Mossbauer neutrinos in quantum mechanics and quantum field theory

TL;DR

This paper compares quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations, demonstrating their correspondence and highlighting the limitations of quantum mechanics in predicting certain emission and detection parameters.

Contribution

It establishes a detailed connection between quantum field theory and quantum mechanics for Mossbauer neutrinos, including effects of line broadening and resonance.

Findings

Quantum field theory yields an emission rate identical to previous results.

Quantum mechanics can reproduce oscillation and coherence terms with Lorentzian wave packets.

Emission rate and detection cross section require external input in quantum mechanics.

Abstract

We demonstrate the correspondence between quantum mechanical and quantum field theoretical descriptions of Mossbauer neutrino oscillations. First, we compute the combined rate $\Gamma$ of Mossbauer neutrino emission, propagation, and detection in quantum field theory, treating the neutrino as an internal line of a tree level Feynman diagram. We include explicitly the effect of homogeneous line broadening due to fluctuating electromagnetic fields in the source and detector crystals and show that the resulting formula for $\Gamma$ is identical to the one obtained previously (Akhmedov et al., arXiv:0802.2513) for the case of inhomogeneous line broadening. We then proceed to a quantum mechanical treatment of Mossbauer neutrinos and show that the oscillation, coherence, and resonance terms from the field theoretical result can be reproduced if the neutrino is described as a superposition of Lorentz-shaped wave packet with appropriately chosen energies and widths. On the other hand, the emission rate and the detection cross section, including localization and Lamb-Mossbauer terms, cannot be predicted in quantum mechanics and have to be put in by hand.