Charmed baryon decays at Belle and Belle II

Using a combined dataset of 1.4 ab⁻¹ from the Belle and Belle II experiments, this paper presents new measurements of branching fractions for $\Xi_c^{0/+}$ and $\Lambda_c^+$ baryons, including several first observations, and reports an initial search for CP violation in singly Cabibbo-suppressed three-body decays to test U-spin symmetry.

The Gist

Imagine the universe is a giant, high-speed particle factory. Inside this factory, scientists are trying to understand the "rules of the road" for the tiniest building blocks of matter. This paper is a report card from two of the world's most advanced particle factories, Belle and Belle II, located in Japan.

Here is the breakdown of what they found, explained simply.

1. The Characters: The "Charm" Baryons

Think of subatomic particles like a family of characters. Some are heavy, some are light. The stars of this show are Charmed Baryons.

• The Analogy: Imagine a "Charm" baryon is like a heavy, three-legged stool made of specific Lego bricks (quarks). It's unstable, meaning it doesn't last long. It quickly falls apart (decays) into smaller, lighter pieces.
• The Goal: Scientists want to know exactly how these stools fall apart. Do they break into a specific set of pieces 50% of the time? Or is it random? By measuring these "break-up" rates (called branching fractions), they can test if our current rulebooks (theories) about how the universe works are correct.

2. The Experiment: A Massive Photo Album

The Belle and Belle II teams didn't just look at one stool; they watched 1.4 billion billion collisions.

• The Analogy: Imagine trying to study how a specific type of glass vase breaks. You can't just drop one vase. You need to smash millions of them in a controlled environment to see the patterns.
• The Setup: They smashed electrons and positrons (matter and anti-matter) together at super high speeds. This created a shower of new particles, including our "Charm" baryons. The detectors acted like ultra-fast cameras, snapping pictures of every break-up.

3. The Discoveries: New Recipes and Firsts

The paper reports several major findings, which can be thought of as discovering new recipes for breaking these particles apart.

• First Observations (The "New Dishes"):
  For three specific ways the particles could break apart, scientists had never seen it happen before. It's like a chef discovering a new way to bake a cake that no one knew was possible.

  • They found the $\Xi^0_c$ particle breaking into a $\Xi^0$ and a $\pi^0$ (a pion).
  • They found it breaking into a $\Xi^0$ and an $\eta$ (eta).
  • They found it breaking into a $\Xi^0$ and an $\eta'$ (eta-prime).
  • Why it matters: These specific break-ups are very sensitive to the "glue" (strong force) holding the particles together. Measuring them helps refine the mathematical models physicists use to predict the future.

• The "Rare" Break-ups:
  Some break-ups are like finding a needle in a haystack. The team found evidence for a very rare break-up of the $\Xi^0_c$ into a $\Lambda$ and an $\eta'$. They also set a "speed limit" (an upper limit) for another rare break-up that they didn't quite see yet, telling us how rare it must be.

• The "Charm" Family Tree:
  They also looked at the $\Xi^+_c$ and $\Lambda^+_c$ cousins. They confirmed some break-ups they already suspected and found a new, rare one for the $\Xi^+_c$ that had never been seen before.

4. The Mystery of "Left vs. Right" (CP Violation)

One of the biggest questions in physics is: Does nature treat "matter" and "anti-matter" exactly the same?

• The Analogy: Imagine you have a mirror. If you look in the mirror, does your reflection move exactly the same way you do? In most cases, yes. But in the subatomic world, sometimes the mirror image behaves slightly differently. This is called CP Violation.
• The Search: The scientists looked at three-body decays (particles breaking into three pieces) to see if the "matter" version of the particle behaved differently than the "anti-matter" version.
• The Result: No difference found. The mirror image behaved exactly like the original.
  • The Good News: This confirms a symmetry rule called U-spin symmetry. It means our current understanding of how these particles interact is holding up well.
  • The Future: While they didn't find a difference yet, the data is still a bit fuzzy (like a low-resolution photo). As the Belle II machine collects more data (aiming for a huge dataset by 2026), they will take a "higher resolution" photo. Maybe the tiny difference is hiding in the pixels we can't see yet.

