Abstract
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.
Highlights
With the help of analytical solutions of the nonsinglet and the singlet DGLAP equation [1], we will determine analytically the ultrahigh energy (UHE) neutrino-nucleon interaction cross-sections both for the charged and the neutral current in the leading order (LO)
In our analytical process of determining UHE neutrinonucleon cross-section, we adopt the process of extrapolating parton densities at ultralow Bjorken x (x < 10−5), which will allow us to obtain reasonable cross-section in the region of x which has not been explored by any existing terrestrial Deep inelastic scattering (DIS)
By using MRST 2004 f4 LO input parton distributions at Q2 = μL2O = 1 GeV2 [14, 15], we estimate the values of extrapolated cross-sections for ]N interactions for the charged and the neutral current from (16)
Summary
With the help of analytical solutions of the nonsinglet and the singlet DGLAP equation [1], we will determine analytically the UHE neutrino-nucleon interaction cross-sections both for the charged and the neutral current in the leading order (LO). We will compare our predictions with the results of several other authors [2,3,4] and study the range of validity of our approach.
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