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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.
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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.
The solar neutrino spectrum measured by the Super-Kamiokande shows an excess in high energy bins, which may be explained by vacuum oscillation solution or $hep$ neutrino effect. Here we reconsider an uncertainty of the data caused by the tail of the energy resolution function. Events observed at energy higher than 13.5 MeV are induced by the tail of the resolution. At Super-Kamiokande precision level this uncertainty is no more than few percent within a Gaussian tail. But a power-law decay tail at 3 $sigma$ results considerable excesses in these bins, which may be another possible explanation of the anomaly in 708d(825d) data.
Neutrino mixing parameters are subject to quantum corrections and hence are scale dependent. This means that the mixing parameters associated to the production and detection of neutrinos need not coincide since these processes are characterized by different energy scales. We show that, in the presence of relatively light new physics, the scale dependence of the mixing parameters can lead to observable consequences in long-baseline neutrino oscillation experiments, such as T2K and NOvA, and in neutrino telescopes like IceCube. We discuss some of the experimental signatures of this scenario, including zero-baseline flavor transitions, new sources of CP-invariance violation, and apparent inconsistencies among measurements of mixing angles at different experiments or oscillation channels. Finally, we present simple, ultraviolet-complete models of neutrino masses which lead to observable running of the neutrino mixing matrix below the weak scale.
Recent Super-Kamiokande data on the atmospheric neutrino anomaly are used to test various mechanisms for neutrino oscillations. It is found that the current atmospheric neutrino data alone cannot rule out any particular mechanism. Future long-baseline experiments should play an important role in identifying the underlying neutrino oscillation mechanism.
The observation of the recent electron neutrino appearance in a muon neutrino beam and the high-precision measurement of the mixing angle $theta_{13}$ have led to a re-evaluation of the physics potential of the T2K long-baseline neutrino oscillation experiment. Sensitivities are explored for CP violation in neutrinos, non-maximal $sin^22theta_{23}$, the octant of $theta_{23}$, and the mass hierarchy, in addition to the measurements of $delta_{CP}$, $sin^2theta_{23}$, and $Delta m^2_{32}$, for various combinations of $ u$-mode and (bar{ u})-mode data-taking. With an exposure of $7.8times10^{21}$~protons-on-target, T2K can achieve 1-$sigma$ resolution of 0.050(0.054) on $sin^2theta_{23}$ and $0.040(0.045)times10^{-3}~rm{eV}^2$ on $Delta m^2_{32}$ for 100%(50%) neutrino beam mode running assuming $sin^2theta_{23}=0.5$ and $Delta m^2_{32} = 2.4times10^{-3}$ eV$^2$. T2K will have sensitivity to the CP-violating phase $delta_{rm{CP}}$ at 90% C.L. or better over a significant range. For example, if $sin^22theta_{23}$ is maximal (i.e $theta_{23}$=$45^circ$) the range is $-115^circ<delta_{rm{CP}}<-60^circ$ for normal hierarchy and $+50^circ<delta_{rm{CP}}<+130^circ$ for inverted hierarchy. When T2K data is combined with data from the NO$ u$A experiment, the region of oscillation parameter space where there is sensitivity to observe a non-zero $delta_{CP}$ is substantially increased compared to if each experiment is analyzed alone.
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