Introduction

The rapid advancements in artificial intelligence (AI) in recent years have transformed our daily lives. The integration of AI with established technologies is particularly notable1. In many cases, such fusion has revitalized long-standing methods and transformed them into cutting-edge tools. This synergy not only modernizes traditional technologies but also opens up entirely new avenues of exploration.

Such progress in AI is now beginning to contribute significantly to addressing some of humanity’s most enduring questions: What is the nature of matter? How did the Universe begin? In the fields of quarks and nuclear physics, which have made substantial contributions to our understanding of both matter and the cosmos, the application of AI has yielded novel and promising insights. We sought to harness AI in combination with nuclear emulsion technology, a well-established and mature technique, to advance our understanding of quantum many-body systems involving two strange quarks with a strangeness degree of freedom, called the double-strangeness (S = −2) sector. This combination allows for detecting diverse double-strangeness hypernuclei that have long eluded observation and lays the foundation for constructing a “double-strangeness factory”.

Double-strangeness quantum many-body systems are fundamental to nuclear, particle, and astrophysics, particularly in understanding neutron stars and ultra-dense supernova remnants with radii of ~10 km but masses approximately twice that of the Sun2. Despite advances in gravitational-wave detections and r-process studies3,4, their internal structure remains elusive. At such densities, matter likely shifts from nucleons to strange-quark-containing hyperons, making hyperon–nucleon and hyperon–hyperon (YY) interactions crucial for the equation of state (EOS). However, limited experimental data, particularly for YY interactions, render the EOS too soft5, which conflicts with observations of massive neutron stars. This mismatch, known as the “hyperon puzzle”, remains unresolved. Addressing this issue requires precise data on YY interactions, which are scarce.

Quantum chromodynamics predicts an attractive short-range baryon–baryon interaction in the double-strange sector, in contrast to the repulsive core of the nucleon–nucleon interaction6,7. A prominent double-strangeness system, the H-dibaryon (a six-quark state: uuddss), remains the subject of intense research8. Despite extensive experimental research9,10,11,12, definitive observations are lacking. Theoretical studies have suggested that H-dibaryon may exist within double-strangeness hypernuclei13,14,15 and neutron star cores16. Although direct observation of nuclear matter is lacking, the measured masses of double-Λ hypernuclei provide crucial constraints on the mass of H-dibaryon17,18,19,20. Investigating the dependence of the ΛΛ interaction on the mass number of double-Λ hypernuclei can provide insights into the existence of H-dibaryon21.

Double-strangeness hypernuclei, containing two strange quarks, which occupy the S = −2 sector and act as “small experimental laboratories" for probing hyperon interactions in nuclei, are a key focus in the context of S = −2 systems. In particular, a double-Λ hypernucleus with two Λ hyperons in the nucleus provides key insights into the ΛΛ interaction22,23. The ΛΛ interaction, confirmed to be weakly attractive through observations of double-Λ hypernuclei, is the only known YY interaction experimentally. In addition, the binding of the three-body ΛΛN system, particularly the ΛΛd configuration, remains unresolved, although several theoretical models predict a bound particle-stable \({4\atop \Lambda \Lambda }{{\rm{H}}}\) if the ΛΛ interaction is sufficiently attractive24,25,26. However, experimental confirmation is lacking because the initial claim from the BNL-AGS E906 experiment27 was later downgraded28.

Despite over 70 years of hypernuclear research since it was first observed in 195329, only 47 double-strangeness hypernucleus candidates have been observed using nuclear emulsion. Notably, the NAGARA event19,20 remains the only confirmed observation of \({6\atop \Lambda \Lambda }{{\rm{He}}}\), the lightest double-Λ hypernucleus. Its fully occupied s-shell reveals a weak (<1 MeV), attractive s-wave ΛΛ interaction, which serves as a critical benchmark for YY interaction calculations and interpretation of less definitive events. However, to date, the NAGARA event remains the only uniquely identified double-Λ hypernucleus, with other double-Λ hypernuclei exhibiting ambiguous identifications. Therefore, information on the ΛΛ interaction in the nuclear medium is not yet precisely known, and substantially more experimental data are required. The short hyperon lifetime (~10−10s) hinders scattering experiments, particularly for multi-hyperon systems. Nuclear emulsion experiments with their sub-micrometer resolution30 offer the unique advantage of visualizing decay chains, enabling nuclide identification through event-by-event analysis of double-Λ hypernuclear production and decays.

