Short baseline neutrino oscillations: when entanglement suppresses coherence

For neutrino oscillations to take place the entangled quantum state of a neutrino and a charged lepton produced via charged current interactions must be disentangled. Implementing a non-perturbative Wigner-Weisskopf method we obtain the correct \emph{entangled} quantum state of neutrinos and charged leptons from the (two-body) decay of a parent particle. The source lifetime and disentanglement length scale lead to a suppression of the oscillation probabilities in short-baseline experiments. The suppression is determined by $\pi\, L_s/L_{osc}$ where $L_s$ is the \emph{smallest} of the decay length of the parent particle or the disentanglement length scale. For $L_s \geq L_{osc}$ coherence and oscillations are suppressed. These effects are more prominent in \emph{short base line experiments} and at low neutrino energy. We obtain the corrections to the appearance and disappearance probabilities modified by both the lifetime of the source and the disentanglement scale and discuss their implications for accelerator and reactor experiments. These effects imply that fits to the experimental data based on the usual quantum mechanical formulation \emph{underestimate} $\sin^2(2\theta)$ and $\delta m^2$, and are more dramatic for $\delta m^2\simeq \,\mathrm{eV}^2$, the mass range for new generations of sterile neutrinos that could explain the short-baseline anomalies.