The measurements themselves are striking. Using just 59.1 days of reactor antineutrino data, the JUNO collaboration reports a best-fit value of the solar mixing angle of sin-squared theta-12 equal to 0.3092, with an uncertainty of only 0.0087, and a solar mass-squared difference of (7.50 plus or minus 0.12) times ten to the minus five electron-volts squared, assuming normal mass ordering. When the new SNO+ reactor measurements are folded in with the Particle Data Group 2025 global dataset, the combined values shift only slightly, to 0.310 plus or minus 0.012 and (7.63 plus or minus 0.17) times ten to the minus five electron-volts squared. Remarkably, JUNO’s standalone determination already surpasses the precision of the existing worldwide oscillation global fits, which pool together decades of data from solar, atmospheric, reactor and accelerator experiments.

That leap in precision matters because the mixing angles are not arbitrary numbers. In the Standard Model extended to include neutrino masses, the leptonic mixing matrix, the analogue of the famous Cabibbo-Kobayashi-Maskawa matrix that governs quark mixing, is built from two pieces: a diagonalization matrix for the charged leptons and one for the neutrinos. The peculiar pattern of its elements has intrigued theorists ever since neutrino oscillations were discovered, and the interest only intensified after reactor experiments revealed that the third mixing angle theta-13 is not zero, while accelerator results from T2K hinted at a nearly maximal value of the CP-violating phase delta, the parameter that controls differences between neutrinos and antineutrinos.

One particularly elegant family of explanations goes by the name of bi-large mixing. The guiding observation is numerical coincidence: the smallest lepton mixing angle is close in size to the largest quark mixing angle, the Cabibbo angle, which has the value lambda equal to 0.22501 with a tiny uncertainty. This suggests that the Cabibbo angle might act as a universal seed for both quark and lepton mixings, hinting at a common origin in some grand unified theory where quarks and leptons are treated on the same footing. In bi-large schemes, two of the three neutrino mixing angles are large, of order one, while all three are expressed as simple multiples or combinations of lambda, producing sharp, testable predictions.

The new analysis, carried out by Gui-Jun Ding, Ranjeet Kumar, Newton Nath, Rahul Srivastava and José W. F. Valle, examines four such patterns, labelled T1 through T4. In the T1 pattern, the atmospheric angle satisfies sin theta-23 equal to one minus lambda, the solar angle sin theta-12 equals two lambda, and the reactor angle sin theta-13 equals lambda, with charged-lepton corrections of a CKM-like form motivated by SO(10) unification. The T2 pattern instead takes sin theta-23 equal to three lambda, with SU(5)-motivated charged-lepton corrections. The T3 and T4 patterns share the same neutrino matrix, with sin theta-12 and sin theta-23 both equal to psi times lambda, where psi is a free parameter near three, but differ in which charged-lepton correction is applied. In each case a phase phi remains as the single adjustable parameter for T1 and T2, making them one-parameter schemes whose predictions are tightly correlated.

Before JUNO, the verdict from global fits was already mixed. The T1 pattern emerged as the most compatible with oscillation data, successfully reproducing the best-fit values in the planes correlating the atmospheric angle with the CP phase, and theta-13 with theta-23. The T2 pattern survived only at the two-sigma level, preferring the lower octant of theta-23. The T3 pattern was excluded at three sigma, while T4 sat barely inside the allowed region and was expected to fall out as measurements of delta improved. In other words, the family of bi-large ideas was already cornered, and the question was whether JUNO’s solar measurement would finish the job or refine the survivors.

The answer is a dramatic tightening. JUNO is a twenty-kiloton liquid-scintillator detector located about 53 kilometres from the Yangjiang and Taishan nuclear power plants, viewed by roughly 18,000 twenty-inch photomultiplier tubes plus some 25,000 three-inch tubes, achieving an energy resolution of about three percent divided by the square root of the energy in MeV. That instrument performance translates into sub-percent goals on the solar parameters. When the JUNO constraint on sin-squared theta-12 is imposed, the T1 pattern is found to be compatible only with the higher atmospheric octant, with sin-squared theta-23 squeezed to a narrow range around 0.57, thereby excluding maximal atmospheric mixing. The T2 pattern, by contrast, still prefers nearly maximal mixing with sin-squared theta-23 near 0.5 at three sigma.

The CP predictions are equally distinctive. Imposing the JUNO solar constraint splits the T1 prediction for the Dirac CP phase into two branches, delta of approximately 0.7 pi and 1.3 pi at one sigma, which simultaneously disfavours maximal CP violation at delta equal to plus or minus pi over two and CP conservation at delta equal to pi, although the latter survives at three sigma. The T2 pattern is harsher still: it excludes CP conservation even at three sigma, because its predicted branch falls outside the JUNO band in that region. For the two-parameter patterns T3 and T4, both are excluded at two sigma in the CP-phase plane, and while one branch remains viable at three sigma, the JUNO one-sigma range pushes the allowed phase near 1.8 pi, excluding CP conservation at that level. Overall, the authors conclude that T3 is expected to be decisively tested, and potentially ruled out, by future precision measurements of the atmospheric angle and the CP phase.

