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Precision three-Dimensional Atmospheric Neutrino Flux Calculation Based on Honda Flux Model

This paper presents a comprehensive three-dimensional atmospheric neutrino flux calculation covering 10 MeV to 10 TeV across seven detector sites, incorporating novel muon propagation effects and updated input models to provide precise, site-dependent flux predictions with reduced systematic uncertainties for current and future neutrino and dark matter experiments.

Original authors: Jie Cheng, Yu-Feng Li, Liang-Jian Wen

Published 2026-07-10

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CC BY 4.0

Original authors: Jie Cheng, Yu-Feng Li, Liang-Jian Wen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Earth is a giant, invisible shield made of a magnetic force field, and the universe is constantly bombarding us with a storm of tiny, high-speed particles called cosmic rays. When these rays hit our atmosphere, they crash into air molecules and create a shower of new particles, including ghostly "atmospheric neutrinos" that pass right through the planet like ghosts through a wall. For decades, scientists have tried to predict exactly how many of these neutrinos hit different detectors around the globe.

In this new study, the authors have built a super-precise, 3D map of this neutrino rain, but they've added a few game-changing twists that previous maps missed.

The "Underground Ghost" Discovery
The biggest surprise in this paper is a new source of low-energy neutrinos that nobody had counted before. Think of the Earth's crust and oceans as a giant sponge. When high-energy cosmic rays hit the atmosphere, they also create muons (a heavier cousin of the electron). Most of these muons stop in the air, but some are so energetic they punch right through the ground and get stuck inside the Earth's "sponge."

Once trapped underground, these muons eventually stop moving. When they stop, they either decay or get captured by atoms in the rock or water. This process releases a fresh batch of low-energy neutrinos (below 100 MeV) that were completely missing from all previous calculations. It's like realizing that while you were counting the raindrops hitting your roof, you forgot to count the water dripping from the gutters into the basement. The authors found that this "underground drip" adds a significant, consistent amount of neutrinos everywhere on Earth, regardless of where you are standing.

The Magnetic Filter Effect
The paper also explains why the neutrino rain isn't the same everywhere. The Earth's magnetic field acts like a giant, invisible bouncer at a club. It checks the "ID" (rigidity) of incoming cosmic rays. At the poles (like where the IceCube detector sits in Antarctica), the bouncer is lenient, letting almost everyone in. At the equator (like where the JUNO detector is in China), the bouncer is strict, blocking most low-energy particles.

Because of this, the paper shows that the neutrino flux at IceCube can be nearly twice as high as at JUNO for energies below 1 GeV. The authors simulated this across seven different detector sites, from the deep underground labs in China to the ice of the South Pole, and found that these location-based differences are huge at low energies but disappear at high energies (above 10 GeV), where the particles are too fast for the magnetic bouncer to stop.

Updating the Recipe
To get these numbers right, the authors didn't just use old data; they updated the entire recipe for their simulation. They swapped out the old cosmic ray data for new measurements from the AMS02 experiment, updated the Earth's magnetic field map to the IGRF2020 model, and recalibrated the rules for how particles crash into each other using new data.

When they compared their new results to the previous gold-standard model (HKKMS15), they found differences of 2% to 10% in the higher energy ranges. These aren't mistakes in the old model; they are just refinements, like adjusting a recipe because you found out the flour has changed. The authors also managed to shrink the "uncertainty" (the margin of error) in their predictions, especially for low energies, by using a clever method that ties their neutrino predictions to actual measurements of muons hitting the ground.

Why This Matters
This isn't just about counting particles; it's about clearing the fog for other experiments.

For Dark Matter Hunters: Scientists looking for dark matter are trying to spot a faint signal in a sea of background noise. This new map helps them understand the "neutrino fog" that could hide their discovery.
For Supernova Watchers: When a star explodes nearby, it sends a burst of neutrinos. To see that burst, scientists need to know exactly how much "background noise" (atmospheric neutrinos) is already there. This paper provides a much clearer picture of that noise, especially in the tricky 10–30 MeV range.
For Neutrino Oscillation Studies: Experiments trying to figure out how neutrinos change their "flavor" as they travel need precise starting numbers. This 3D map gives them a better baseline.