The J-PARC E07 experiment21, a recent hybrid-emulsion study at the Japan Proton Accelerator Research Complex (J-PARC), aims to detect approximately 102 double-Λ hypernuclei events to broaden our understanding of strangeness physics. The experiment used a 1.81 GeV/c K− beam at the K1.8 beam line of the Hadron Experimental Facility at J-PARC. Ξ− hyperons were produced via the quasifree “p”(K−, K+)Ξ− reaction on a diamond target and subsequently injected into an emulsion module positioned downstream of the target. In the nuclear emulsion, the Ξ− hyperons captured by nuclei within the emulsion stacks were subsequently tracked, while the associated K+ were tracked using silicon strip detectors to measure their positions and angles. However, the detection efficiency for all double-strangeness hypernuclear events in emulsion sheets has been estimated to be approximately 10%31,32, mainly due to the limited spectrometer acceptance and tracking, as well as the fact that the cross-section of the reaction “n”(K−, K0)Ξ−, which cannot be detected using the hybrid method, is about twice that of “p”(K−, K+)Ξ−33. Although 33 candidate events triggered by Ξ− hyperons were detected, only three events could be identified: Mino34, Ibuki35, and Irrawaddy36. Unfortunately, no double-Λ hypernucleus was uniquely identified. Nervertheless, the entire emulsion volume is estimated to contain over a thousand double-strangeness events33, including untriggered events generated by the “n”(K−, K0)Ξ− reaction. Therefore, it is essential to develop a new and efficient detection method for mining these events.

In this study, we developed an efficient analysis pipeline based on machine learning techniques for detecting double-Λ hypernuclear events, characterized by a “three-vertex" topology, within nuclear emulsion from the J-PARC E07 experiment37. Here, we report the first uniquely identified observation of a double-Λ hypernucleus \({13\atop \Lambda \Lambda }{{\rm{B}}}\) achieved using our AI-driven nuclear emulsion approach; this is also the second unique identification in history, 24 years after the discovery of the NAGARA event19. This success paves the way for further discoveries of double-strangeness hypernuclei, ultimately establishing a “Double-Strangeness Factory".

Results

We developed a machine learning method37 that combines generative adversarial networks (GANs)38 and Geant4 Monte Carlo simulations39 for training data generation, along with a Mask Region-based Convolutional Neural Network (Mask R-CNN)40 for object detection, as discussed in Section “Methods”. Our model has already detected six double-Λ hypernuclear event candidates, one of which was uniquely identified, as discussed below; this is the second uniquely identified double-Λ hypernucleus since the discovery of hypernuclei with nuclear emulsion in 1953.

Figure 1 illustrates this event. Following Ξ− capture at vertex A, a double-Λ hypernucleus is produced, undergoing sequential cascade decays at vertices B and C. All the emitted particles were brought to rest within the emulsion. The range and emission angle measurements for each particle are detailed in Table 1. A detailed description is provided in Fig. 1 and Table 1.

Fig. 1: Detection of the double-Λ hypernuclear event using machine learning.
Fig. 1: Detection of the double-Λ hypernuclear event using machine learning.
Full size image

a The detection result of the event from the machine learning analysis pipeline. The left panel depicts the input emulsion image, acquired under an optical microscope with a 20× objective lens, and the right panel presents the model’s output, highlighting the event topology with a confidence score of 0.8. b Photograph and schematic diagram of the event. An incoming Ξ− particle (red arrow) is captured at vertex A, producing a double-Λ hypernucleus (#1) and particle #3. Cascade decay (blue arrows) of double-Λ hypernucleus (#1) occurred at vertices B and C, with emitted particles #4 and #5 from B, and #6, #7, and #8 from C, all stopping in the emulsion. Track #7 is identified as a π− particle, represented by a dashed line. Particle length and angle measurements are detailed in Table 1.

