Cross sections of the neutrino-nucleon interaction at ultra high energy

We determine the ultra-high-energy (UHE) neutrino-nucleon cross sections analytically both for charged and neutral currents to leading order by using the solutions of the non-singlet Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation and the singlet DGLAP equation, respectively. Next, we determine the cross sections for both charged and neutral currents at the one-loop level by carrying out a numerical integration of the double differential cross-section. Our analytical, as well as our numerically-determined, results are compared with the next-to-leading order (NLO) results of various authors. We find our numerically-determined result to be in sufficient agreement with the results obtained by those authors. On the other hand, our analytical result matches better with other results at the lower end of the energy spectrum of the UHE neutrino rather than with results at the higher end.