The team centered their investigation on the Daya Bay Reactor Neutrino Experiment, whose gadolinium-doped liquid scintillator detectors sit under 250 meters-water-equivalent of rock in Experimental Hall 1. Daya Bay had previously performed a precision measurement of muon-induced neutron production with relative systematic uncertainties below 10 percent, making it an ideal yardstick. Earlier comparisons had exposed a troubling gap: default simulations overpredicted the measured neutron yield by roughly 20 percent, while at KamLAND the discrepancy reached 30 percent or more. For future experiments like the Jiangmen Underground Neutrino Observatory, JUNO, which will need exquisitely accurate background models, closing that gap is not a luxury but a necessity.

To dissect the problem, the researchers built a full GEANT4-based simulation of the Daya Bay detector geometry, complete with the surrounding water Cherenkov veto, and tested three representative hadronic physics lists: FTFP_BERT_HP, QGSP_BERT_HP, and QGSP_BIC_HP. These lists differ in two crucial ways. At high energies, hadronic interactions are described by string models, either the Fritiof model or the quark-gluon string model, while at low and intermediate energies the intranuclear cascade is handled by either the Bertini or the binary cascade model. All three lists share the high-precision neutron package, which uses evaluated data-driven cross sections below 20 MeV to describe neutron moderation and capture with high fidelity.

The muon flux itself was modeled with care. Starting from a modified version of Gaisser’s sea-level formula adapted for the Daya Bay site, the team propagated muons through a digitized mountain profile using the MUSIC code, reproducing a simulated muon rate of 1.27 per second per square meter and an average muon energy of 63.9 GeV underground. Both values agree well with the measured flux of 1.21 plus or minus 0.12 per second per square meter and with the angular distributions validated by Daya Bay’s resistive plate chamber telescope system. Roughly 61 percent of muons depositing at least 20 MeV in the scintillator were found to traverse the gadolinium-loaded target, with an average path length of 206.3 centimeters, closely matching the 204.1 centimeters from Daya Bay’s own simulations.

The heart of the study lies in its innovative hybrid correction scheme. The TALYS nuclear reaction code, version 1.8, was used to compute more accurate inelastic cross sections for neutrons, protons, and gamma rays striking carbon-12 below 200 MeV, the energy range where most secondary cascade particles reside. Because a single muon-induced cascade contains many individual neutron-producing vertices, the authors implemented a vertex-level reweighting: each neutron-producing interaction was rescaled by the ratio of the TALYS to the GEANT4 exclusive cross section for that channel and projectile energy. Crucially, the method preserves GEANT4’s final-state kinematics rather than substituting TALYS event-by-event, avoiding violations of momentum balance with the nuclear remnant.

The cross-section comparison itself was revealing. Inclusive inelastic cross sections from the three GEANT4 lists were nearly identical for each projectile type, but TALYS predicted values about 20 percent higher for neutrons and 30 percent higher for protons, while its gamma-ray cross-section peak sat at lower energies with a magnitude roughly 50 percent below GEANT4’s. In exclusive neutron-multiplying channels, the choice of intranuclear cascade proved far more influential than the high-energy string model. The BIC-based list shifted production weight away from neutron-induced reactions, about 32.8 percent versus 37.9 percent for the BERT lists, toward charged pion and proton channels, and favored final states with higher neutron multiplicity.

When the corrected simulations were benchmarked against the Daya Bay measurement of the neutron yield, the improvement was striking. The original GEANT4 lists overestimated the measured value of 10.26 times ten to the minus five per muon per gram per square centimeter by roughly 13 to 20 percent. After TALYS-based reweighting, the deviation for the BERT-based model shrank from about 20 percent to approximately 6 percent, while for the BIC-based model it collapsed from roughly 13 percent to the sub-percent level, about 0.3 percent. The correction systematically reduced yields by 12 to 14 percent, demonstrating that the total neutron yield is acutely sensitive to inelastic cross sections in the 50 to 200 MeV window, where TALYS values run systematically lower than GEANT4’s.

Yet the story is not one of unqualified triumph. The team also compared the tagged neutron multiplicity, the number of neutrons captured on gadolinium following each muon, against Daya Bay data. Here a clear tension persists across every model tested: simulations systematically underproduce single-neutron events while overproducing multi-neutron events. The deficit at multiplicity one, the dominant category, had already been flagged in Daya Bay’s earlier comparison using GEANT4 version 9.2, and the TALYS correction actually worsens it, since the fraction of gamma-carbon reactions contributing to single-neutron events drops in the corrected simulation. Quantitative chi-squared tests confirm that the BIC-based model agrees better with data than the BERT-based one across all multiplicities, but the single-neutron deficit remains the largest residual discrepancy.

The authors trace this deficit to the final-state modeling of highly excited carbon-12 nuclei, pointing to GEANT4’s Fermi break-up and evaporation models as the components most in need of refinement. Their analysis shows that single-tagged-neutron events are predominantly induced by gamma-carbon and neutron-carbon reactions, whereas multi-neutron events arise mainly from secondary neutron interactions. This diagnosis suggests a concrete two-step strategy for future work: first, apply TALYS-based cross-section adjustments to nail down the overall normalization of the cosmogenic neutron yield for background subtraction; second, use the residual multiplicity discrepancies, especially the single-neutron deficit, as quantitative constraints for tuning intranuclear cascade parameters and channel-specific reweighting.

The implications reach well beyond liquid scintillator. The authors emphasize that the same framework applies to water Cherenkov detectors like Hyper-Kamiokande and liquid-argon time-projection chambers like DUNE, where cosmogenic neutrons pose equally serious background threats. The methodology may even transfer to atmospheric neutrino neutral-current interactions, whose final-state particle energies overlap the range probed here. By establishing a reproducible, data-driven benchmark and a clear refinement roadmap, the study transforms cosmogenic neutron modeling from a source of nagging uncertainty into a tractable engineering problem, one that the next generation of rare-event searches will be better equipped to solve.

Subject of Research: Cosmogenic neutron production and hadronic simulation modeling in large underground liquid scintillator detectors

Article Title: Comprehensive study of cosmogenic neutron production in large liquid scintillator detectors

Article References: Jiang, Y., Cheng, J., Lu, H., & Wang, Y. (2026). Comprehensive study of cosmogenic neutron production in large liquid scintillator detectors. The European Physical Journal C, 86(9), Article 1082. https://doi.org/10.1140/epjc/s10052-026-16173-2

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16173-2

Keywords: cosmogenic neutrons, liquid scintillator, Daya Bay, GEANT4, TALYS, hadronic physics lists, neutron yield, neutron multiplicity, cosmic-ray muons, underground experiments, JUNO, background modeling

The motivation is stark. The Large Hadron Collider’s physics programme depends on Monte Carlo simulation, in which the fates of billions of proton collisions are computed particle by particle, interaction by interaction. The workflow has four stages: generating the physics events, propagating particles through a virtual detector, digitising the deposited energy into signals that mimic real detector readout, and reconstructing tracks with the same algorithms used on actual data. The detector response step, traditionally handled by the Geant4 toolkit, is the most computationally punishing, and the problem is about to get dramatically worse. By the end of the High-Luminosity LHC programme, the ATLAS and CMS experiments will have collected up to ten times more data than in their first three runs combined, and many precision analyses will find their sensitivity limited not by the data themselves but by the statistical size of the simulated samples needed to model backgrounds.

Generative machine learning has already made inroads on the calorimeter problem, where the goal is to reproduce the showers of energy deposited when particles slam into dense material. Generative adversarial networks, variational autoencoders, normalising flows, diffusion models and continuous flow models have all been applied, and the ATLAS experiment already uses GANs in production for fast photon shower simulation. But tracking detectors present a fundamentally different challenge. A calorimeter response can be interpreted as an image with correlated entries. A tracking detector, by contrast, records a sparse sequence of discrete interactions: a particle crossing thin layers of silicon widely separated in space. Rendering that as an image would produce a picture that is almost entirely empty, which is precisely why the Slovenian team turned to sequence-based models instead.

The conceptual leap is elegant. In a large language model, text is broken into tokens and the network learns to predict the next token given everything that came before. Novak and Kerševan applied the same logic to particle tracks. Each hit in a silicon sensor is described by seven features: a discrete particle identifier encoding type and charge, a geometry identifier for the detector module, two local coordinates on the sensor surface, and three components of the particle momentum after the hit. Every feature is tokenised into a shared dictionary of integers, with continuous quantities rounded to two decimal places. A track becomes a flat sequence of tokens, bookended by virtual start and end hits representing the particle’s birth at the beamspot and its exit from the tracker. The transformer’s job is then exactly what GPT does with words: predict the next element of the sequence, one feature at a time.