What the Paper Doesn't Say
The authors are careful to note that while their simulation is incredibly detailed, it still relies on models. They haven't included the specific shape of every mountain around the detectors yet, which might tweak the numbers slightly for very low energies. They also suggest that future updates could include how the Sun's 11-year cycle changes the cosmic ray storm, which would make the map even more accurate over time.

In short, this paper doesn't claim to have solved the mystery of the universe, but it has handed scientists a much sharper, more detailed flashlight to look into the dark, low-energy corners of the neutrino world.

Problem Statement

Atmospheric neutrinos ( $\nu_{\text{atm}}$ ) are critical backgrounds and probes for neutrino oscillation studies, diffuse supernova neutrino background (DSNB) searches, dark matter detection, and nucleon decay searches. While three-dimensional (3D) flux calculation frameworks like HKKMS, Bartol, and FLUKA exist, they face three specific limitations in the context of current and future experiments:

Outdated Input Models: Previous calculations often rely on older primary cosmic ray models (e.g., AMS01-based) and geomagnetic field models (e.g., IGRF2010) that do not reflect the latest experimental measurements.
Missing Low-Energy Physics: No previous 3D flux calculation has accounted for the propagation of atmospheric muons ( $\mu_{\text{atm}}$ ) inside the Earth, their subsequent stopping, and their decay or nuclear capture. This omission is significant for the sub-100 MeV energy range, crucial for DSNB and dark matter searches.
Incomplete Site Comparison: Systematic differences in flux across diverse geomagnetic environments (from the South Pole to low-latitude sites) have not been comprehensively compared using a unified, updated framework.

Methodology

The authors present a comprehensive 3D atmospheric neutrino flux calculation based on the established HKKMS15 framework, incorporating several key methodological updates:

Muon Propagation Inside Earth: For the first time, the simulation tracks charged secondaries (primarily muons) that penetrate the Earth's crust or ocean. The framework models their energy loss, stopping, and subsequent fate:
- $\mu^+$ decay freely ( $\mu^+ \to e^+ \nu_e \bar{\nu}_\mu$ ).
- $\mu^-$ either decay in orbit or undergo nuclear capture ( $\mu^- + p \to \nu_\mu + n$ ).
- The stopping medium is identified using the CRUST1.0 global crustal model.
- This process generates a supplementary flux of low-energy neutrinos, with nuclear capture producing $\nu_\mu$ extending up to $\sim95$ MeV.
Updated Input Models:
- Primary Cosmic Rays: Replaced the AMS01-based model with an AMS02-based model, incorporating data from AMS02, BESS-polar, PAMELA, JACEE, RUNJOB, and CREAM.
- Geomagnetic Field: Updated to the IGRF2020 model to accurately calculate site-dependent rigidity cutoffs and muon bending.
- Hadronic Interactions: Employed a muon-recalibrated combination of JAM and modified DPMJET-III models, tuned to reduce $\mu_{\text{atm}}$ flux discrepancies to within 5% over 1–100 GeV.
- Atmosphere: Used the NRLMSISE-00 global atmospheric model for site- and time-dependent air density profiles.
Simulation Scope: The calculation covers seven detector sites (JUNO, Super-Kamiokande, CJPL, KM3NeT/ORCA, IceCube, DUNE, and TRIDENT) across an energy range of 10 MeV to $10^4$ GeV. It utilizes full spherical geometry and 3D geomagnetic fields to preserve transverse momentum and Earth's curvature.

Key Contributions

First Inclusion of Earth-Propagating Muons: The paper introduces the contribution of stopped atmospheric muons inside the Earth to the neutrino flux, a qualitatively new source absent in all prior 3D calculations (HKKMS11/15, Bartol, FLUKA).
Global Multi-Site Framework: Provides precise, site-specific flux predictions for seven major experimental locations, enabling direct comparison of geomagnetic effects from the South Pole (IceCube) to low-latitude sites (TRIDENT).
Low-Energy Precision: Delivers the first precise flux results below 100 MeV for these sites, a regime previously lacking detailed 3D modeling.
Re-estimated Uncertainties: Updates the hadronic uncertainty estimation using the muon-constrained method (Honda et al.), significantly reducing systematic errors compared to previous calculations.

