the conditions are very different from a race car on a track.

There is a slight disagreement in the physics community about the exact value of this number based on those old "neighborhood" studies.

This paper says: "Let's try a different approach. Let's study the Top Quark."

The Top Quark is like a Formula 1 car moving at maximum speed. It decays so fast it doesn't even have time to "wear out" or get messy (a process called hadronization). This allows physicists to see the "pure" interaction between the particles, like watching the engine run in a vacuum without the noise of the road.

The Experiment: Finding a Needle in a Haystack

The ATLAS detector is a giant, 3D camera surrounding the collision point. The team looked at 140 femtobarns of data (a massive amount of collision data from 2015–2018).

The Challenge:
They were looking for a specific event:

1. A Top and Anti-Top pair is created.
2. One Top decays into a lepton (an electron or muon) and a neutrino (easy to spot).
3. The other Top decays into a Bottom quark and a W Boson.
4. The Crucial Step: That W Boson must decay into a Charm and a Bottom quark.

The Analogy:
Imagine you are at a massive concert (the collision). You are looking for a specific VIP guest (the Top quark decay).

• Most VIPs bring a standard entourage (light quarks).
• You are looking for the VIP who brings a very rare, specific entourage (Charm + Bottom).
• The problem is, the VIPs are wearing masks, and the crowd is so loud that you can't always hear who they brought. Sometimes, a random person in the crowd looks like the VIP's entourage (background noise).

The Solution: The "Smart Filter" (Neural Network)

To solve the "noise" problem, the ATLAS team built a Neural Network (AI).

Think of the AI as a super-smart bouncer at the club. It looks at the shape, speed, and energy of the particles coming out of the collision.

• Signal: "This looks exactly like a Top quark decaying into a W, which then splits into Charm and Bottom." -> Let them in.
• Background: "This looks like a random collision of light quarks that just happened to look similar." -> Turn them away.

The AI was trained on millions of simulated events to learn the difference between the "real thing" and the "fake it."

The Results: A New Perspective

After filtering the data, the team counted the events. They found a value for $|V_{cb}|$ of roughly 0.050 (with some uncertainty).

What does this mean?

1. Consistency: This new measurement agrees with the old measurements made in the "slow" B-meson experiments. It's like checking your watch against a clock tower; they both say it's 3:00 PM. This is good news for the Standard Model (our current theory of physics).
2. Different Conditions: Even though the numbers match, this measurement was taken in a completely different environment (high energy, fast decay) than the old ones. It's like measuring the speed of light in a vacuum and then measuring it in water; if they match, it proves our understanding of how light behaves is solid.
3. Future Potential: The measurement isn't as precise as the old ones yet (the error bars are a bit wide), but it proves the method works. It's the first time we've successfully measured this number using Top quarks.

The Takeaway

This paper is a proof-of-concept. It shows that we can use the Top Quark as a new laboratory to test the fundamental rules of the universe.

• Old Way: Studying slow, messy B-mesons (like studying a car in a traffic jam).
• New Way: Studying fast, clean Top quarks (like studying a car on a test track).

The fact that both methods give the same answer suggests that our "map" of the subatomic world (the Standard Model) is still accurate, even when we zoom in on the most extreme, high-speed collisions. It also opens the door for future experiments to measure this with even greater precision, potentially uncovering new physics if the numbers ever start to disagree.

Technical Summary

1. Problem and Motivation

The Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cb}|$ is a fundamental parameter of the Standard Model (SM), governing the coupling strength of the $W$ boson to the $b$ and $c$ quarks.

• Current Status: The current Particle Data Group (PDG) average is $|V_{cb}| = (41.1 \pm 1.2) \times 10^{-3}$. However, a significant discrepancy of approximately $3\sigma$ exists between "inclusive" and "exclusive" determinations derived from $B$-hadron decays.
• The Gap: Traditional measurements rely on low momentum-transfer ($q^2 \approx m_b^2$) processes involving $B$-hadrons, which require complex non-perturbative theoretical inputs (e.g., Lattice QCD or Heavy Quark Expansion).
• The Goal: This paper presents the first measurement of $|V_{cb}|$ at the weak scale ($q^2 \approx M_W^2$) using top-quark decays. This probes a distinct physical regime (high $q^2$, parton-level decays) where the top quark decays before hadronization, offering a theoretically cleaner environment with different systematic uncertainties. If the value differs significantly from $B$-decay measurements, it could indicate New Physics in $t \to b\bar{b}c$ transitions or flaws in low-$q^2$ phenomenology.

2. Methodology

Data Sample

• Source: Proton-proton ($pp$) collision data collected by the ATLAS detector at the LHC.
• Conditions: Center-of-mass energy $\sqrt{s} = 13$ TeV, collected during Run 2 (2015–2018).
• Integrated Luminosity: $140 \text{ fb}^{-1}$.