The technical implementation relies on a decoder-only transformer built on Karpathy’s nanoGPT codebase, with eight layers and eight attention heads each, feed-forward dimensions four times the input dimension, and dropout of 0.2. Model sizes range from 9.1 to 35 million parameters depending on the token dictionary. Because self-attention scales quadratically with sequence length, the authors employed a sliding-window training scheme, chopping full tracks into rolling windows of four hits. This is physically justified since correlations between hits weaken with distance and the dominant feature, local track curvature, is captured by nearby hits. The trick also augments the training data by an order of magnitude, letting the graphics accelerators work with much larger batches. Training used the AdamW optimiser with gradient clipping and a carefully scheduled learning rate, running for roughly 5000 epochs on Slovenian supercomputing hardware.

Validation proceeded at two levels. At the hit level, the researchers compared distributions of individual hit properties between Geant4 and the neural network, always against the rounded Geant4 data on which the model was trained. For single muons, which barely interact with the detector beyond multiple scattering, the agreement is impressive. The number of hits per track is well modelled, with the largest discrepancy for any muon model being just six hits, and directly tokenised quantities such as the momentum component p_x agree at the percent level. Derived global coordinates fluctuate up to about five percent, with deviations growing in the distribution tails. At the higher level, the simulated hits were fed into the ACTS tracking software and reconstructed using the standard Open Data Detector configuration, allowing a direct comparison of seeding and tracking efficiencies.

Those reconstruction results are the heart of the paper. The technical seeding efficiency measures how often the algorithm finds viable track seeds, while the technical tracking efficiency measures how often full tracks are successfully fitted. A benchmark 11.2-million-parameter model reaches 94.9 percent tracking efficiency with only a slight seeding efficiency drop, comparable to the rounded Geant4 reference. Scaling the model’s layer dimensions by a factor of two improves both metrics further, though they remain below the reference sample. One persistent weakness emerged: the azimuthal angle phi is poorly modelled when the full detector coverage is included, and a dedicated test with a wider phase space showed that the model learns probabilities less accurately as the training domain grows. The authors conclude that detector-aware rounding and tokenisation strategies will be essential for production-quality models.

Electrons and pions exposed the limits of the approach. Electrons undergo bremsstrahlung and pair production, processes that can abruptly change their direction and momentum, and the model’s token dictionary grew 1.4 times larger to accommodate the added variety. Although overall track quality remained comparable to muons, the momentum modelling proved insufficient, with a sizeable fraction of generated electrons carrying too much transverse momentum; the network learns the shape of the momentum tail but is biased toward smaller changes. Pions, which can decay inside the tracker, revealed a related failure: rare, low-probability processes are systematically under-learned, so machine-generated pions almost never decay, artificially inflating the tracking efficiency even though the tracks themselves remain good quality. Reweighting such rare events could help, but the authors note it would erode the statistical power that makes fast simulation worthwhile in the first place.

Computing performance adds a further caveat. GPU inference runs at roughly the same speed as Geant4 simulation on same-generation CPUs, scaling linearly with model size, so better physics currently means slower generation. CPU inference is orders of magnitude too slow to replace conventional simulation, and given the much higher cost of high-performance GPUs, the authors judge the present speed insufficient for general production use. Still, benchmarks across Nvidia hardware generations show clear gains, and half-precision bf16 computation speeds up training by about a third with no loss of physics performance. The team has released its SiliconAI training and validation code and datasets openly, and sees paths forward in extending the sequence representation to secondary particles and in exploring alternative sequence-based architectures. The message is provocative: the same technology that writes essays can, with careful tokenisation, learn to write the passage of a muon through a silicon tracker, and with further work it may help the LHC’s next generation of experiments simulate their way to new discoveries.

Subject of Research: Generative transformer models for fast simulation of silicon tracking detectors in high energy physics

Article Title: GPT-like transformer model for silicon tracking detector simulation

Article References: Novak, T., & Kerševan, B. P. (2026). GPT-like transformer model for silicon tracking detector simulation. The European Physical Journal C, 86(9), Article 1090. https://doi.org/10.1140/epjc/s10052-026-16362-z

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16362-z

Keywords: transformer, GPT, silicon tracker, detector simulation, Geant4, machine learning, LHC, High-Luminosity LHC, particle physics, generative models, Open Data Detector, computing