CKM determination from $W$ decays with jet flavor tagging at CEPC

This study demonstrates that the CEPC, utilizing jet flavor tagging on simulated $W$-pair decay data at $\sqrt{s}=240\,\mathrm{GeV}$, can achieve high-precision, largely model-independent determinations of CKM matrix elements $|V_{cb}|$ and $|V_{cs}|$ with projected statistical uncertainties of $0.59\%$ and $0.01\%$, respectively, thereby offering stringent tests of the Standard Model and sensitivity to new physics.

The Gist

Imagine the universe as a giant, complex puzzle where tiny particles called quarks are the pieces. These quarks come in different "flavors" (like up, down, charm, strange, top, and bottom), and they constantly switch identities when they interact. The rulebook for these switches is called the CKM matrix. It's like a secret code that tells us how likely one flavor is to turn into another.

Physicists have been trying to crack this code for decades. While they know some parts of the code very well, other parts are still fuzzy. This paper proposes a new, high-tech way to read the code more clearly by looking at how a specific particle, the W boson, falls apart.

Here is the story of how they plan to do it, explained simply:

1. The Setup: A Particle "Factory"

The authors are planning to use a future machine called the CEPC (Circular Electron Positron Collider). Think of this as a massive, 100-kilometer-long racetrack where they smash particles together at incredibly high speeds.

They aren't just looking for any crash; they are specifically hunting for a rare event where two W bosons are created. One of these W bosons will decay into a muon (a heavy cousin of an electron) and a neutrino (a ghost-like particle), while the other decays into two jets of particles (quarks). This specific "signature" is like finding a unique fingerprint in a crowd.

2. The Challenge: Sorting the Trash

When the W boson decays into two jets, those jets are made of different types of quarks. Sometimes it's a "charm" quark and a "strange" quark; other times it's an "up" and a "down."

The problem is that once these quarks fly out, they turn into a spray of particles (jets) that look almost identical to the naked eye. It's like trying to tell the difference between a bag of red M&Ms and a bag of red Skittles just by looking at the pile of candy without opening the bags. In the past, this was very hard to do, leading to messy data.

3. The Solution: The "Super-Scanner" (ParticleNet)

To solve this, the researchers are using a piece of artificial intelligence called ParticleNet. Think of this AI as a super-sophisticated scanner that doesn't just look at the pile of candy; it looks at the shape of every single grain, the texture, and how they are arranged.

The AI is trained to recognize the subtle differences between jets made of heavy quarks (like charm and bottom) and light quarks (like up, down, and strange). It's like giving the physicist a pair of X-ray glasses that can instantly tell, "Ah, this jet is definitely a charm quark," even if it looks like a strange one.

4. The Experiment: Counting the Pieces

The team simulated what would happen if they ran this experiment for a very long time (collecting a massive amount of data equivalent to 21.6 "inverse attobarns"—a huge number of collisions).

They used a method called a "template fit." Imagine you have a bag of mixed coins (pennies, nickels, dimes) and you want to know exactly how many of each you have. You can't just count them one by one easily because they are mixed up. Instead, you weigh the whole bag and compare the total weight to the known weights of pure pennies, nickels, and dimes. By seeing how the total weight matches the "templates" of each coin, you can calculate the exact number of each coin in the bag.

In this paper, the "coins" are the different types of W boson decays, and the "weight" is the data collected by the detector.

5. The Results: Cracking the Code

The simulation shows that with this new method, the CEPC could measure the CKM matrix elements with incredible precision:

• For the "Charm-Strange" connection ($|V_{cs}|$): They could measure this with a precision of 0.01%. This is like measuring the distance from New York to Los Angeles and being off by less than the width of a human hair. This would be a massive improvement over what we know today.
• For the "Charm-Down" connection ($|V_{cd}|$): They could improve the precision by about ten times compared to current measurements.
• For the "Charm-Bottom" connection ($|V_{cb}|$): This is a long-standing puzzle in physics. Current measurements disagree with each other. This new method offers a completely different way to measure it (using W bosons instead of B-mesons), which could finally settle the argument.

Why This Matters

The paper claims that this approach is "model-independent." In plain English, this means they don't have to rely on complicated theoretical guesses to get the answer; the data speaks for itself.

If built, the CEPC would act as a giant, ultra-precise microscope for the fundamental rules of the universe. By sorting these particle jets with AI, physicists could check if the Standard Model (our current best theory of physics) is perfect or if there are cracks in the foundation that hint at "new physics" we haven't discovered yet.

In short: This paper says, "If we build this machine and use this AI to sort the particle debris, we can read the universe's secret code with a level of sharpness we've never achieved before."

Technical Summary

Technical Summary: CKM Determination from W Decays with Jet Flavor Tagging at CEPC

Problem Statement
The Cabibbo-Kobayashi-Maskawa (CKM) matrix is a fundamental component of the Standard Model (SM), describing quark flavor mixing. While elements $|V_{ud}|$ and $|V_{us}|$ are known with high precision from nuclear beta and kaon decays, the determination of $|V_{cd}|$, $|V_{cs}|$, and particularly $|V_{cb}|$ currently relies heavily on semileptonic decays of D and B mesons. These measurements depend on theoretical inputs from lattice QCD for hadronic form factors, leading to long-standing tensions between inclusive and exclusive $|V_{cb}|$ determinations. Hadronic W boson decays offer a theoretically clean alternative for extracting CKM elements, as the partial widths depend on $|V_{ij}|^2$ and higher-order corrections that are largely flavor-independent. However, experimentally, this approach has been hindered by the difficulty of identifying specific quark flavors (u, d, s, c, b) in hadronic final states and the combinatorial backgrounds present at hadron colliders. Previous measurements at LEP were limited by statistics and the jet flavor tagging capabilities of that era.

