Mossbauer neutrinos in quantum mechanics and quantum field theory

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.

LaTeX, 16 pages, 1 figure; v2: typos corrected; matches published version

References in corpus (7)

• Oscillations of Mossbauer neutrinos
• Time-Energy Uncertainty Relations for Neutrino Oscillation and MÖssbauer Neutrino Experiment
• Recoilless Resonant Absorption of Monochromatic Neutrino Beam for Measuring Delta m^2_{31} and theta_{13}
• Recoilless resonant neutrino capture and basics of neutrino oscillations
• Mass Hierarchy via Mossbauer and Reactor Neutrinos
• Hypersharp Resonant Capture of Neutrinos as a Laboratory Probe of the Planck Length
• Recoilless Resonant Emission and Detection of Electron Antineutrinos

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• Towards a Localised S-Matrix Theory
• Testing Nonstandard Neutrino Properties with a Mössbauer Oscillation Experiment
• Inference solves a boundary-value collision problem, with relevance to neutrino flavor transformation
• Mössbauer Antineutrinos: Recoilless Resonant Emission and Absorption of Electron Antineutrinos
• Virtual neutrino propagation at short baselines