Robust flavor equalization of cosmic neutrino flux by quasi bi - maximal mixing ⋆

The observed L/E flatness of the electron-like event ratio in the Super-Kamiokande atmospheric neutrino data strongly favors a quasi bi-maximal mixing matrix. This situation is here exploited to understand the numerical results of Yasuda on the high energy cosmic neutrino flux. In agreement with the Yasuda result, we analytically show how the quasi bi-maximal neutrino mixing makes the high energy cosmic neutrino flux at the AGN/GRB source, F (νe) : F (νμ) : F (ντ ) ≈ 1 : 2 : 0, oscillates to, F (νe) : F (νμ) : F (ντ ) ≈ 1 : 1 : 1. Apart from its independence from the underlying mass-squared differences, we find that this prediction is quite robust in that it is independent of the mixing angle responsible for the resolution of the solar/LSND neutrino anomaly. The solar neutrino anomaly, the LSND excess events, and the Super-Kamiokande data on atmospheric neutrinos, find their natural explanation in terms of oscillations of neutrinos from one flavor to another [1–3]. The only experiment so far that provides a direct evidence of oscillation from one flavor to another is the LSND experiment. However, the LSND result is still debated by the KARMEN collaboration [4]. It is expected to be settled by the dedicated Fermi Lab. experiments. Nevertheless, a strong tentative evidence for neutrino oscillations seems established. In the context of this experimental setting, this Letter establishes the abstracted result. It turns out that the detailed numerical analysis of Ref. [5] is in fact a direct consequence of the quasi bi-maximal mixing [6,7] implied by the indicated aspect of the Super-Kamiokande data[3]. In will also become transparent that Yasuda’s result on the high energy cosmic neutrinos is independent of the mixing angle that defines the quasi bi-maximal mixing. This ⋆ Work supported by Consejo Nacional de Ciencia y Tecnoloǵia (CONACyT) under grant number 32067-E. robustness has the consequence that by studying the departures from the Yasuda’s predictions on the cosmic high energy flux one may be able to explore other interesting sources/physics of high energy cosmic neutrinos. Without CP violation, the three-flavor neutrino oscillation framework carries five phenomenological parameters. These are the two mass-squared differences, ∆m 32 and ∆m 21 , and the three mixing angles: