Charmed baryon decays at BESIII

This paper summarizes recent BESIII results on charmed-baryon decays derived from the world's largest sample of $\Lambda_c^+\bar{\Lambda}_c^-$ pairs, highlighting the observation of the rare semi-leptonic decay $\Lambda_c^+\to ne^+\nu_e$, the first measurement of the decay asymmetry in $\Lambda_c^+\to\Xi^0K^+$, and various branching fraction measurements and partial wave analyses.

The Gist

Imagine the subatomic world as a bustling, chaotic construction site. At the center of this site is a very special, heavy worker called the $\Lambda_c^+$ (Lambda-c-plus) baryon. Think of him as the "foreman" of the charm-quark family. He is the lightest and most stable version of his kind, which means that when other, heavier, or more excited workers (particles) fall apart, they almost always end up turning into him.

Because he is so central to the process, understanding how he breaks down (decays) is like reading the blueprints for the entire construction site. However, the rules governing his breakdown are tricky. Unlike simpler particles that follow predictable, "factorized" rules, the Lambda-c-plus is influenced by complex, messy forces that are hard to calculate with current math.

The BESIII experiment at the BEPCII accelerator in Beijing is like a massive, ultra-high-speed camera crew stationed at this construction site. They have been filming millions of collisions, creating the world's largest "movie reel" of these Lambda-c-plus particles being born and dying.

Here is a breakdown of the new discoveries from their latest "movie," explained simply:

1. The "Ghost" Particle Hunt (Inclusive Decays)

Sometimes, the foreman breaks down into a specific, known set of parts. But often, he breaks down into a messy pile of "anything allowed" (called inclusive decays).

• The Discovery: The team measured exactly how often the foreman turns into an electron and other random particles, or a neutron and other random things.
• The Analogy: Imagine trying to count how many times a magician pulls a rabbit out of a hat, but sometimes the rabbit is hidden inside a box of random toys. They found that the "rabbit" (electron) appears about 4% of the time, and a "neutron" appears about 32% of the time.
• Why it matters: Their numbers are much more precise than before. They found that the "rabbit" appears slightly more often than some old theories predicted, suggesting our understanding of the "magic trick" (the physics) needs an update.

2. Spotting the Invisible with AI (The Rare Decay)

One specific decay, $\Lambda_c^+ \to n e^+ \nu_e$ (turning into a neutron, a positron, and a neutrino), is incredibly rare and hard to see.

• The Problem: The background noise is loud. The main culprit is a similar-looking decay where the foreman turns into a Lambda particle instead of a neutron. Since a Lambda particle quickly turns into a neutron anyway, it's like trying to tell the difference between a real apple and a very realistic plastic apple that looks exactly the same.
• The Solution: The team used a Graph Neural Network (GNN), a type of advanced AI. Think of the detector as a room where particles leave footprints. The AI was trained to look at the pattern of these footprints (energy deposits) to distinguish the "real" neutron from the "plastic" one.
• The Result: They found the rare decay! It happens about 0.36% of the time. This allowed them to calculate a fundamental number of the universe (the CKM matrix element) for the first time using this specific particle, like finding a new key to unlock a door in the Standard Model.

3. The "Forbidden" Door (Singly Cabibbo-Suppressed Decay)

There is a decay called $\Lambda_c^+ \to p \pi^0$ (proton and a neutral pion) that is "forbidden" or very unlikely to happen.

• The Conflict: Two other experiments (Belle and an older BESIII run) couldn't agree. One said it didn't happen; the other said it did, but weakly.
• The Fix: The team used a Deep Neural Network (DNN) and a new counting method (Single-Tag) to boost their signal. It's like using a super-zoom lens and a better microphone to hear a whisper in a noisy room.
• The Result: They confirmed it happens! The rate is about $1.79 \times 10^{-4}$. This settles the argument and gives theorists a new data point to test their models.

4. The "Mirror" Test (K0 Asymmetries)

The team looked at how the foreman decays into neutral Kaons ($K^0$). These particles have a weird property where they can oscillate between being "short-lived" and "long-lived."

• The Discovery: They measured if there was a difference (asymmetry) between the short-lived and long-lived versions.
• The Result: They found no huge difference (the numbers are close to zero). This is a crucial "control test" for future experiments looking for even stranger physics that might break the rules of symmetry.

5. The "Pure Exchange" Puzzle ($\Lambda_c^+ \to \Xi^0 K^+$)

This decay is unique because it happens only through a specific mechanism called "W-exchange."

• The Challenge: Theorists have struggled to predict both how often this happens and how the particles fly apart (the asymmetry) at the same time.
• The Result: They measured the "flight path" angles precisely. They found a strange feature: the phase difference between the particles is close to 90 degrees. This is a new clue that previous theories missed, forcing physicists to rewrite their scripts for this specific interaction.

6. The "Resonance" Orchestra (Partial Wave Analysis)

Finally, they looked at complex decays where the foreman breaks down into three or more pieces ($\Lambda \pi^+ \pi^0$ and $\Lambda \pi^+ \eta$).