5. Why Should You Care?

You might ask, "Why do we care about a heavy stool made of quarks breaking apart?"

• Testing the Rulebook: Every time we measure a new break-up rate, we are stress-testing the Standard Model (the rulebook of physics). If the numbers don't match the predictions, it means there is New Physics hiding somewhere—perhaps a new force or a new particle we haven't discovered yet.
• Understanding the Universe: The universe is made of matter, not anti-matter. Understanding exactly how these particles behave helps us understand why the universe exists in its current form.

Summary

In short, the Belle and Belle II teams took a massive dataset of particle collisions and successfully:

1. Discovered new ways for heavy particles to break apart.
2. Measured exactly how often these break-ups happen.
3. Checked if matter and anti-matter behave differently, finding that for now, they are still perfect mirror images.

It's a successful "check-up" of the subatomic world, confirming our current theories while keeping the door open for future surprises as they collect even more data.

Technical Summary

1. Problem and Motivation

Charmed baryons ($\Xi_c$ and $\Lambda_c$) serve as a unique laboratory for investigating the interplay between strong and weak interactions. While theoretical frameworks such as $SU(3)_F$ flavor symmetry, pole models, and topological diagrammatic approaches exist, they often yield conflicting predictions for specific decay channels.

• The Gap: There is a lack of precise experimental data for various decay modes, particularly those involving neutral mesons ($\pi^0, \eta, \eta'$) and rare singly Cabibbo-suppressed (SCS) transitions.
• The Goal: To measure branching fractions for previously unobserved or poorly measured decay modes, test the validity of theoretical models (specifically regarding factorizable vs. non-factorizable amplitudes), and search for CP violation in three-body decays to test U-spin symmetry.

2. Methodology

The analysis utilizes a combined dataset of 1.4 ab$^{-1}$ collected by the Belle and Belle II experiments at the KEKB and SuperKEKB $e^+e^-$ colliders, operating at or near the $\Upsilon(4S)$ resonance.

• Reconstruction Strategy:
  • Charm baryons are reconstructed from the continuum $e^+e^- \to c\bar{c}$ process.
  • Signal candidates are identified via specific decay chains (e.g., $\Xi^0 \to \Lambda \pi^0$, $\Lambda \to p\pi^-$, $K^0_S \to \pi^+\pi^-$).
  • Normalization: Absolute branching fractions are determined by normalizing signal yields to well-measured reference modes (e.g., $\Xi^0_c \to \Xi^-\pi^+$, $\Xi^+_c \to \Xi^-\pi^+\pi^+$, $\Lambda^+_c \to pK^-\pi^+$).
• Statistical Analysis:
  • Signal yields are extracted using unbinned extended maximum-likelihood fits to the invariant mass spectra of reconstructed candidates.
  • Background modeling includes "broken-signal" shapes and sideband subtraction.
  • Systematic uncertainties are evaluated based on reconstruction efficiencies (particularly for $\pi^0, \gamma, K^0_S$), fitting model dependencies, and external uncertainties from normalization modes.
• CP Violation Search:
  • Raw charge asymmetries ($A_N$) are measured for three-body decays.
  • Production and instrumental asymmetries are corrected by averaging forward/backward hemispheres and subtracting control channel asymmetries.

3. Key Contributions and Results

A. First Observations and Branching Fraction Measurements

The paper reports the first observations of several decay modes and provides improved precision for others:

1. $\Xi^0_c \to \Xi^0 h$ ($h = \pi^0, \eta, \eta'$):

   • Result: First observation of all three modes.
   • Significance: These are Cabibbo-favored (CF) processes dominated by non-factorizable amplitudes (internal W-emission and W-exchange).
   • Findings: Results are consistent with $SU(3)_F$ flavor symmetry-breaking models but show marginal disagreement with the covariant confined quark model.

