By combining the color dipole model of the nucleon with the assumption that cross sections behave asymptotically as ${\ln }^2(s)$, we are able to describe the data for photon, neutrino and hadron interactions with protons at all energies; $s$ is the center-of-mass energy of the interacting particles. Specifically, we extrapolate the perturbative QCD calculations into the regime of small fractional parton momenta $x$ using a color dipole description of the proton target that guarantees an asymptotic ${\ln }^2(s)$ behavior of all cross sections. The ambiguity of introducing a parametrization associated with the dipole approximation is mitigated by the requirement that the saturation of the small-$x$ structure functions produce ${\ln }^2(s)$-behaved asymptotic cross sections, in agreement with the data. The same formalism allows us to calculate the cross section for the hadronic pair production of charm particles. The results, in particular those for the high-energy neutrino and charm cross sections, are relevant for evaluating the sensitivity as well as the background in neutrino telescopes.

• Received 22 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.074040