• The Analogy: Imagine the foreman doesn't just break into three pieces at once. Instead, he might first break into a "duo" (a temporary, short-lived particle) which then breaks into the final pieces. It's like a musical chord resolving into individual notes.
• The Discovery:
  • They mapped out the "music" (the intermediate particles) for the first time.
  • They found a very loud "note" (the $a_0(980)$ particle) that is much louder than anyone expected (10 to 100 times louder!).
  • They found strong evidence for a particle called $\Sigma(1380)^+$, which had been suspected but never clearly seen.
• The Takeaway: No current theory can explain the volume and the pitch of all these notes simultaneously. The orchestra is playing a tune that our sheet music doesn't have yet.

The Future

The paper ends with a look ahead. The machine (BEPCII) is getting an upgrade. Imagine upgrading the camera crew from a standard HD camera to a 4K, high-speed, super-sensitive camera. The "luminosity" (the number of collisions) will triple, and they will be able to see heavier, more exotic particles (like $\Sigma_c$, $\Xi_c$, and $\Omega_c$).

In summary: The BESIII team used massive data and cutting-edge AI to solve several long-standing mysteries about how the "foreman" of the charm-baryon family breaks down. They found new particles, settled old arguments, and discovered that nature is playing a more complex tune than our current theories can explain.

Technical Summary

1. Problem and Motivation

The $\Lambda_c^+$ baryon is the lightest charmed baryon and serves as a crucial endpoint for the decay chains of most bottom baryons and excited charmed baryons. Understanding its decays is essential for heavy-flavor spectroscopy and testing Quantum Chromodynamics (QCD) in the transition region between perturbative and non-perturbative regimes.

Key theoretical challenges include:

• Non-factorizable Contributions: Unlike charm mesons, $\Lambda_c^+$ decays involve W-exchange amplitudes that are neither color-suppressed nor helicity-suppressed. These non-factorizable contributions are difficult to calculate theoretically, with existing models (constituent quark, MIT bag, pole models, SU(3) flavor symmetry) often yielding conflicting predictions.
• Data Deficiencies: Many decay modes, particularly rare semi-leptonic decays, singly Cabibbo-suppressed (SCS) modes, and specific intermediate resonances, lacked precise measurements or had conflicting results between experiments (e.g., Belle vs. BESIII).
• Background Separation: Distinguishing specific decay channels (e.g., $\Lambda_c^+ \to n e^+ \nu_e$ vs. $\Lambda_c^+ \to \Lambda e^+ \nu_e$) is challenging due to the difficulty in distinguishing prompt neutrons from $\Lambda \to n \pi^0$ decays using traditional reconstruction methods.

2. Methodology and Data Set

The analysis utilizes data collected by the BESIII detector at the BEPCII storage ring.

• Data Sample: 4.5 fb$^{-1}$ of $e^+e^-$ collision data collected in the center-of-mass energy range of 4.6–4.7 GeV. This corresponds to the world's largest sample of $\Lambda_c^+ \bar{\Lambda}_c^-$ pairs. An additional 1.9 fb$^{-1}$ was collected between 4.74 and 4.95 GeV.
• Techniques:
  • Tagging: Both Single-Tag (ST) and Double-Tag (DT) techniques are employed. The ST method is specifically used to increase statistics for rare decays (e.g., $\Lambda_c^+ \to p \pi^0$).
  • Machine Learning (Deep Learning):
    • Graph Neural Networks (GNN): Used to classify energy-deposition patterns in the electromagnetic calorimeter to distinguish neutrons from $\Lambda$ decays in semi-leptonic channels. A data-driven pipeline was established to address simulation mismatches.
    • Particle Transformer (ParT) / Deep Neural Networks (DNN): Used for signal-background classification in hadronic decays. Low-level detector information (point clouds) is fed into the ParT architecture. The reference channel $\Lambda_c^+ \to p \eta$ is included in training to improve generalization.
  • Partial Wave Analysis (PWA): Performed using the helicity-amplitude formalism to decompose multi-body decays ($\Lambda_c^+ \to \Lambda \pi^+ \pi^0$ and $\Lambda_c^+ \to \Lambda \pi^+ \eta$) into intermediate resonant states.
  • Angular Analysis: Used to extract decay asymmetry parameters for pure W-exchange decays.

3. Key Contributions and Results

A. Inclusive Decay Measurements

• Branching Fractions: Measured absolute branching fractions for inclusive decays with improved precision:
  • $\mathcal{B}(\Lambda_c^+ \to X e^+ \nu_e) = (4.06 \pm 0.10_{\text{stat}} \pm 0.09_{\text{syst}})\%$. Precision improved by >3x.
  • $\mathcal{B}(\bar{\Lambda}_c^- \to \bar{n} X) = (32.4 \pm 0.7_{\text{stat}} \pm 1.5_{\text{syst}})\%$.
  • $\mathcal{B}(\Lambda_c^+ \to K_S^0 X) = (10.9 \pm 0.2 \pm 0.1)\%$.
• Implications: The ratio $\Gamma(\Lambda_c^+ \to X e^+ \nu_e)/\Gamma(D \to X e^+ \nu_e) = 1.28 \pm 0.05$ agrees with Heavy Quark Expansion predictions (1.2) but disfavors effective-quark estimates (1.67). The results suggest ~25% of neutron final states remain unobserved.