Methodology
This study investigates the sensitivity of the Circular Electron Positron Collider (CEPC) to CKM matrix elements using the semileptonic channel $e^+e^- \to W^+W^- \to \mu\nu\bar{q}q'$. The analysis assumes an integrated luminosity of $21.6 \text{ ab}^{-1}$ at a center-of-mass energy of $\sqrt{s} = 240 \text{ GeV}$.

1. Simulation and Event Selection:

   • Signal and background Monte Carlo samples were generated using Whizard 1.9.5 and Pythia 6.4, with detector response modeled via Delphes using a dedicated CEPC detector card.
   • The signal topology consists of an isolated muon, missing momentum (neutrino), and two hadronic jets.
   • A cut-based selection strategy was employed to isolate the signal from dominant backgrounds (2-fermion, 4-fermion processes like ZZ, single-W/Z, and ZH). Key selection criteria included track multiplicity ($5 \le N_{trk} \le 30$), muon isolation ($E_{ratio} \ge 0.9$), di-jet invariant mass ($50 \le M_{di-jet} \le 120 \text{ GeV}$), and kinematic constraints on missing momentum.
   • The selection achieves a signal efficiency of approximately 54–58% for light and charm channels and 44–48% for bottom channels, reducing total background contamination to roughly 0.43% of the inclusive signal yield.

2. Jet Flavor Tagging:

   • To distinguish between the six exclusive hadronic W decay modes ($\bar{ud}, \bar{us}, \bar{ub}, \bar{cd}, \bar{cs}, \bar{cb}$), the study employs ParticleNet, a graph-neural-network-based jet flavor tagger.
   • The tagger classifies jets into four categories: $b$, $c$, $s$, and $ud$ (where $u$ and $d$ are merged).
   • Input features include particle kinematics, displacement/vertexing variables (impact parameters), and particle identification observables.
   • A lightweight model architecture was optimized to prevent overfitting, achieving a multi-class classification accuracy of 79.6% on the validation sample. The model demonstrates strong discrimination between heavy-flavor ($b, c$) and light-flavor jets, with useful separation for $s$-quarks.

3. Extraction of CKM Elements:

   • An event-level flavor discriminant ($P_{ij}$) was constructed from the symmetrized product of jet probabilities for each event.
   • A binned extended maximum-likelihood template fit was performed on the discriminant distributions to extract the yields ($N_{ij}$) for the five free signal channels ($\bar{cb}, \bar{cd}, \bar{cs}, \bar{ud}, \bar{us}$). The $\bar{ub}$ component was fixed due to its negligible yield.
   • The branching fractions were derived from the fitted yields and selection efficiencies, and subsequently converted to CKM magnitudes using the relation $BR(W \to \bar{q}_i q'_j) = \frac{1}{2}|V_{ij}|^2$ (assuming CKM unitarity).

Key Contributions and Results
The study provides projected statistical precisions for CKM matrix elements based on the simulated CEPC dataset:

• $|V_{cs}|$: Projected statistical precision of 0.01%. This represents a significant improvement over current direct measurements.
• $|V_{cb}|$: Projected statistical precision of 0.59%. This offers a direct, model-independent determination from hadronic W decays, independent of semileptonic B-decay form factors.
• $|V_{cd}|$: Projected statistical precision of 0.18%, an order of magnitude improvement over current PDG direct averages.
• $|V_{ud}|$ and $|V_{us}|$: Projected statistical precisions of 0.01% and 0.20%, respectively. While these do not surpass the precision of low-energy determinations, they provide an independent cross-check with different systematics.

Systematic Uncertainties
The authors discuss several sources of systematic uncertainty, noting that the current estimates are preliminary and conservative:

• Detector Resolution: A conservative estimate of 0.82% is assigned, though the authors expect this to be reducible to below 0.1% with detailed data-driven calibrations.
• Modeling: Jet flavor tagging and hadronization modeling uncertainties are estimated at ~0.8% based on generator comparisons, with potential for reduction to ~0.1% using control samples (e.g., from the Z pole).
• Theoretical Corrections: Higher-order QCD and electroweak corrections are flavor-independent to a good approximation and largely cancel in the ratio; residual uncertainties are considered subdominant for this projection.

Significance
The paper concludes that the CEPC, with its large $W^+W^-$ sample and clean experimental environment, can transform hadronic W decays into a statistically powerful probe of the CKM structure. The integration of advanced machine-learning techniques (ParticleNet) for multi-class jet flavor tagging is identified as a central enabler for this program. The results suggest that the CEPC can provide direct, high-precision, and largely model-independent determinations of CKM elements, offering stringent consistency tests of the SM charged-current flavor structure and sensitivity to potential new physics effects through deviations from SM expectations. The study proposes a dedicated future program for direct CKM measurements using on-shell W decays, complementary to low-energy flavor physics and hadron collider results.