Flavor composition of ultrahigh energy neutrinos at source and at neutrino telescopes

We parametrize the initial flux composition of high energy astrophysical neutrinos as $({\Phi }_e^0:{\Phi }_{\mu }^0:{\Phi }_{\tau }^0)=(1:n:0)$, where $n$ characterizes the source. All usually assumed neutrino sources appear as limits of this simple parametrization. We investigate how precise neutrino telescopes can pin down the value of $n$. We furthermore show that there is a neutrino mixing scenario in which the ratio of muon neutrinos to the other neutrinos takes a constant value regardless of the initial flux composition. This occurs when the muon neutrino survival probability takes its minimal allowed value. The phenomenological consequences of this very predictive neutrino mixing scenario are given.

Figure 1

Range of allowed values of $T={\Phi }_{\mu }/{\Phi }_{\mathrm{tot}}$ (upper plot) and $R={\Phi }_e/{\Phi }_{\tau }$ (lower plot) as a function of the flux composition parameter $n$, when the oscillation parameters are varied within their $3\sigma$ ranges.

Figure 2

Phenomenology of a PMNS matrix with all elements of the second row equal to each other. Shown are the atmospheric neutrino parameter ${sin}^2{\theta }_{23}$ against $|U_{e3}|$, the solar neutrino parameter ${sin}^2{\theta }_{12}$ against $\delta$ for different values of $|U_{e3}|$, and ${sin}^2{\theta }_{12}$ against ${sin}^2{\theta }_{23}$. Also given are the current best-fit value and the $1\sigma$ as well as $3\sigma$ ranges of the oscillation parameters.

Figure 3

${\chi }^2$ as a function of $n_{\mathrm{fit}}$ for $n_{\mathrm{true}}=2$, for different values of errors on the flux ratios $T$ (left panel) and $R$ (right panel). All oscillation parameters are fixed in the fit.

Figure 4

${\chi }^2$ as a function of $n_{\mathrm{fit}}$ for $n_{\mathrm{true}}=2$, for different values of errors on the flux ratios $R$. All oscillation parameters are allowed to vary freely within their current $3\sigma$ limits in the fit. Corresponding ${\chi }^2$ for $T$ is found to be zero for all values of $n_{\mathrm{fit}}$ and all errors $\Delta T/T$.

Figure 5

For each $n_{\mathrm{true}}$ on the $x$ axis, the shaded region shows the values of $n_{\mathrm{fit}}$ which can be excluded at $2\sigma$. We assumed 10% (black/darkest), 20% (green/dark), and 30% (cyan/lightest) uncertainty on $\Delta R/R$. The four panels are for the four benchmark values of the oscillation parameters assumed in the data.

Figure 6

For each $n_{\mathrm{true}}$ on the $x$ axis, the shaded region shows the values of $n_{\mathrm{fit}}$ which can be excluded at $2\sigma$. We assumed 5% (black/darkest), 10% (green/dark), and 20% (cyan/lightest) uncertainty on $\Delta T/T$. The two panels are for the benchmark values TBM and EX2 of the oscillation parameters assumed in the data. Scenarios EX1 and SPL have no sensitivity at all.