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 story begins with the physics of cosmic rays themselves. Most primary cosmic rays are protons, electrically charged particles whose trajectories are bent by Earth’s magnetic field before they ever reach the atmosphere. When they arrive, they collide with atomic nuclei in the air and generate cascades of secondary particles. Among these secondaries are muons, short-lived charged particles produced at high energies that travel at nearly the speed of light and penetrate deep into the atmosphere. As Sunil Gupta of the Tata Institute of Fundamental Research (TIFR) in Mumbai, one of the authors of the study, explains, the cosmic rays detected at ground level consist predominantly of these highly penetrating muons. The GRAPES-3 facility includes a 560-square-metre muon telescope that records around four billion muons every day, providing an extraordinarily dense stream of data.

Crucially, those muons are not evenly balanced in electric charge. Because the primary cosmic rays are mostly positively charged, positive muons are more abundant in the atmosphere than negative ones. Physicists quantify this imbalance with the muon charge ratio, the number of positive muons divided by the number of negative ones, which normally exceeds one. That small excess is what allows GRAPES-3 to do something it was never originally designed to do. Inside a thundercloud, electric charges become separated, producing intense electric fields and large potential differences. When muons cross these regions, the field acts on positive and negative particles in opposite ways, generally slowing positive muons while accelerating negative ones. If the two charges were present in equal numbers, these effects would cancel almost perfectly, leaving no detectable change in the total muon flux.

Hari Haran Balakrishnan of TIFR, first author of the new study, puts the point starkly: if nature provided equal numbers of positive and negative muons throughout the telescope’s field of view, the thunderstorm phenomenon simply could not be observed with the current setup. Because positive muons dominate, however, each thunderstorm leaves a small but measurable imprint on the total muon count, and from that imprint researchers can infer the electrical potential inside the cloud. Gupta describes muons as an ideal gift for these kinds of studies, likening them to an electric current flowing through the atmosphere. In an earlier analysis, the team reported a striking result: a potential of 1.3 gigavolts measured in a single thunderstorm, a figure that dwarfs anything obtained by conventional means.

The idea that thunderstorms might generate potentials on that scale is not new. As early as the 1920s, the physicist Charles Thomson Rees Wilson, who would later win the 1927 Nobel Prize in Physics, suggested that thunderclouds could reach such enormous voltages. Direct measurements, however, had previously topped out at only around 130 million volts, more than an order of magnitude lower. The difficulty is practical as much as conceptual: sampling the interior of a large, rapidly evolving storm generally requires instruments carried by aircraft or weather balloons into or near active weather, a hazardous and spatially limited approach. Muons invert the problem entirely. They pass through the atmosphere continuously, they can be monitored from the safety of the ground, and they sample the whole volume of the cloud along their paths.

But the earlier GRAPES-3 observations carried an unexpected puzzle alongside their headline result. Between April 2011 and December 2020, the telescope detected 487 thunderstorm events, and their distribution across the sky was strikingly lopsided. Fully 81.5 percent of the events appeared in the eastern part of the instrument’s field of view, while only 13.7 percent appeared in the west, a difference of almost six to one. The obvious suspicion was local weather: perhaps storms in this part of India genuinely favour the east. An independent array of instruments that monitors the atmospheric electric field said otherwise. Actual thunderstorms, measured directly, showed no comparable preference for the eastern sky, which meant the asymmetry had to originate in the detector rather than in the atmosphere.

The answer lies in an effect that atmospheric and cosmic-ray physicists have known about for nearly a century: the east-west effect. Because cosmic-ray protons are charged, Earth’s magnetic field filters their arrival directions. Lower-energy positive particles arriving from the east are screened out more strongly than those arriving from the west, so the mix of cosmic rays, and therefore of secondary muons, depends on direction. This directional threshold, known as the geomagnetic cutoff, varies significantly across GRAPES-3’s field of view. The consequence is that the muon charge ratio, the very quantity that makes thunderstorm sensing possible in the first place, is itself direction-dependent, and the telescope is therefore more sensitive to thunderstorms in some parts of the sky than in others.

To test whether this could account for the observed lopsidedness, the researchers turned to computer simulations that model the production and propagation of muons through the atmosphere. The simulations showed that the balance between positive and negative muons changes markedly with direction: the muon charge ratio is about 1.37 in the east but only 1.14 in the west. That difference, they found, is more than enough to explain the event counts. As Gupta emphasizes, it is not that the voltage is different; thunderstorms to the east are not necessarily more electrically powerful than those to the west. Rather, the larger imbalance between positive and negative muons arriving from that direction makes the telescope more responsive to their electrical effects. The simulations confirmed the mechanism in both directions: when the direction-dependent charge ratio was included, a strong east-west asymmetry emerged, closely resembling the observations, and when the same ratio was imposed in both directions the asymmetry disappeared entirely.

The resolution of the puzzle matters well beyond bookkeeping for one detector. Understanding this directional sensitivity is essential if GRAPES-3 is to serve as a reliable, calibrated probe of thunderstorm electricity, because any inferred potential must account for how efficiently the instrument responds along each line of sight. With that correction in hand, the technique offers something no balloon campaign can match: continuous, ground-based monitoring of the largest electric fields in nature, drawn from a particle flux that arrives whether or not anyone is watching. The broader significance is considerable, since thunderstorm electrification is linked to lightning initiation, to terrestrial gamma-ray flashes, and to the still-uncertain role of storms in the global atmospheric electrical circuit. What began as an instrument for studying particles from the cosmos has ended up illuminating one of the most familiar and, remarkably, still one of the most mysterious phenomena on our own planet. The same muons that carry messages about distant astrophysical sources now carry, quite literally, the voltage of the storm overhead.

Subject of Research: Using cosmic-ray muons to probe electric fields and potentials inside thunderclouds

Article Title: From the cosmos to thunderstorms

Article References: From the cosmos to thunderstorms. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: cosmic rays, muons, thunderstorms, GRAPES-3, electric fields, geomagnetic field, muon charge ratio, atmospheric electricity, lightning, particle physics, TIFR, JCAP