Hard pomeron enhancement of ultrahigh-energy neutrino-nucleon cross-sections

Abstract

An unknown small-x behavior of nucleon structure functions gives appreciable uncertainties to high-energy neutrino-nucleon cross-sections. We construct structure functions using at small x Regge inspired description by A. Donnachie and P. V. Landshoff with soft and hard pomerons, and employing at larger x the perturbative QCD expressions. The smooth interpolation between two regimes for each Q^2 is provided with the help of simple polynomial functions. To obtain low-x neutrino-nucleon structure functions $F_2^{νN, \bar νN}(x,Q^2)$ and singlet part of $F_{3}^{νN,\bar νN}(x,Q^2)$ from Donnachie-Landshoff function $F_2^{ep}(x,Q^2)$, we use the Q^2-dependent ratios R_2(Q^2) and R_3(Q^2) derived from perturbative QCD calculations. Non-singlet part of F_3 at low x, which is very small, is taken as power-law extrapolation of perturbative function at larger x. This procedure gives a full set of smooth neutrino-nucleon structure functions in the whole range of x and Q^2 at interest. Using these structure functions, we have calculated the neutrino-nucleon cross-sections and compared them with some other cross-sections known in literature. Our cross-sections turn out to be the highest among them at the highest energies, which is explained by contribution of the hard pomeron.