Cross sections and inelasticity distributions of high-energy neutrino deep inelastic scattering

This study presents a comprehensive model for neutrino deep inelastic scattering (DIS) cross sections spanning energies from 50 to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>5</a:mn><a:mo>×</a:mo><a:msup><a:mrow><a:mn>10</a:mn></a:mrow><a:mrow><a:mn>12</a:mn></a:mrow></a:msup><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>GeV</a:mi></a:mrow></a:math> with an emphasis on applications to neutrino telescopes. We provide calculations of the total charged-current DIS cross sections and inelasticity distributions up to next-to-next-to-leading order for isoscalar nucleon targets and up to next-to-leading order for nuclear targets. Several modifications to the structure functions are applied to improve the modeling of the cross sections at low energies where perturbative QCD is less accurate and at energies above <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msup><c:mn>10</c:mn><c:mn>4</c:mn></c:msup><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi>GeV</c:mi></c:math> where there is non-negligible top quark production and small-<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>x</e:mi></e:math> logarithms need to be resummed. Using the Fixed-order next-to-leading logarithm (FONLL) general-mass variable-flavor number scheme, we account for heavy quark mass effects and separate the heavy flavor components of the structure functions, obtaining predictions of their relative contributions to the cross sections and the uncertainties arising from the parton distribution functions. Additionally, the effects of final state radiation are implemented in the calculation of the double-differential cross section and discussed in terms of their impact on measurements at neutrino telescopes.