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Register a new userDifferent Schemes of Neutrino Oscillations in MOssbauer Neutrino Experiment
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We comment on the paper On application of the time-energy uncertainty relation to Mossbauer neutrino experiments (see arXiv: 0803.1424) in which our paper Time-energy uncertainty relations for neutrino oscillation and Mossbauer neutrino experiment (see arXiv: 0803.0527) has been criticized. We argue that this critique is a result of misinterpretation: The authors of (arXiv: 0803.1424) do not take into account (or do not accept) the fact that at present there exist different schemes of neutrino oscillations which can not be distinguished in usual neutrino oscillation experiments. We stress that a recently proposed Mossbauer neutrino experiment provides the unique possibility to discriminate basically different approaches to oscillations of flavor neutrinos.
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Using the Mandelstam-Tamm method we derive time-energy uncertainty relations for neutrino oscillations. We demonstrate that the small energy uncertainty of antineutrinos in a recently considered experiment with recoilless resonant (Mossbauer) production and absorption of tritium antineutrinos is in conflict with the energy uncertainty which, according to the time-energy uncertainty relation, is necessary for neutrino oscillations to happen. A Mossbauer neutrino experiment could provide a unique possibility to test the applicability of the time-energy uncertainty relation to neutrino oscillations and to reveal the true nature of neutrino oscillations.
We demonstrate that an experiment with recoilless resonant emission and absorption of tritium antineutrinos could have an important impact on our understanding of the origin of neutrino oscillations.
Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries. We elucidate the $2^7=128$ symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an additional set of $2^7=128$ symmetries exist of the matter parameters for a total of $2^{14}=16,384$ symmetries of the vacuum and/or matter parameters in the oscillation probabilities in matter. Due to the complexity of the exact expressions for neutrino oscillations in matter, we show that under certain assumptions, approximate expressions have at most $2^6=64$ additional symmetries of the matter parameters for a total of $2^{13}=8,192$ symmetries. We investigate which of these symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.
We study distances of propagation and the group velocities of the muon neutrinos in the presence of mixing and oscillations assuming that Lorentz invariance holds. Oscillations lead to distortion of the $ u_mu$ wave packet which, in turn, changes the group velocity and the distance $ u_mu$ travels. We find that the change of the distance, $d_{osc}$, is proportional to the length of the wave packet, $sigma_x$, and the oscillation phase, $phi_p$, acquired by neutrinos in the $pi-$ and $K-$ meson decay tunnel where neutrino wave packet is formed: $d_{osc} propto sigma phi_p$. Although the distance $d_{osc}$ may effectively correspond to the superluminal motion, the effect is too tiny ($sim 10^{- 5}$ cm) to be reconciled with the OPERA result. We analyze various possibilities to increase $d_{osc}$ and discuss experimental setups in which $d_{osc}$ (corresponding to the superluminal motion) can reach an observable value $sim 1$ m.
In the last decades, a very important breakthrough has been brought in the elementary particle physics by the discovery of the phenomenon of the neutrino oscillations, which has shown neutrino properties beyond the Standard Model. But a full understanding of the various aspects of the neutrino oscillations is far to be achieved. In this paper the theoretical background of the neutrino oscillation phenomenon is described, referring in particular to the paradigmatic models. Then the various techniques and detectors which studied neutrinos from different sources are discussed, starting from the pioneering ones up to the detectors still in operation and to those in preparation. The physics results are finally presented adopting the same research path which has crossed this long saga. The problems not yet fixed in this field are discussed, together with the perspectives of their solutions in the near future.
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