Table 1 Measured ranges and emission angles of particles from the observed double-Λ hypernuclear event
Full size table

We analyzed the single-Λ hypernuclear (track #2) decay at vertex C. Three charged particles (tracks #6, #7, and #8) are emitted from vertex C. The coplanarity, calculated as \((\vec{{n}_{1}}\times \vec{{n}_{2}})\cdot \vec{{n}_{3}}\), where \(\vec{{n}_{i}}\) represents the unit vector of the angles of tracks #6, #7, and #8, respectively, was measured as 0.004 ± 0.013. This value suggests that the three particles were emitted within a single plane, significantly reducing the likelihood of neutron emission. The constraints of the energy and momentum conservation are as follows:

$${M}_{\#2} = {\sum}_{\#6,\#7,\#8}\sqrt{{M}_{i}^{2}+| {\overrightarrow{P}}_{i}{| }^{2}}\\ {\overrightarrow{P}}_{m}+{\overrightarrow{P}}_{\#6}+{\overrightarrow{P}}_{\#7}+{\overrightarrow{P}}_{\#8}=\overrightarrow{0}$$
(1)

where Mi and \({\overrightarrow{P}}_{i}\) denote the mass and momentum of the particle for tracks #6, #7 and #8, respectively, and \({\overrightarrow{P}}_{m}\) denotes the missing momentum. For momentum balance, we defined χ2 as:

$${\chi }^{2}={\left(\frac{{P}_{mx}}{{\sigma }_{mx}}\right)}^{2}+{\left(\frac{{P}_{my}}{{\sigma }_{my}}\right)}^{2}+{\left(\frac{{P}_{mz}}{{\sigma }_{mz}}\right)}^{2}$$
(2)

Pmx, Pmy, and Pmz are the three components of the missing momentum and σmx, σmy and σmz are the corresponding errors. Momentum conservation was considered satisfied when χ2 was less than 13.898. This χ2 threshold, with a degree of freedom of 3, corresponds to a p-value of 0.003. In addition, after considering the energy conservation within the 3σ confidence level, all the decay modes at vertex C are listed in Table 2. The momentum and kinetic energy of each particle were obtained using the calibrated range-energy relationship described in Section “Methods”. Given the observed coplanarity and thus the assumption of no neutron emission, \({5\atop \Lambda }{{\rm{He}}}\) and \({9\atop \Lambda }{{\rm{He}}}\) remain as possible decay modes. However, the termination of track #6 without any visible decay products, as depicted in Fig. 1b, rules out the possibility of it being 8He for the decay mode of \({9\atop \Lambda }{{\rm{He}}}\); this is because 8He undergoes a beta decay41,42, which produces visible tracks of electron and lighter nuclei in nuclear emulsion.

Table 2 Possible decay modes of the single-Λ hypernucleus (#2) at vertex C
Full size table

