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 multiparticle 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 nonstandard 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.

Figure 1

Predictions of the photoabsorpative ionization (PAI) model. Top: the decoherence function for the pion in interaction with decay-pipe gas for $\beta \gamma =10$. Bottom: pion scattering rate and other related quantities for pions of different momenta.

Figure 2

The time-dependent coherent position-space width of pions with $\beta \gamma =100$. Gaussian pure states of various widths are used as initial states in a quantum Monte Carlo. Each simulation is stopped when the wave packet no longer fits on the simulation grid in the position or momentum basis. Evolution towards a stable equilibrium width is observed.

Figure 3

Convergent widths for pions and kaons of different initial energies.

Figure 4

Coherence distance for neutrinos of different energies produced in conventional neutrino beams. Solid: Two-body ${\pi }^{\pm }$ decay. Dotted: Two-body $K^{\pm }$ decay. Larger neutrino energies correspond to longer distances.

Figure 5

The coherence distances for pion-induced neutrinos at several values of $\mathrm{\Delta }{m}^2$ compared with the configurations of existing and proposed accelerator neutrino experiments. The lines use the relativistic expression (8a), whereas the diamonds show the prediction of the nonrelativistic expression (8b) at the lowest energies.

Figure 6

The energy resolution required to observe coherence loss without fast oscillation in some part of the $\mathrm{\Delta }{m}^{2}L$ parameter space as a function of neutrino energy.

Figure 7

Elements of the PAI model. The two panels of interest to us are the top panel, showing the photoabsorption cross section of argon gas, and the second panel, showing the calculated $dE/dx$ from this model for $\beta =1$. This figure is reproduced from [22].

Figure 8

dEdx calculated using PAI model (diamonds) overlaid on the prediction from [2].

Figure 9

Top: The momentum transfer distribution predicted by the PAI model for various values of $\beta \gamma$. Above $\beta \gamma =1$ the distributions are very similar. Bottom: The energy transfer distribution calculated in our PAI model implementation, compared with that given in [22].

Figure 10

Cross-checks of the model. Top left: baseline. Top right: measure width after unitary evolution, rather than after scatter. Bottom left: adjusted grid size 1024. Bottom right: $n_{\text{scat}}=0.1$ approximation. The red line represents an identical width in each plot.