Neutrino Velocity and Neutrino Oscillations

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 effect is too tiny ($\sim 10^{- 5}$ cm) to be reconciled with the OPERA result. 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.