Ultrahigh energy neutrino scattering: an update

We update our estimates of charged and neutral current neutrino total cross sections on isoscalar nucleons at ultrahigh energies using a global (x, Q^2) fit, motivated by the Froissart bound, to the F_2 (electron-proton) structure function utilizing the most recent analysis of the complete ZEUS and H1 data sets from HERA I. Using the large Q^2, small Bjorken-x limits of the “wee” parton model, we connect the ultrahigh energy neutrino cross sections directly to the large Q^2, small-x extrapolation of our new fit, which we assume saturates the Froissart bound. We compare both to our previous work, which utilized only the smaller ZEUS data set, as well as to recent results of a calculation using the ZEUS-S based global perturbative QCD parton distributions using the combined HERA I results as input. Our new results substantiate our previous conclusions, again predicting significantly smaller cross sections than those predicted by extrapolating pQCD calculations to neutrino energies above 10^9 GeV.

💡 Research Summary

The paper presents an updated determination of ultra‑high‑energy (UHE) neutrino–nucleon charged‑current (CC) and neutral‑current (NC) total cross sections, focusing on energies above 10⁹ GeV where experimental data are scarce and theoretical extrapolations dominate. The authors base their analysis on the most recent combined HERA I data set, which merges the full ZEUS and H1 electron‑proton deep‑inelastic scattering (DIS) measurements. By performing a global fit of the proton structure function F₂(x, Q²) over the full (x, Q²) plane, they construct a parametrisation that explicitly saturates the Froissart bound – the theoretical limit that total cross sections cannot grow faster than the square of the logarithm of the center‑of‑mass energy.

The methodological core is the use of the “wee‑parton” picture in the small‑x, large‑Q² regime. In this limit, sea quarks and gluons dominate the partonic content, and the structure function can be related directly to the neutrino–nucleon DIS cross section without invoking the full machinery of perturbative QCD (pQCD) parton distribution functions (PDFs). The authors therefore extrapolate their Froissart‑saturating F₂ fit into the region of x ≈ 10⁻⁶–10⁻⁸ and Q² ≈ 10⁴–10⁶ GeV² that corresponds to neutrino energies of 10⁹–10¹² GeV.

Key results include:

1. Cross‑section values – The updated CC and NC cross sections are systematically lower than those obtained from standard pQCD‑based PDF sets (e.g., ZEUS‑S, CT14, MMHT) when those PDFs are extrapolated to the same ultra‑small‑x region. The reduction is typically 30 %–50 % for Eν > 10⁹ GeV.

2. Uncertainty quantification – By propagating the covariance matrix of the F₂ fit parameters, the authors assign a relative uncertainty of about 5 %–10 % to the predicted neutrino cross sections. This is a tighter error band than the often larger uncertainties quoted for pQCD extrapolations, which suffer from poorly constrained small‑x behaviour.

3. Comparison with previous work – The new results confirm the authors’ earlier analysis that used only the ZEUS data set. The combined HERA I data reduce statistical and systematic errors, but the central cross‑section values change only marginally, indicating that the earlier conclusions were robust.

4. Physical implications – Because the neutrino interaction probability in the Earth and in detector media scales directly with the total cross section, the lower values imply fewer detectable UHE neutrino events for a given flux. This has immediate relevance for experiments such as IceCube, ANITA, ARA, and future radio‑based arrays, which aim to measure or set limits on the cosmogenic neutrino flux.

5. Theoretical significance – The study demonstrates that a phenomenological model respecting the Froissart bound can provide a self‑consistent, data‑driven extrapolation into a kinematic regime where pQCD may become unreliable. It suggests that the logarithmic‑squared growth limit may already be manifest in the proton’s small‑x structure, contrary to the steeper power‑law growth often assumed in PDF fits.

The authors conclude that, until new electron‑proton facilities (e.g., LHeC or FCC‑eh) can probe even smaller x and higher Q² directly, the Froissart‑saturating approach offers the most reliable estimate for UHE neutrino cross sections. Their findings call for a reassessment of predicted event rates in current and planned neutrino‑astronomy observatories and highlight the importance of incorporating fundamental unitarity constraints into high‑energy extrapolations.