While the coplanarity of the three tracks at vertex C suggests planar emission for single-Λ hypernucleus decay, low-probability neutron emission within the plane remains possible. With the energy and momentum conservation as mentioned above, neutron emission from \({3\atop \Lambda }{{\rm{H}}}\), \({5\atop \Lambda }{{\rm{H}}}\), \({5\atop \Lambda }{{\rm{He}}}\), and \({10\atop \Lambda }{{\rm{He}}}\) is kinematically allowed, yet experimental evidence of those decay branches is scarce. For decays involving neutron emission, the missing momentum was assigned to a neutron (\({\overrightarrow{P}}_{m}={\overrightarrow{P}}_{n}\)), where \({\overrightarrow{P}}_{n}\) represents its momentum. For \({3\atop \Lambda }{{\rm{H}}}\), fewer than 30 neutron-emission decays were observed out of 2000 events in previous emulsion experiments43, which is consistent with the theoretical predictions of a 0.6% branching ratio44. \({5\atop \Lambda }{{\rm{H}}}\) remains unobserved, which suggests a low probability of its existence as a bound state. Although \({6\atop \Lambda }{{\rm{He}}}\) was detected45, all 31 observed decays were mesonic without neutron emission, similar to \({5\atop \Lambda }{{\rm{He}}}\) (1784 events), as depicted in Table 2. Finally, \({10\atop \Lambda }{{\rm{He}}}\) decay, involving 8He as a daughter nucleus, was excluded because of the absence of the characteristic shape of the tracks associated with the decay of 8He. Given the value of coplanarity and previous experimental evidences, the single-Λ hypernucleus (#2) is most likely \({5\atop \Lambda }{{\rm{He}}}\), and its decay mode at vertex C is:

$${5\atop \Lambda }{{\rm{He}}}{\to }^{4}{{\rm{He}}}+{\pi }^{-}+p$$
(3)

The production mode of the double-Λ hypernucleus at vertex A was analyzed. A Ξ− was captured at rest in the emulsion, emitting two charged particles (tracks #1 and #3). Although the emulsion contains both heavy (Ag, Br) and light (C, N, O) nuclei, the short range of track #1 (3.5 ± 0.2 μm) implies that its energy was insufficient to overcome the Coulomb barrier of the heavy nuclei18. Additionally, capture by heavy nuclei typically results in the emission of Auger electrons46, which were not observed in this event. Thus, our analysis considered capture by 12C, 14N, or 16O in double-Λ hypernucleus production.

From Table 1, tracks #1 and #3 are not back-to-back with p-value cut condition of 0.003, which indicates at least one neutron emission. After considering momentum and energy conservation as mentioned above, the possible production modes are listed in Table 3. For decays with neutron emission, the missing momentum was assigned to the neutron(s). In the cases of multiple neutron emissions, it was assumed that the neutrons share the same momentum, producing a minimum kinetic energy and a lower limit for ΔBΛΛ  − BΞ, where ΔBΛΛ is the ΛΛ interaction energy and BΞ is the Ξ− binding energy. ΔBΛΛ is derived from the binding energies of the single-Λ (BΛ) and double-Λ (BΛΛ) hypernuclei:

$$\Delta {B}_{\Lambda \Lambda }\left({A\atop \Lambda \Lambda }{{\rm{Z}}}\right)={B}_{\Lambda \Lambda }\left({A\atop \Lambda \Lambda }{{\rm{Z}}}\right)-2{B}_{\Lambda }\left({A-1\atop \Lambda }{{\rm{Z}}}\right)$$
(4)
Table 3 Possible production modes of double-Λ hypernucleus (#1) at vertex A
Full size table

Most of the production modes in Table 3 result in large ΔBΛΛ − BΞ values, except for \({13\atop \Lambda \Lambda }{{\rm{B}}}\). Notably, all measured ΔBΛΛ values, including uniquely identified NAGARA event with ΔBΛΛ = 0.67 ± 0.1720 MeV, and other double-Λ hypernuclear events with ambiguous identifications, were below 5 MeV47. This is consistent with the femtoscopy results from ALICE48, which estimated \(\Delta {B}_{\Lambda \Lambda }=3.{2}_{-2.4}^{+1.6}{({{\rm{stat}}})}_{-1.0}^{+1.8}({{\rm{syst}}})\) MeV for ΛΛ bound state. With this constraint of 5 MeV for ΛΛ interaction, only \({13\atop \Lambda \Lambda }{{\rm{B}}}\) is most likely to produce a double-Λ hypernucleus at vertex A. However, the ΔBΛΛ values for \({11\atop \Lambda \Lambda }{{\rm{Be}}}\) and \({14\atop \Lambda \Lambda }{{\rm{C}}}\) could also be consistent with this constraint within three-sigma uncertainty.

