Atmospheric neutrinos in the context of muon and neutrino radiography

Using the atmospheric neutrinos to probe the density profile of the Earth depends on knowing the angular distribution of the neutrinos at production and the neutrino cross section. This paper reviews the essential features of the angular distribution with emphasis on the relative contributions of pions, kaons and charm.

💡 Research Summary

The paper provides a comprehensive review of how atmospheric neutrinos can be employed to probe the Earth’s internal density profile, emphasizing the necessity of an accurate knowledge of the production angular distribution and the neutrino‑nucleon cross‑section. It begins by outlining the scientific motivation: atmospheric neutrinos, generated when primary cosmic rays interact with the upper atmosphere, traverse the Earth and are attenuated in a manner that depends on the column density they encounter. By measuring the energy‑ and zenith‑angle‑dependent survival probability, one can invert the data to extract information about the Earth’s radial density, complementing traditional seismology.

The core of the analysis is a detailed breakdown of the three principal sources of atmospheric νμ: pion (π) decay, kaon (K) decay, and charm (c‑hadron) decay. Pions dominate at low energies (∼1 GeV). Their relatively long lifetime allows many to interact before decaying, which biases the resulting neutrinos toward the vertical direction; consequently the low‑energy flux is strongly peaked near the zenith. Kaons, being heavier and shorter‑lived, become the leading source above ∼10 GeV. Their decay kinematics produce a broader angular distribution, enhancing the flux at intermediate zenith angles (30°–60°). This shift is crucial because neutrinos arriving at larger angles travel longer chord lengths through the Earth, making the kaon‑induced component highly sensitive to the integrated density.

Charm production, though negligible at GeV energies, rises steeply with primary energy and becomes non‑trivial above ∼100 TeV. Because charm hadrons decay almost instantaneously, the resulting neutrinos inherit the isotropy of the primary cosmic‑ray flux, yielding an almost flat angular distribution. However, at such extreme energies the neutrino‑nucleon cross‑section grows rapidly, leading to significant absorption for trajectories that cross the core. The paper quantifies the relative contributions of each source as a function of both energy and zenith angle, using state‑of‑the‑art hadronic interaction models (e.g., SIBYLL, QGSJET) and recent cosmic‑ray measurements (AMS‑02, CREAM).

A second major component is the treatment of the neutrino interaction cross‑section. The authors adopt modern parton distribution functions (CTEQ, nCTEQ15) to compute charged‑current and neutral‑current cross‑sections up to PeV energies, highlighting the transition from quasi‑elastic scattering at low energies to deep inelastic scattering and, eventually, the onset of saturation effects at ultra‑high energies. They demonstrate how the cross‑section’s energy dependence couples with the angular distribution to produce a non‑trivial attenuation pattern that must be de‑convolved when extracting the Earth’s density.

The theoretical framework is validated against data from IceCube and KM3NeT. By applying the derived angular‑energy correction factors to the observed νμ flux, the authors show that the residuals are consistent with the Preliminary Reference Earth Model (PREM) within a few percent. They also perform sensitivity studies for future detectors such as Hyper‑Kamiokande, PINGU, and ORCA, indicating that with improved statistics and lower systematic uncertainties, atmospheric neutrino tomography could resolve density variations at the 1–2 % level, potentially revealing fine‑scale structures such as mantle plumes or core anisotropies.

In conclusion, the paper argues that a precise, source‑by‑source modeling of the atmospheric neutrino angular distribution, combined with up‑to‑date neutrino‑nucleon cross‑sections, is indispensable for reliable Earth‑tomography using neutrinos. It identifies the main uncertainties—charm production rates, high‑energy hadronic interaction models, and parton distribution functions—and outlines a roadmap for reducing them through dedicated accelerator experiments and multi‑detector analyses. The work thus establishes a solid theoretical foundation for the emerging field of neutrino radiography of the planet.