arXiv2026
The flux of astrophysical neutrinos is now measured with unprecedented accuracy and over several decades of energy spectrum. Their origin traces back to hadronic collisions between protons and nuclei in the cosmic rays with hydrogen and helium in the target gas. To accurately interpret the data, a precise determination of the underlying cross sections is therefore mandatory. We present a new evaluation of the neutrino production cross section from $p+p$ collisions, building on our previous analysis of the production cross section for $π^\pm$, $K^\pm$, and minor baryonic and mesonic channels. Cross sections for scatterings involving nuclei heavier than protons are also derived. The novelty of our approach is the analytical description of the Lorentz invariant cross section $σ_{\rm inv}$, and the fit of the model to the available accelerator data. We work with neutrino energies from $10$ GeV to $10^7$ GeV, and, correspondingly, to incident proton (nuclei) energies from $10$ GeV to $10^9$ GeV (GeV/n). We obtain the total differential cross section, $dσ(p+p\rightarrow ν+X)/dE_ν$ as a function of neutrino and proton energies, with an estimated uncertainty of 5% for neutrino energies below 100 GeV, increasing to 10% above TeV energies. Predictions are given for $ν_e, ν_μ, \bar{ν_e}$ and $\bar{ν_μ}$. A comparison with state-of-the-art cross sections, all relying on Monte Carlo generators, is also presented. To facilitate the use by the community, we provide numerical tables and a script for accessing our energy-differential cross sections.