Although the production analysis at vertex A suggests \({13\atop \Lambda \Lambda }{{\rm{B}}}\) as the most likely double-Λ hypernucleus, we further analyzed its decay at vertex B. Track #2 was identified as \({5\atop \Lambda }{{\rm{He}}}\) from vertex C. The emission of tracks #4 and #5 at vertex B indicates that their total charge should be 3e and that one track must have a larger charge than the other if the analyses at vertices A and C are consistent.

To identify the charges of tracks #4 and #5 of the newly observed double-Λ hypernuclear event, as illustrated in Fig. 1, we employed the method described in Ref. 49. We collected 57 α tracks from the α decay chain, all with a θ angle similar to that of track #4 in three degrees and 50 α tracks associated with track #5. Fig. 2a, b show the distribution of the measured volume of these α tracks relative to tracks #4 (a) and #5 (b), respectively, at different distances from the stopping point to the initial point in the emulsion sheet. In nuclear emulsion, the track volume is correlated with the energy deposition. As tracks are formed by developed grains, particles with different charges exhibit variations in both track thickness and volume49.

Fig. 2: Charge identification for tracks #4 and #5.
Fig. 2: Charge identification for tracks #4 and #5.
Full size image

The distribution of α track volumes relative to that of track #4 (a) and track #5 (b), respectively, at different distances from the stopping point to the initial point of tracks in the emulsion sheet. From these volume distributions, a statistical hypothesis test was conducted to determine whether tracks #4 and #5 were similar to the alpha tracks (null hypothesis, H0) or not (alternative hypothesis, H1). c clearly displays an increasing confidence level for rejecting H0 as the range of track #4 increases, ultimately reaching a cumulative confidence level of 2.4σ at the maximum range of track #4. In contrast, d exhibits no significant confidence in rejecting H0 across the entire range of track #5.

Figure 2a, b shows that track #4 exhibits smaller track volumes than the α tracks at various distances, whereas track #5 displays a volume distribution identical to that of the α tracks. From these volume distributions, a statistical hypothesis test was conducted to determine whether tracks #4 and #5 were similar to the α tracks (null hypothesis, H0) or not (alternative hypothesis, H1). The results of the statistical test are depicted in Fig. 2c, d as a function of the range of tracks #4 and track #5. These figures illustrate the confidence level for rejecting the H0 hypothesis (i.e., similarity to the α track) for tracks #4 and #5. Fig. 2c shows an increasing confidence level for rejecting H0 as the range of track #4 increases, ultimately reaching a cumulative confidence level of 2.4σ at the maximum range of track #4. Conversely, Fig. 2d exhibits no significant confidence in rejecting H0 across the entire range of track #5. This evidence demonstrates that track #4 has a smaller charge than α nuclei, whereas track # 5 has the same charge as α nuclei.

Kinematic analysis at vertex B, shown in Table 4, lists possible decay modes for \({11\atop \Lambda \Lambda }{{\rm{Be}}}\), \({13\atop \Lambda \Lambda }{{\rm{B}}}\), and \({14\atop \Lambda \Lambda }{{\rm{C}}}\). The decay modes of \({13\atop \Lambda \Lambda }{{\rm{B}}}\) are unique owning to the inclusion of tracks #4 (Z=1) and #5 (Z=2), which align with the charge identification from both the track volume analysis at vertex B and the analyses at vertices A and C.

