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 a Regge description inspired by Donnachie and Landshoff with soft and hard Pomerons, and employing at larger x the perturbative QCD expressions. Smooth interpolation between the two regimes for each ${Q}^{2}$ is provided with the help of simple polynomial functions. To obtain low-$x$ neutrino-nucleon structure functions ${F}_{2}^{\ensuremath{\nu}N,\overline{\ensuremath{\nu}}N}{(x,Q}^{2})$ and the singlet part of ${F}_{3}^{\ensuremath{\nu}N,\overline{\ensuremath{\nu}}N}{(x,Q}^{2})$ from the Donnachie-Landshoff function ${F}_{2}^{\mathrm{ep}}{(x,Q}^{2}),$ we use the ${Q}^{2}$-dependent ratios ${R}_{2}{(Q}^{2})$ and ${R}_{3}{(Q}^{2})$ derived from perturbative QCD calculations. The nonsinglet part of ${F}_{3}$ at low x, which is very small, is taken as a power-law extrapolation of the 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 calculate the neutrino-nucleon cross sections and compare them with some other cross sections known in the literature. Our cross sections turn out to be the highest among them at the highest energies, which is explained by the contribution of the hard Pomeron.