Deep Inelastic Scattering Cross Section Uncertainties in Tau Neutrino Appearance Measurements

TL;DR

This paper evaluates the uncertainties in tau neutrino charged current deep inelastic scattering cross sections, highlighting their dependence on parton distribution functions and implications for neutrino oscillation experiments.

Contribution

It provides a detailed analysis of PDF-driven uncertainties in tau neutrino DIS cross sections and discusses their treatment in different neutrino experiment contexts.

Findings

PDF-driven uncertainty on cross section ratio is less than 3% above 5 GeV

Antineutrino cross section uncertainties range from 2-30% below 10 GeV

Coupled treatment of tau and muon neutrino cross sections is recommended for atmospheric analyses

Abstract

In neutrino experiments sensitive to multiple flavors, the analyzers may be presented with a choice of treating the uncertainties on the respective cross sections in a correlated or an uncorrelated manner. This study focuses on the charged current deep inelastic scattering (CC DIS) channel in experiments sensitive to both muon and tau neutrinos. We evaluate the ratio of the leading-order $\nu_{\tau}$ and $\nu_{\mu}$ cross sections and derive its uncertainty from the underlying parton distribution functions (PDFs). We find that, for neutrino energies above 5 GeV, the PDF-driven uncertainty on the cross section ratio is less than 3%, with a larger (2-30%) variation seen in antineutrinos at energies below 10 GeV. These results suggest that for atmospheric tau neutrino appearance analyses, the uncertainties in $\nu_{\tau}$ and $\nu_{\mu}$ DIS cross sections should be coupled, while separate treatment for the two flavors may be warranted in long-baseline experiments with an antineutrino beam. We further explore the role of the invariant hadronic mass threshold defining the onset of the DIS regime. We argue that its impact may be incorporated only if it is applied to both DIS and resonance cross sections, and if the correlations with other DIS and resonance cross section parameters are taken into account.