UHE Neutrinos: Fusing gluons within diffraction cone

TL;DR

This paper refines the estimate of gluon-fusion effects in ultra-high energy neutrino interactions by defining a precise impact parameter profile, solving the dipole BFKL equation, and finding saturation effects are weak up to extremely high energies.

Contribution

It introduces a method to specify the impact parameter profile function based on scattering data, reducing uncertainties in gluon-fusion estimates at ultra-high energies.

Findings

Impact parameter profile is well-defined and proportional to diffraction cone slope.

Saturation effects are weak, less than 25%, up to 10^{12} GeV neutrino energy.

Numerical solution of the non-linear color dipole BFKL equation supports these conclusions.

Abstract

Currently available estimates of the gluon-fusion effect in ultra-high energy neutrino-nucleon interactions as well as in DIS on protons suffer from uncertainty in defining the scattering profile function $\Gamma(b)$. Indeed, the area, $S$, in the impact parameter space populated with interacting gluons varies by a factor of $4 - 5$ from one analysis to another. To get rid of uncertainties we specify the dipole-nucleon partial-wave amplitude $\Gamma(b)$ which meets the restrictions imposed by both the total dipole-nucleon cross section and the small angle elastic scattering amplitude. The area $S$ becomes a well defined quantity proportional to the diffraction cone slope. We solve numerically the non-linear color dipole BFKL equation and evaluate the UHE neutrino-nucleon total cross section. Our finding is that the saturation is a rather weak effect, $\lsim 25%$, up to $E_{\nu}\sim 10^{12}$ GeV.