Measuring the 13 Neutrino Mixing Angle and the $CP$ Phase with Neutrino Telescopes

The observed excess of high-energy cosmic rays from the Galactic plane in the energy range around ${10}^{18}\mathrm{eV}$ may be explained by neutron primaries generated in the photodissociation of heavy nuclei. In this scenario, lower-energy neutrons decay before reaching the Earth and produce a detectable flux in a $1{\mathrm{km}}^3$ neutrino telescope. The initial flavor composition of the neutrino flux, $\varphi ({\overline{\nu }}_e):\varphi ({\overline{\nu }}_{\mu }):\varphi ({\overline{\nu }}_{\tau })=1:0:0$, permits a combined ${\overline{\nu }}_{\mu }/{\overline{\nu }}_{\tau }$ appearance and ${\overline{\nu }}_e$ disappearance experiment. The observable flux ratio $\varphi ({\overline{\nu }}_{\mu })/\varphi ({\overline{\nu }}_e+{\overline{\nu }}_{\tau })$ at Earth depends on the 13 mixing angle ${\theta }_{13}$ and the leptonic $CP$ phase ${\delta }_{CP}$, thus opening a new way to measure these two quantities.

Figure 1

Flux ratio $R={\varphi }_{\mu }^D/({\varphi }_e^D+{\varphi }_{\tau }^D)$ at Earth as a function of ${\theta }_{13}$ for ${\theta }_{23}=35°$ (blue, dotted-dash curve), ${\theta }_{23}=45°$ (red, solid curve), ${\theta }_{23}=55°$ (green, dashed curve); for initial fluxes ${\varphi }_e:{\varphi }_{\mu }:{\varphi }_{\tau }=1:0:0$ at the source and ${\delta }_{CP}=0$. The ratio $R=0.5$ expected for standard astrophysical sources is shown for comparison.

Figure 2

Flux ratio $R={\varphi }_{\mu }^D/({\varphi }_e^D+{\varphi }_{\tau }^D)$ at Earth as a function of ${\delta }_{CP}$ for ${\theta }_{13}=10°$ (red, solid curve), ${\theta }_{13}=5°$ (green, dashed curve), and ${\theta }_{13}=2°$ (blue, dotted-dash curve); for ${\theta }_{23}=45°$ and initial fluxes ${\varphi }_e:{\varphi }_{\mu }:{\varphi }_{\tau }=1:0:0$ at the source.