Table 4 Possible decay modes of the double-Λ hypernucleus based on kinematic analysis at vertex B
Full size table

Based on the analyses at vertices A, B, and C, the newly observed double-Λ hypernucleus is uniquely identified as \({13\atop \Lambda \Lambda }{{\rm{B}}}\), which is produced by the reaction described in Eq. (5).

$${\Xi }^{-}{+}^{14}{{\rm{N}}}\to {13\atop \Lambda \Lambda }{{\rm{B}}}+p+n$$
(5)

Because of the multi-neutron emission of the decay of the double-Λ hypernucleus, only the upper limit of the ΔBΛΛ value can be determined, as listed in Table 4. Therefore, \(\Delta {B}_{\Lambda \Lambda }-{B}_{{\Xi }^{-}}=2.66\pm 1.18\) MeV, which is constrained by the production mode at vertex A.

According to theoretical calculations for the nuclear absorption rate of Ξ− hyperons, Ξ− hyperon capture from an atomic 3D state is dominant50,51, whereas only a small percentage of the probability was estimated for 2P state capture52. Thus, we assumed that the Ξ− capture in the atomic 3D state of 14N is most probable. Using a theoretical \({B}_{{\Xi }^{-}}\) value of 0.174 MeV50,51, which is primarily determined by the Coulomb potential, we obtained the binding energy of two Λ hyperons in \({13\atop \Lambda \Lambda }{{\rm{B}}}\):

$${B}_{\Lambda \Lambda }=25.57\pm 1.18({{\rm{stat}}}.)\pm 0.07({{\rm{syst}}}.){{\rm{MeV}}}$$
(6)

and the ΛΛ interaction energy is:

$$\Delta {B}_{\Lambda \Lambda }=2.83\pm 1.18({{\rm{stat}}}.)\pm 0.14({{\rm{syst}}}.){{\rm{MeV}}}$$
(7)

Statistical errors arise from kinematic fitting, while systematic errors are due to the masses of the Ξ− hyperon (1321.71 ± 0.07 MeV), Λ hyperon (1115.683 ± 0.006 MeV)53, and \({B}_{\Lambda }({12\atop \Lambda }{{\rm{B}}})=11.37\pm 0.06\) MeV45.

Discussion

Using advanced machine learning, we analyzed 0.2% of the E07 emulsion data and achieved the first unambiguous identification of a double-Λ hypernucleus \({13\atop \Lambda \Lambda }{{\rm{B}}}\). Extrapolating from the observed candidate rate, the entire dataset is expected to contain more than 2000 double-strangeness hypernuclear events, with hundreds still awaiting identification. This work marks the dawn of a double-strangeness factory, where AI-driven analysis unlocks unprecedented access to rare double-strangeness hypernuclei.

The ΛΛ binding energy in \({13\atop \Lambda \Lambda }{{\rm{B}}}\) was determined as BΛΛ = 25.57 ± 1.18(stat. ) ± 0.07(syst. ) MeV with an interaction energy of ΔBΛΛ = 2.83 ± 1.18(stat. ) ± 0.14(syst. ) MeV. This result confirms the existence of \({13\atop \Lambda \Lambda }{{\rm{B}}}\) and is the second unambiguous identification of a double-Λ hypernucleus since the first observation of hypernuclei in 195329.

Previous experiments have suggested possible interpretations of \({13\atop \Lambda \Lambda }{{\rm{B}}}\); however, without unique identification, definitive conclusions regarding its binding properties were prevented. The E176 experiment47 reported BΛΛ = 23.3 ± 0.7 MeV and ΔBΛΛ = 0.6 ± 0.8 MeV, while the Demachiyanagi event from E373 yielded \({B}_{\Lambda \Lambda }=27.8{1}_{-2.02}^{+3.16}\) MeV and \(\Delta {B}_{\Lambda \Lambda }=5.0{7}_{-2.03}^{+3.17}\) MeV20. Although the divergences of those ΔBΛΛ values are within 3σ from the well-established ΔBΛΛ = 0.67 ± 0.17 MeV for the uniquely identified \({6\atop \Lambda \Lambda }{{\rm{He}}}\)20, they suggests a possible nuclear species dependence of ΔBΛΛ. However, the ambiguity surrounding the nuclide and the mass number of the previously observed double-Λ hypernuclei precluded a firm conclusion. This study provides the first unambiguous measurement of BΛΛ and ΔBΛΛ for \({13\atop \Lambda \Lambda }{{\rm{B}}}\), thereby eliminating nuclide identification uncertainties. Notably, our ΔBΛΛ value was larger than that of \({6\atop \Lambda \Lambda }{{\rm{He}}}\), providing the first direct indication that the strength of the ΛΛ interaction depends on the nuclear medium.

