Measurement of the gluon parton distribution function at small x with neutrino telescopes

We analyze the possibility that neutrino telescopes may provide an experimental determination of the slope λ of the gluon distribution in the proton at momentum fractions x smaller than the accelerator reach. The method is based on a linear relation between λ and the spectral index (slope) of the down-going atmospheric muon flux above 100 TeV, for which there is no background. Considering the uncertainties in the charm production cross section and in the cosmic ray composition, we estimate the error on the measurement of λ through this method, excluding the experimental error of the telescopes, to be ±0.2.