New determination of the neutrino hadronic production cross sections from GeV to beyond PeV energies

TL;DR

This work delivers a new, data-driven analytic model for the inclusive neutrino production cross section in hadronic $p+p$ collisions by formulating and fitting the Lorentz-invariant cross section $σ_{ m inv}$ to accelerator data across broad kinematics. By integrating π±, kaon, and hyperon channels and including nuclear target corrections, the approach yields the energy-differential cross section $dσ/dE_ν$ with a quantified $5$–$20\%$ uncertainty depending on $E_ν$, and provides ν and $\bar{ν}$ spectra across flavors. Compared with state-of-the-art Monte Carlo generators, the new cross sections agree well with Bhatt~(≈10%) and AAfrag (≤≈20%), while revealing notable deviations from Kamae and Kelner in several regimes. The paper also computes the ν emissivity $ε(E_ν)$ for various CR and ISM compositions, illustrating how high-energy CR assumptions propagate into neutrino predictions, and offers public numerical tables and code to facilitate use by the astrophysics community. This work thus improves the reliability of neutrino flux predictions for Galactic and extragalactic sources and informs forward-detector backgrounds, while calling for new collider data to further constrain forward production and He-target processes.

Abstract

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.

Figures (6)

• Figure 1: This diagram shows the $\nu_\mu$ and $\nu_e$ production channels from $p+p$ collisions considered in our analysis. The same scheme applies to $\bar{\nu}_\mu$ and $\bar{\nu}_e$ under charge conjugation (with the exception of the initial $p+p$ state). Only channels contributing at least 0.5% of the total yield are reported (see main text for details).
• Figure 2: Differential cross section for the production of $\nu_\mu$, $\nu_e$ and relative antiparticles from $\pi^\pm$ in $p+p$ collisions, computed for different incident kinetic energies of the proton $T_p$.
• Figure 3: Differential cross section for the inclusive production of the different $\nu$ flavors and relative antiparticles in $p+p$ collisions, derived from fits to the data as described in Secs. \ref{['sec:pi_charged']} and \ref{['sec:other_channels']}. We plot separate production of $\pi^\pm$, $K^\pm$, $K_0^S$, $K_0^L$, and $\Lambda$ plus subdominant channels (S.C.), and their sum. Each plot is computed for incident proton energies $T_p=10^6$ GeV. The curves are displayed along with their 1$\sigma$ error band. At the bottom of each panel the 1$\sigma$ uncertainty band is displayed around the best fit individually for each contribution.
• Figure 4: Comparison among our differential cross sections and the one reported in Kamae:2006bf (Kamae), Bhatt_2020 (Bhatt), Koldobskiy:2021nld (AAfrag) and kelner+06 (Kelner) as a function of $E_\nu$, for incident proton energy $T_p = 10^8, 10^6, 10^4$ and $10^2$ GeV.
• Figure 5: Relative difference between our differential cross section and the one reported in Kamae:2006bf (Kamae), Bhatt_2020 (Bhatt), Koldobskiy:2021nld (AAfrag) and kelner+06 (Kelner), for incident proton energy $T_p = 10^2, 10^4, 10^6$ and $10^8$ GeV for $\nu_\mu$. We also show the statistical uncertainty of our model as a gray band.