At present, the machine learning model focuses primarily on the topological features of the \({6\atop \Lambda \Lambda }{{\rm{He}}}\) event in nuclear emulsion. Because the training dataset is based on simulated events, potential biases may arise from differences between the simulated and real emulsion data, including variations in background structures. The general topology of other possible double-strangeness events will need to be incorporated in future training to improve model robustness against unforeseen backgrounds. As more double-strangeness candidates are discovered and confirmed through conventional visual and kinematic analyses, the model can be progressively validated and refined. Extending the machine learning framework to include kinematic information will be an important step toward establishing a more comprehensive and reliable identification method.

An AI-driven double-strangeness factory will transform our understanding of baryonic interactions in multi-strangeness systems. Using this approach, a large-scale analysis of nuclear emulsion will reveal a vast population of double-strangeness hypernuclei, enabling high-precision studies of ΛΛ interactions, quantum three-body forces through ΛΛ-ΞN coupling, and exotic multi-baryon states. These breakthroughs will provide deeper insights into the composition of neutron star cores and the possible existence of the H-dibaryon, marking a significant step forward in double-strangeness hypernuclear physics.

Methods

In this study37, we employed GANs38 and Geant4 Monte Carlo simulations39 to generate training data for the Mask R-CNN40, which was used to detect double-Λ hypernuclear events in nuclear emulsion. Mask R-CNN training requires images with objects of double-Λ hypernuclear events and their corresponding mask images. However, for double-Λ hypernuclear events, there are insufficient data to train the model, as only one event has been uniquely identified to date. To address this issue, Geant4 simulations were used to generate double-Λ hypernuclear events in nuclear emulsion, as illustrated in Fig. 3a. Combined with background tracks, these simulated events were processed using an image-style transformation via pix2pix38 with GANs to produce training images. Mask images were automatically generated from Geant4 track information. The Mask-R CNN model was subsequently trained using the generated training datasets, including images containing double-Λ hypernuclear objects and mask images, as illustrated in Fig. 3b, c, respectively. The model evaluation detailed in Section “Model performance and event detection with AI” demonstrated the effective detection of double-Λ hypernuclear events in the produced images. Notably, the model accurately detected and segmented the NAGARA event with a confidence score of 0.974, as shown in Fig. 3f. Subsequently, we applied the trained model to 0.2% of the E07 emulsion data, which led to the discovery and unique identification of a double-Λ hypernuclear event, as discussed in Section “Result”.

Fig. 3: Training image and model performance on NAGARA event.
Fig. 3: Training image and model performance on NAGARA event.
Full size image

a displays the topology of a double-Λ hypernuclear event generated with Geant4 Monte Carlo simulations. One of the example images for the training of the machine learning model (Mask R-CNN), including an image of a goal object (b) and the images with its mask image (c). d shows the images of the NAGARA event taken from ref. 19, which is the only uniquely identified double-Λ hypernuclear event thus far. e is the input image of the Nagara event for the developed model. f shows the detection result of the developed model for the NAGARA event.

