Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2012-02-05
Physics
High Energy Physics
High Energy Physics - Phenomenology
LaTeX, 23 pages, 1 eps figure, typos corrected, discussion at the end of sect. VA modified
Scientific paper
We study distances of propagation and the group velocities of the muon neutrinos in the presence of mixing and oscillations assuming that Lorentz invariance holds. Oscillations lead to distortion of the $\nu_\mu-$ wave packet which, in turn, changes the group velocity and the distance $\nu_\mu$ travels. We find that the change of the distance, $d_{osc}$, is proportional to the length of the wave packet, $\sigma_x$, and the oscillation phase, $\phi_p$, acquired by neutrinos in the $\pi-$ and $K-$ meson decay tunnel where neutrino wave packet is formed: $d_{osc} \propto \sigma \phi_p$. Although the distance $d_{osc}$ may effectively correspond to the superluminal motion, the OPERA result can not be explained. For OPERA we obtain $d_{osc} \sim - 10^{-5}$ cm using $\Delta m^2 = 2.5 \times 10^{-3}$ eV$^2$. We analyze various possibilities to increase $d_{osc}$ and discuss experimental setups in which $d_{osc}$ (corresponding to the superluminal motion) can reach an observable value $\sim 1$ m.
Minakata Hisakazu
Smirnov Alexei Yu.
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