Probing $CP$ violation with the first three years of ultrahigh energy neutrinos from IceCube

The IceCube Collaboration has recently announced the discovery of ultrahigh energy neutrino events. These neutrinos can be used to probe their production source, as well as leptonic mixing parameters. In this work, we have used the first IceCube data to constrain the leptonic $CP$ violating phase ${\delta }_{CP}$. For this, we have analyzed the data in the form of flux ratios. We find that the fit to ${\delta }_{CP}$ depends on the assumptions made on the production mechanism of these astrophyscial neutrinos. Consequently, we also use this data to impose constraints on the sources of the neutrinos.

Figure 1

Fit to ${\delta }_{CP}$ considering a single source, i.e., $\pi \mathrm{S}$ ($k_1=1$, $k_2=0$, $k_3=0$, solid red), $\mu \mathrm{DS}$ ($k_1=0$, $k_2=1$, $k_3=0$, dashed blue), $n\mathrm{S}$ ($k_1=0$, $k_2=0$, $k_3=1$, dotted magenta), considering all the events being from astrophysical environment. Panel [A]: Three-year data, without background. Panel [B]: Three-year data, with background. Panel [C]: Two-year data, without background. Panel [D]: Two-year data, with background.

Figure 2

Analysis for neutrinos within energy 60 TeV to 3 PeV.

Figure 3

Fit to ${\delta }_{CP}$ considering contribution from two sources at a time, in equal proportion, i.e., $k_1=k_2=0.5$, $k_3=0$ (solid, red), $k_1=0$, $k_2=k_3=0.5$ (dashed, blue), $k_1=k_3=0.5$, $k_2=0$ (dotted, magenta) for both old $\mathbf{a}$ and new $\mathbf{B}$.

Figure 4

Fit to ${\delta }_{CP}$ considering equal contribution from all the sources, i.e., $k_1=k_2=k_3=0.33$ for both old $\mathbf{a}$ and new $\mathbf{B}$.

Figure 5

Contour plots for allowed region in the $k_1-{\delta }_{CP}$ plane, for three representative values of $k_2$. The points marked in the respective colors indicate the best-fit point with new IceCube data.

Figure 6

Contour plots for allowed region in the $k_2-{\delta }_{CP}$ plane, for three representative values of $k_1$. The points marked in the respective colors indicate the best-fit point.

Figure 7

Contour plots for allowed region in the $k_3-{\delta }_{CP}$ plane, for three representative values of $k_1$. The points marked in the respective colors indicate the best-fit point.