The implications extend beyond oscillations into the hunt for neutrinoless double beta decay, the hypothetical process that would reveal whether neutrinos are their own antiparticles. The decay amplitude depends on the effective Majorana mass, a coherent sum over the three neutrino masses weighted by mixing matrix elements and two Majorana phases that oscillation experiments cannot access. Because the bi-large patterns do not predict the mass-squared differences or the Majorana phases, all four schemes yield similar double-beta predictions, and the analysis focuses on T1. JUNO’s precise theta-12 and solar mass-squared values slightly shrink the allowed region of the effective Majorana mass for normal mass ordering, and the T1 pattern occupies a smaller slice of that region than the JUNO-allowed band itself.

The experimental stakes are high. The current KamLAND-Zen limit corresponds to an effective mass window of 36 to 156 milli-electron-volts, while next-generation searches, including JUNO-beta-beta with 5 to 12 milli-electron-volts sensitivity, KamLAND2-Zen below 20, LEGEND-1000 at 8.5 to 19.4, nEXO at 5.7 to 17.7, and SNO+ Phase II at 19 to 46 milli-electron-volts, will probe much of the remaining parameter space, though a substantial portion of the normal-ordering region will stay out of reach. Cosmological constraints from Planck and the latest KATRIN direct-mass bound of 0.45 electron-volts further bracket the lightest neutrino mass. Taken together, the first JUNO results mark the moment when flavour model building enters a precision era: one-parameter schemes like T1 now make predictions sharp enough to be confirmed or killed within a decade, and the era of comfortable theoretical ambiguity in neutrino mixing is rapidly drawing to a close.

Subject of Research: Testing bi-large neutrino mixing patterns with the first JUNO oscillation measurements

Article Title: Zooming in on ‘bi-large’ neutrino mixing with the first JUNO results

Article References: Ding, G.-J., Kumar, R., Nath, N., Srivastava, R., & Valle, J. W. F. (2026). Zooming in on ‘bi-large’ neutrino mixing with the first JUNO results. The European Physical Journal C, 86(9), Article 1037. https://doi.org/10.1140/epjc/s10052-026-16285-9

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16285-9

Keywords: neutrino oscillations, JUNO, bi-large mixing, Cabibbo angle, lepton mixing matrix, CP violation, theta-12, neutrinoless double beta decay, flavour models, grand unified theories, mass ordering, liquid scintillator

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 core difficulty is one of crowding. Each photon that strikes a PMT’s photocathode ejects a single photoelectron, which is amplified into a characteristic pulse lasting tens of nanoseconds. When photons arrive within a few nanoseconds of one another, their pulses pile up into a single tangled waveform, and disentangling how many photoelectrons contributed becomes genuinely hard. Traditional approaches rely on waveform fitting or deconvolution: matching observed signals against expected templates, or mathematically inverting the detector’s response function to recover the underlying signal. These methods, used by experiments such as IceCube and Daya Bay, work well when photons are sparse, but their performance degrades markedly when multiple photoelectrons overlap, and they depend heavily on accurate prior knowledge of how the detector responds.

Machine learning has recently offered a powerful alternative. Supervised convolutional neural networks, trained on simulated waveforms with known photoelectron content, have been shown to improve the energy resolution of liquid scintillator detectors like JUNO by roughly two to three percent. But there is a catch that has limited their real-world impact: supervised learning requires ground-truth labels, meaning the exact number and arrival times of the photoelectrons underlying each waveform. In Monte Carlo simulations, such labels come for free. In real detector data, they simply do not exist. Calibration sources such as lasers and gamma emitters can provide approximate information, but nothing approaching the precision of simulation truth. This gap between what works in simulation and what is possible with real data has been a persistent obstacle for the field.

A team of researchers at Wuyi University in Jiangmen, China, led by Kainan Liu, Jingyu Huang, Guihong Huang and Jianyi Luo, has now proposed an ingenious workaround built on denoising diffusion probabilistic models, the same class of generative networks that powers modern text-to-image systems. Their framework, called a bidirectional conditional diffusion network, consists of two diffusion models that work as a pair. The first, Diffusion-A, is conditioned on a photoelectron sequence and learns to generate realistic PMT waveforms from it. The second, Diffusion-B, is conditioned on a waveform and learns to reconstruct the photoelectron sequence that produced it. Because each model’s output can serve as training material for the other, the two networks can bootstrap each other toward ever better performance, starting from only raw waveforms and coarse, imperfect estimates of the photoelectron content.