2. $\Xi^0_c \to \Lambda h$ ($h = \pi^0, \eta, \eta'$):

   • Result: First evidence for $\Xi^0_c \to \Lambda \eta'$ ($5.3\sigma$ for $\Lambda\eta$, $3.3\sigma$ for $\Lambda\eta'$, $1.4\sigma$ for $\Lambda\pi^0$). An upper limit was set for $\Lambda\pi^0$.
   • Significance: These are SCS processes involving both factorizable and non-factorizable amplitudes. The results provide new constraints on the relative contributions of these diagrams.

3. $\Xi^+_c \to p K^0_S, \Lambda \pi^+, \Sigma^0 \pi^+$:

   • Result: First observation of all three SCS modes. Statistical significances exceed $10\sigma$ (except $\Lambda\pi^+$ in Belle data at $7.6\sigma$).
   • Findings: The measurements show varying agreement with $SU(3)_F$ and topological diagrammatic models, offering critical constraints on $SU(3)$ amplitudes.

4. $\Xi^+_c \to \Sigma^+ K^0_S, \Xi^0 \pi^+, \Xi^0 K^+$:

   • Result: Improved measurements for CF modes and the first observation of the SCS mode $\Xi^+_c \to \Xi^0 K^+$ ($4.7\sigma$ in Belle, $5.5\sigma$ in Belle II).
   • Findings: Results broadly agree with irreducible $SU(3)$ models.

5. $\Lambda^+_c \to p K^0_S \pi^0$:

   • Result: Measured the branching fraction ratio relative to $\Lambda^+_c \to p K^-\pi^+$ with high precision ($0.339 \pm 0.002 \pm 0.009$).
   • Finding: A distinct peaking structure was observed in the $p\pi^0$ invariant mass spectrum near the $p\eta$ threshold, suggesting a threshold cusp effect associated with the $N(1535)^+$ resonance.

B. Search for CP Violation

• Scope: First individual measurements of CP asymmetries ($A_{CP}$) for three-body decays: $\Xi^+_c \to \Sigma^+ h^+ h^-$ and $\Lambda^+_c \to p h^+ h^-$ ($h = \pi, K$).
• Results: All measured asymmetries are consistent with zero (CP conservation).
  • Example: $A_{CP}(\Xi^+_c \to \Sigma^+ K^- K^+) = 3.7 \pm 6.6 \pm 0.6\%$.
• U-Spin Test: The sum rules $A_{CP}(\Xi^+_c \to \Sigma^+ \pi^+ \pi^-) + A_{CP}(\Lambda^+_c \to p K^+ K^-)$ and $A_{CP}(\Xi^+_c \to \Sigma^+ K^+ K^-) + A_{CP}(\Lambda^+_c \to p \pi^+ \pi^-)$ were calculated. Both sums are consistent with U-spin symmetry predictions within current statistical precision.

4. Significance

• Theoretical Constraints: The new branching fraction measurements provide essential data to discriminate between competing theoretical models (e.g., pole models vs. quark models) and refine our understanding of non-factorizable amplitudes in charmed baryon decays.
• Symmetry Tests: The results validate the utility of $SU(3)_F$ flavor symmetry while highlighting areas where symmetry breaking or specific resonance effects (like the $N(1535)^+$) play a crucial role.
• CP Violation: The null results for CP violation in these specific channels set the baseline for future searches. The lack of observed asymmetry is consistent with the Standard Model expectation for these modes but leaves room for discovery with higher statistics.
• Future Outlook: The paper highlights that with the upcoming 1 ab$^{-1}$ dataset from Belle II Run 2 (targeted for 2026), the field will move from "first observations" to "precision tests," enabling the observation of even rarer decay modes and more stringent CP violation tests.