The BESIII Collaboration recently reported the first observation of the Cabibbo-suppressed semi-leptonic decay Λ_c⁺ -> ne⁺v_e, which employs a novel neutron reconstruction method based on a machine learning technology of Graph Neural Network (GNN). The result has been published in Nature Communications on January 15th, 2025 [Nat. Commun. 16, 681 (2025)].
The semi-leptonic decay of the lightest charmed baryon Λ_c⁺ provides unique insights into the fundamental mechanism of strong and electro-weak interactions, serving as a testbed for investigating non-perturbative quantum chromodynamics (QCD) effects and constraining the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters. The Cabibbo-favored semi-leptonic decay Λ_c⁺ -> Λl⁺v_l (l=e, μ) has been extensively studied at BESIII, taking advantage of the unique threshold production of Λ_c⁺ pairs at energies between 4.6 and 4.7 GeV, where the missing neutrino can be inferred using the missing-mass technique. However, the study of the Cabibbo-suppressed decay Λ_c⁺ -> ne⁺v_e presents significant challenges. The neutron is hard to reconstruct from the Electromagnetic Calorimeter (EMC) in the BESIII spectrometer, leading to two missing particles in the Λ_c⁺ -> ne⁺v_e final states. Besides, the dominant background events from Λ_c⁺ -> Λe⁺v_e, Λ -> nπ⁰ outnumber the signal yields by approximately tenfold, requiring an advanced signal identification method to discriminate the energy deposition patterns of neutrons from those of Λ hyperons in the EMC.

Figure 1. (Right) Visualization of a Λ_c⁺-> pK^-π⁺, Λbar_c^- -> nbar e-v_e event in the BESIII detector. (Left) Typical EMC hit patterns from neutron, anti-neutron, Λ hyperon and Λbar hyperon, respectively.

In this study, the BESIII Collaboration leveraged a machine learning approach to tackle these challenges. By representing the EMC particle showers as a point cloud and processing it with a GNN architecture, a classification model is trained to separate neutron-like and Λ-like patterns. The training, calibration, validation, and systematic uncertainty quantification of the GNN model are carried out in a data-driven manner utilizing rich control samples from 10 billion J/ψ events collected at BESIII. The Λ_c⁺ -> ne⁺v_e signal yields is extracted from the GNN output probability distributions, revealing clear enhancements at the high end with a statistical significance exceeding 10 sigma.

Figure 2. Fits to the GNN output distributions for the signal candidates of (a) Λ_c⁺ -> ne⁺v_e and (b) Λbar_c^- -> nbar e^-v_e in data.

Based on 4.5 fb-1 data collected at center-of-mass energies from 4.6 to 4.7 GeV, the absolute branching fraction of Λ_c⁺ -> ne⁺v_e is measured to be (0.357±0.034±0.014)%, where the first uncertainty is statistical and the second is systematic. This result provides an important calibration point for various QCD-inspired phenomenological models and lattice QCD (LQCD) calculations. Additionally, the CKM matrix element |Vcd| is determined from charmed baryon decays for the first time, yielding 0.208±0.011±0.007±0.001, where the uncertainties correspond to statistical, systematic, LQCD calculation, and Λ_c⁺ lifetime, respectively. This work highlights a new approach to further understand fundamental interactions in the charmed baryon sector, and showcases the power of modern machine learning techniques in experimental particle physics.

Figure 3. Comparison of the branching fraction measurement with the theoretical predictions.

Reference:
•    Nat Commun 16, 681 (2025).
•    Journal publication: https://www.nature.com/articles/s41467-024-55042-y
•    DOI: https://doi.org/10.1038/s41467-024-55042-y