Short baseline neutrino oscillations: When entanglement suppresses coherence

Abstract

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 nonperturbative Wigner-Weisskopf method we obtain the correct 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 $\ensuremath{\pi}{L}_{s}/{L}_{\mathrm{osc}}$ where ${L}_{s}$ is the smallest of the decay length of the parent particle or the disentanglement length scale. For ${L}_{s}\ensuremath{\ge}{L}_{\mathrm{osc}}$ coherence and oscillations are suppressed. These effects are more prominent in 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 underestimate ${sin}^{2}(2\ensuremath{\theta})$ and $\ensuremath{\delta}{m}^{2}$, and are more dramatic for $\ensuremath{\delta}{m}^{2}\ensuremath{\simeq}{\mathrm{eV}}^{2}$, the mass range for new generations of sterile neutrinos that could explain the short-baseline anomalies and long disentanglement length scales.