Training data prepared with Geant4 simulation and generative AI

In Geant4 Monte Carlo simulations, the composition of the nuclear emulsion was replicated by referring to the emulsion layer used in the J-PARC E07 experiment. For the double-Λ hypernuclear events generated, we first considered the case of \({6\atop \Lambda \Lambda }{{\rm{He}}}\) and its sequential decay. As illustrated in Fig. 3a, \({6\atop \Lambda \Lambda }{{\rm{He}}}\) is produced by the Ξ− capture of 12C in the nuclear emulsion at vertex A. We assumed that Ξ− is bound in the 3D atomic orbit of 12C with a binding energy of 0.13 MeV50. As shown in Fig. 3b, the thickness of each track in the nuclear emulsion, which is related to the grain density, was calculated and displayed for different tracks based on their velocity and angle. Because the tracks in the nuclear emulsion were recorded with three-dimensional information, the trajectories were converted into three different colors, as discussed in ref. 37. To ensure an accurate classification and detection performance, negative samples, K− beam interaction events, were generated using the JAM package54 as main background events. Additional background tracks were extracted from the microscopic images of the E07 emulsion data using an image filter and binarization37.

After generating all the particle tracks in the emulsion images, image-style transfer using GANs was applied to generate emulsion images that closely mimicked real emulsion images. Based on the capabilities of GANs, the pix2pix model was employed to convert the RGB image into an image similar to a real emulsion image, as shown in Fig. 3b. The pix2pix model is an implementation of the conditional GANs framework, which shows a significant improvement in performance for image-style transformation, especially for high-resolution images. The parameters used for training the pix2pix model in this study are aligned with those specified in our previous study55. The image produced by the trained pix2pix model in Fig. 3b, combined with the corresponding mask images in Fig. 3c, served as training data for the object detection model, Mask R-CNN.

Model performance and event detection with AI

After training with the produced data, the developed model can detect double-Λ hypernuclear events in both the produced and actual nuclear emulsion images. For the produced images, the method achieved detection efficiencies of 93.8% and 82.0% for \({6\atop \Lambda \Lambda }{{\rm{He}}}\) and \({5\atop \Lambda \Lambda }{{\rm{H}}}\), respectively, with corresponding purities of 98.2–98.3%. Furthermore, it successfully detected the NAGARA event with a confidence score of 0.974. When applied to E07 emulsion images, the method drastically reduced the background images to 0.17% of the original level. It successfully detected six candidates of double-Λ hypernuclear events in over 0.2% of the entire nuclear emulsion dataset from the E07 experiment. The number of detected candidates suggests that more than 2000 double-strangeness hypernuclear events were recorded in the entire dataset. The proposed method demonstrates great potential for use across the entire E07 nuclear emulsion dataset, potentially improving the visual inspection efficiency by approximately 500 times. Details of the developed method are summarized in ref. 37.

Calibration of range–energy relationship

Before the kinematic analysis of the event, the range-energy relationship in the emulsion sheet was calibrated using α tracks, which have a monochromatic energy of 8.784 MeV from the decay of 212Po existing in the emulsion. The α track can be identified in the thorium series isotopes because it has the largest kinetic energy. Such α decay chains were searched for around the observed events using the so-called overall scanning method56. In total, 217 α tracks were scanned in the emulsion sheet for calibration. The relationship between the ranges and the kinetic energies of the charged particles was obtained using the range-energy formula given by Barkas et al.57,58. The equivalent density of the emulsion sheet was determined to be 3.622 ± 0.014 g/cm3 for the emulsion layer in which the newly observed event was detected. The ranges of particles needed to be corrected for the shrinkage effect because the emulsion layers shrunk perpendicular to the surface due to photographic development. The range of 217 α tracks can also determine this shrinkage factor. Finally, the mean range of α tracks was obtained as 49.57 ± 0.12 μm and the shrinkage factor was corrected to be 1.93 ± 0.01.

The kinetic energy of the π− particle was determined using a range–energy calibration based on μ+ particles from π+ meson decays at rest, which provided a monochromatic energy of 4.1205 MeV. Although ATIMA59 calculations indicated a difference in composition between E07 and standard emulsions, primarily affecting long-range particles such as π−, the density was determined to be 3.379 ± 0.006 g/cm3 using 160 μ+ tracks and ATIMA calculations60. This density value was then used to calculate the π− particle’s kinetic energy.