Upward shower rates at neutrino telescopes directly determine the neutrino flux

TL;DR

This paper demonstrates that upward shower rates at neutrino telescopes are solely determined by neutrino flux, independent of cross section, enabling flux measurement without cross section uncertainties.

Contribution

It reveals that upward shower rates are independent of the neutrino-nucleon cross section, allowing direct flux determination from observed rates.

Findings

Upward shower rates depend only on neutrino flux, not cross section.

Downward shower rates vary linearly with the cross section.

Flux spectral shape can be inferred from neighboring energy bins.

Abstract

We show that the rate for upward showers from an isotropic cosmic neutrino flux at neutrino telescopes like IceCube is independent of the neutrino-nucleon cross section. For bins that span a relatively narrow range in energy, neither scaling the cross section, nor changing its power-law energy behavior affects the upward shower rate, which depends only on the flux. The neutrino flux can be completely known since its spectral shape can be determined by comparing the rates in neighboring bins. We also show that the downward shower rate varies linearly with cross section with a proportionality constant determined by the energy-dependence of the cross section, independent of the power-law behavior of the flux. The normalization and energy dependence of the cross section can be known by comparing the downward rates in neighboring bins.