Signal Process

The analysis focuses on $t\bar{t}$ events where:

1. One top quark decays leptonically ($t \to b \ell \nu$).
2. The other top quark decays hadronically via the specific channel $t \to b W^+ \to b \bar{b} c$.
   The measurement relies on the ratio of the branching fraction $\mathcal{B}(W^+ \to c\bar{b})$ to the total hadronic $W$ decay width $\mathcal{B}(W^+ \to c\bar{q})$, where $q \in \{d, s, b\}$. In the SM, $|V_{cb}|^2 \approx \mathcal{B}(t \to b\bar{b}c) / \mathcal{B}(t \to b\bar{q}c)$.

Event Selection

• Topology: Exactly one isolated electron or muon ($p_T > 25$ GeV) and exactly four reconstructed jets ($p_T > 25$ GeV, $|\eta| < 2.5$).
• Flavor Tagging: Jets are tagged using the DL1r deep neural network algorithm.
  • At least one jet must be $b$-tagged.
  • Events are categorized into 8 Tagging Categories (TCs) based on the number of $b$-tagged ($m$) and $c$-tagged ($n$) jets (e.g., $3b1c$, $2b1c$, etc.).
• Signal Region: The primary sensitivity comes from the $3b1c$ category (signal-enriched) relative to the $2b1c$ category.

Backgrounds and Systematics

• Major Backgrounds: $t\bar{t}$ events with additional heavy-flavor (HF) production ($t\bar{t}+c$, $t\bar{t}+b$) where extra partons are not resolved as jets. These mimic the signal topology but have different kinematic properties.
• Neural Network (NN): A classifier is trained to distinguish correctly reconstructed $t\bar{t}$ signal events from background events (including $t\bar{t}+HF$). The NN uses kinematic variables (e.g., $W_{had}$ mass, jet $p_T$, angular separations) but excludes flavor-tagging information to avoid bias.
• Fit Strategy: A binned profile-likelihood fit is performed across 24 regions (8 TCs $\times$ 3 NN score bins).
  • Free Parameters: $|V_{cb}|$ (via a normalization factor $\mu_{|V_{cb}|}$), total $t\bar{t}$ rate, rates of $t\bar{t}+c$ and $t\bar{t}+b$, and the $c$-jet tagging efficiency ($\epsilon_c$) and $c \to b$ mistag rate ($f_{cb}$).
  • In-situ Calibration: Since standard $c$-jet calibrations assume the SM $|V_{cb}|$, the analysis determines $\epsilon_c$ and $f_{cb}$ simultaneously with the measurement using the data itself.

3. Key Contributions

1. Novel Physical Regime: First determination of $|V_{cb}|$ at the electroweak scale ($q^2 \approx M_W^2$) using on-shell $W$ bosons from top decays, bypassing the non-perturbative hadronization uncertainties inherent in $B$-physics.
2. Simultaneous Calibration: Development of an in-situ method to calibrate $c$-jet tagging efficiencies and mistag rates directly from the data, removing reliance on external SM assumptions for these specific parameters.
3. Advanced Background Handling: Implementation of a neural network to separate signal from $t\bar{t}+HF$ backgrounds, which are the dominant systematic uncertainty source, and a sophisticated treatment of their modeling uncertainties.
4. Comprehensive Uncertainty Treatment: Detailed decomposition of systematic uncertainties, particularly distinguishing between parton shower/hadronization modeling in different flavor channels ($t\bar{t}+light$, $t\bar{t}+c$, $t\bar{t}+b$).

4. Results

The analysis yields the following measurement:
$$|V_{cb}| = (50^{+11}_{-14}) \times 10^{-3}$$

• Breakdown:
  • Statistical uncertainty: $^{+7}_{-9} \times 10^{-3}$
  • Systematic uncertainty: $^{+9}_{-10} \times 10^{-3}$
• Significance: The result has an observed significance of $2.0\sigma$ relative to the hypothesis $|V_{cb}| = 0$.
• Comparison: The measured value is consistent with the PDG world average ($41.1 \pm 1.2$) and both inclusive and exclusive $B$-decay measurements within one standard deviation.
• Branching Fraction: Reinterpreting the result within the SM, the branching fraction for the rare decay is determined as:
  $$\mathcal{B}(t \to b\bar{b}c) = (8 \pm 4) \times 10^{-4}$$

5. Significance and Conclusion

• Validation of SM: The consistency of the high-$q^2$ measurement with low-$q^2$ $B$-decay results supports the Standard Model description of CKM unitarity and the running of couplings (or lack thereof) between the weak scale and the $b$-quark mass scale.
• Systematic Independence: The measurement demonstrates that $|V_{cb}|$ can be extracted with systematic uncertainties of a different nature (dominated by parton shower modeling and jet flavor tagging) compared to $B$-physics (dominated by Lattice QCD and HQE).
• Future Prospects: While the current precision is limited by the small signal yield ($|V_{cb}|^2 \approx 1.7 \times 10^{-3}$) and modeling uncertainties, this analysis establishes a viable methodology. Future runs with higher luminosity and improved flavor-tagging algorithms will allow for more precise tests of New Physics in top-quark decays.

In summary, this paper successfully demonstrates the feasibility of measuring CKM elements in top-quark decays, providing a crucial cross-check of the Standard Model in a high-energy, parton-level environment.