Results

1. Flux Characteristics for $E_\nu > 100$ MeV:

Site Dependence: Significant site-dependent differences appear at $E_\nu < 10$ GeV due to geomagnetic cutoffs. For instance, the $\nu_\mu$ flux at IceCube is approximately twice that at JUNO below 1 GeV. Above 10 GeV, fluxes converge across sites.
Zenith and Azimuth: The flux exhibits strong zenith-angle dependence (up/down and horizontal/vertical ratios) driven by production geometry and geomagnetic shielding. Azimuthal asymmetries (East-West effect) are prominent at sub-GeV energies but vanish at higher energies.
Comparison with HKKMS15: Deviations of 2%–10% are observed compared to HKKMS15, attributed primarily to the updated primary cosmic ray spectral shape (higher flux below 40 GeV, lower above) and the recalibrated hadronic interaction model.

2. Flux Characteristics for $E_\nu < 100$ MeV (Muon Propagation Contribution):

Global Absolute Increment: The contribution from muon propagation inside the Earth is a global effect. The absolute increase in flux ( $\Delta \phi_\nu$ ) is approximately site-independent, peaking in the 10–50 MeV range.
Relative Enhancement: Because the baseline flux varies by site (due to geomagnetic cutoffs), the relative enhancement varies inversely. Sites with lower baseline flux (e.g., JUNO) show a larger fractional increase than high-flux sites (e.g., IceCube).
Flavor Hierarchy: The contribution follows the hierarchy $\nu_e \approx \bar{\nu}_\mu > \nu_\mu > \bar{\nu}_e$ . This is driven by the charge asymmetry of stopping muons ( $\mu^+ > \mu^-$ ) and the nuclear capture process, which produces $\nu_\mu$ with energies extending to $\sim95$ MeV, well above the Michel endpoint ( $\sim52.8$ MeV).

3. Uncertainty Estimation:

Using the muon-constrained method, the hadronic uncertainty ( $\delta_{\text{had}}$ ) is significantly reduced. For the horizontal direction at 1–10 GeV, $\delta_{\text{had}}$ is reduced to $\sim3\%$ for $\nu_\mu/\bar{\nu}_\mu$ and $\sim4\%$ for $\nu_e/\bar{\nu}_e$ .
The total relative uncertainty ( $\delta_{\text{tot}}$ ) is reduced to $\sim5\%$ – $7\%$ in the 1–10 GeV range (horizontal), a marked improvement over previous estimates.

Significance

The paper claims that these results provide essential, precise inputs for a wide range of physics programs:

Neutrino Oscillations: The 3D flux predictions and reduced uncertainties serve as improved inputs for atmospheric neutrino experiments (JUNO, Super-Kamiokande, Hyper-Kamiokande, DUNE, KM3NeT/ORCA, IceCube).
DSNB Searches: The precise low-energy flux calculations (including the new muon-propagation component) define the dominant irreducible background for DSNB searches in the 10–30 MeV window.
Dark Matter Searches:
- Indirect: The updated fluxes improve background characterization for searches for WIMP annihilation (IceCube) and light dark matter annihilation (JUNO, Borexino, Super-K).
- Direct: The precise low-energy predictions constrain the "neutrino fog" that limits the sensitivity of direct dark matter detectors (LZ, XENONnT, PandaX-4T).
Nucleon Decay: The better-constrained atmospheric neutrino background directly impacts the sensitivity limits for nucleon decay searches in current and next-generation detectors.

The authors conclude that while the current calculation provides a robust baseline, future refinements—such as incorporating local mountain profiles, time-dependent solar modulation, and updated hadronic models using NA61/SHINE and LHCf data—will further reduce systematic uncertainties, particularly in the low-to-intermediate energy regions.

Problem Statement

Methodology

Key Contributions

Results

Significance

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