B. First Observation of Rare Semi-Leptonic Decay

• Process: $\Lambda_c^+ \to n e^+ \nu_e$ (and charge conjugate).
• Result: First observation with a statistical significance $>10\sigma$.
• Branching Fraction: $\mathcal{B} = (0.358 \pm 0.334_{\text{stat}} \pm 0.014_{\text{syst}})\%$.
• CKM Element: Using lattice-QCD form factors, the CKM matrix element $|V_{cd}|$ was determined for the first time from charmed-baryon decays: $|V_{cd}| = 0.208 \pm 0.011_{\text{exp}} \pm 0.007_{\text{LQCD}} \pm 0.011_{\tau}$.

C. Singly Cabibbo-Suppressed (SCS) Decay

• Process: $\Lambda_c^+ \to p \pi^0$.
• Context: Previous results from Belle ($<8.0 \times 10^{-5}$) and BESIII ($1.56^{+0.72}_{-0.58} \times 10^{-4}$) were in tension.
• Method: ST method + DNN (ParT) classifier increased statistics by an order of magnitude and suppressed hadronic backgrounds.
• Result: Measured ratio $\mathcal{B}(\Lambda_c^+ \to p \pi^0)/\mathcal{B}(\Lambda_c^+ \to p \eta) = 0.120 \pm 0.026$.
• Absolute Branching Fraction: $(1.79 \pm 0.39_{\text{stat}} \pm 0.11_{\text{syst}} \pm 0.08_{\text{ref}}) \times 10^{-4}$. This resolves the tension with previous measurements.

D. Asymmetry and CP Studies

• $K_S^0 - K_L^0$ Asymmetries: First measurements in charmed-baryon decays for channels $\Lambda_c^+ \to p K_{L,S}^0$, $\Lambda_c^+ \to p K_{L,S}^0 \pi^+ \pi^-$, and $\Lambda_c^+ \to p K_{L,S}^0 \pi^0$. Results are consistent with zero, providing inputs for searches for doubly Cabibbo-suppressed amplitudes.
• Decay Asymmetry ($\Lambda_c^+ \to \Xi^0 K^+$): First measurement of the decay asymmetry parameter $\alpha$ for this pure W-exchange decay.
  • $\alpha = 0.01 \pm 0.16_{\text{stat}} \pm 0.03_{\text{syst}}$.
  • The phase difference $\delta_p - \delta_s$ was found to be close to $\pm \pi/2$, a feature not previously considered in theoretical models.

E. Partial Wave Analyses (PWA)

• $\Lambda_c^+ \to \Lambda \pi^+ \pi^0$: First PWA performed. Identified intermediate states: $\Lambda \rho(770)^+$, $\Sigma(1385)^+ \pi^0$, and $\Sigma(1385)^0 \pi^+$.
  • Finding: No existing theoretical model can simultaneously describe the measured branching fractions and decay asymmetries.
• $\Lambda_c^+ \to \Lambda \pi^+ \eta$: First PWA performed. Observed intermediate states: $\Lambda a_0(980)^+$, $\Sigma(1385)^+ \eta$, and $\Lambda(1670) \pi^+$.
  • Finding: The branching fraction for $\Lambda_c^+ \to \Lambda a_0(980)^+$ exceeds theoretical expectations by 1–2 orders of magnitude.
  • New State: Provided the first experimental evidence for the $\Sigma(1380)^+$ state with significance $>3\sigma$.

4. Significance

• Theoretical Constraints: The results provide critical inputs for testing phenomenological models (SU(3) flavor symmetry, quark models) and lattice QCD calculations. The discrepancies found (e.g., in $\Lambda_c^+ \to \Lambda a_0(980)^+$ and the inability of models to fit both branching fractions and asymmetries simultaneously) highlight gaps in current theoretical understanding of non-perturbative QCD.
• Standard Model Tests: The determination of $|V_{cd}|$ from baryon decays offers a new, independent constraint on the CKM matrix.
• Methodological Advancement: The successful application of Graph Neural Networks and Particle Transformers to particle physics problems (specifically for neutron identification and background suppression) sets a precedent for future analyses in high-energy physics.
• Future Prospects: With the planned upgrade of BEPCII/BESIII (increasing luminosity by a factor of 3 and extending energy to 5.6 GeV), these techniques will enable even more precise studies of $\Lambda_c^+$ and open new avenues for exploring $\Sigma_c$, $\Xi_c$, and $\Omega_c$ baryons.