Analytical Evaluation of the Neutrino-Nucleon Interaction Cross-Sections at Ultrahigh Energy

The ultrahigh energy (UHE) neutrino-nucleon interaction cross-sections are evaluated analytically in one loop by using the solutions of Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equations. Since the genesis of the UHE neutrinos is various sources which have energy more than 105 GeV, so parton distributions are extrapolated at ultralow x to determine the charged current and the neutral current cross-sections. We then compare our analytically obtained extrapolated results with the next-to-leading order (NLO) results of various other authors. A good agreement between the two reflects the veracity of our approach of extrapolation at ultralow x .