Deep inelastic scattering cross section uncertainties in tau neutrino appearance measurements

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>ν</a:mi><a:mi>τ</a:mi></a:msub></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ν</c:mi><c:mi>μ</c:mi></c:msub></c:math> cross sections and derive its uncertainty from the underlying parton distribution functions (PDFs). We find that, for neutrino energies above 8 GeV, the PDF-driven uncertainty on the cross section ratio is less than 1.5%, with a larger (up to 9%) variation seen in antineutrinos at the lowest DIS energies. These results suggest that for atmospheric tau neutrino appearance analyses, the uncertainties in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>ν</e:mi><e:mi>τ</e:mi></e:msub></e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>ν</g:mi><g:mi>μ</g:mi></g:msub></g:math> 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.