The architecture underlying each model is a modified U-Net adapted for one-dimensional waveform data. The condition vector, which encodes the number of photoelectrons in each of a thousand time bins, is mapped through a fully connected layer and fused with the convolutional features, while the diffusion time step is encoded through sinusoidal positional embeddings and injected into every residual block. Group normalization replaces batch normalization for training stability, the Swish activation improves gradient flow, and attention modules at coarser resolutions allow the network to capture long-range temporal dependencies in the waveform. The diffusion process itself runs over 200 steps, with carefully tuned noise schedules: a broad range for the waveform generator, which must recover both the overall envelope and fine temporal structure, and a narrower range for the reconstruction model, which must focus on precisely identifying photoelectron features within noisy sequences.

To train and evaluate the framework, the researchers built an electronics Monte Carlo simulation that reproduces the key characteristics of PMT waveforms in liquid scintillator detectors, drawing on measured pulse shapes from the Daya Bay experiment and parameters inspired by JUNO’s microchannel plate PMTs, including a transit-time spread of eight nanoseconds. They generated four datasets of one million training waveforms each, spanning scenarios from idealized conditions with widely separated photoelectrons to realistic physical events with Poisson-distributed multiplicities and severe overlap. The simulations modeled every ingredient that shapes a real waveform: the scintillation time distribution, the single-photoelectron pulse with its main peak, overshoot and reflection peaks, the charge spectrum with its 0.3 photoelectron-equivalent resolution, and white electronic noise with a standard deviation of 0.7 millivolts, all digitized at one gigahertz with ten-bit precision.

Under fully supervised conditions, where the networks had access to perfect Monte Carlo truth, the results were striking. The waveform generator reproduced single-photoelectron waveforms and charge spectra with deviations below two percent, and captured the statistics of overlapping multi-photoelectron waveforms with charge linearity and resolution consistent with the ideal simulation. The reconstruction model, in turn, recovered photoelectron counts with biases below three percent for up to seven photoelectrons, and achieved timing resolutions better than half a nanosecond, outperforming simple charge-based estimates particularly in the low-multiplicity regime where neutrino physics is most demanding. A ResNet50 classifier trained under identical conditions performed comparably on the counting task, confirming that diffusion networks are well suited to this problem.

The real breakthrough, however, came in the weakly supervised setting. Here the researchers began with only raw waveforms and crude initial photoelectron estimates obtained through a pipeline of bilateral filtering, peak finding and careful selection criteria that discarded severely overlapping signals. Training the reconstruction model directly on these rough labels produced poor results, because the initial waveforms contained almost no photon pile-up and taught the network nothing about overlap. But the iterative refinement changed everything. After the first round of mutual training between the two diffusion models, reconstruction improved substantially; a second iteration brought further gains, and performance converged after roughly five iterations. The mechanism is elegant: the generator learns to synthesize realistic overlapping waveforms, which then teach the reconstruction model to untangle them, and the improved reconstructions in turn refine the generator’s training labels.

The final numbers tell a compelling story. Training on waveforms with an average intensity of about 0.1 photoelectrons, a regime that provides enough clean single-photoelectron pulses to characterize the detector response while including mild overlap without the severe pile-up that corrupts initial labels, the weakly supervised method achieved an average normalized photoelectron-number resolution of 0.18 photoelectrons over the one-to-five photoelectron range, only about one percent worse than fully supervised learning. Its timing resolution of 0.5 nanoseconds was about 25 percent worse than the supervised ceiling, and all weakly supervised models showed a small systematic bias of 0.1 to 0.3 nanoseconds, but both metrics comfortably outperformed a deconvolution method optimized following the Daya Bay scheme, which suffered from missed photoelectrons at higher multiplicities and inherently limited timing precision.

The implications reach well beyond a single detector. Neutrino experiments around the world, from JUNO’s quest to determine the neutrino mass ordering to Hyper-Kamiokande’s pursuit of CP violation and KM3NeT’s hunt for astrophysical neutrinos, all depend on extracting maximal information from PMT waveforms. A method that needs no ground-truth labels, only raw data and coarse calibration estimates, could be applied directly to real detector data, closing the gap between simulation-era promise and operational reality. The authors note that the accuracy of the initial photoelectron estimates remains the critical factor governing performance, and they plan to optimize the network architecture further and extend the approach to vertex and energy reconstruction. But the demonstration that two diffusion models can teach each other to decode the flickering light of a neutrino detector marks a genuinely new chapter in the intersection of generative AI and experimental particle physics, one that may quietly sharpen every future measurement of the universe’s most elusive particles.

Subject of Research: Weakly supervised deep learning for PMT waveform simulation and reconstruction in neutrino detectors

Article Title: Pmt waveform simulation and reconstruction with conditional diffusion network

Article References: Liu, K., Huang, J., Huang, G., & Luo, J. (2026). Pmt waveform simulation and reconstruction with conditional diffusion network. The European Physical Journal C, 86(9), Article 1132. https://doi.org/10.1140/epjc/s10052-026-16415-3

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16415-3

Keywords: photomultiplier tubes, diffusion models, neutrino detectors, JUNO, waveform reconstruction, machine learning, weakly supervised learning, liquid scintillator, particle physics, generative AI, photoelectron counting, denoising diffusion probabilistic models