Dynamical Pion Collapse and the Coherence of Conventional Neutrino Beams

In this paper we consider the coherence properties of neutrinos produced by the decays of pions in conventional neutrino beams. Using a multi-particle density matrix formalism we derive the oscillation probability for neutrinos emitted by a decaying pion in an arbitrary quantum state. Then, using methods from decoherence theory we calculate the pion state which evolves through interaction with decay-pipe gases in a typical accelerator neutrino experiment. These two ingredients are used to obtain the distance scales for neutrino beam coherence loss. We find that for the known neutrino mass splittings, no non-standard oscillation effects are expected on terrestrial baselines. Heavy sterile neutrinos may experience terrestrial loss of coherence, and we calculate both the distance over which this occurs and the energy resolution required to observe the effect. By treating the pion-muon-neutrino-environment system quantum mechanically, neutrino beam coherence properties are obtained without assuming arbitrary spatial or temporal scales at the neutrino production vertex.