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Register a new userUncertainty of the Solar Neutrino Energy Spectrum
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Q.Y. Liu
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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.
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There may be a high-energy cutoff of neutrino events in IceCube data. In particular, IceCube does not observe either continuum events above 2 PeV, or the Standard Model Glashow-resonance events expected at 6.3 PeV. There are also no higher energy neutrino signatures in the ANITA and Auger experiments. This absence of high-energy neutrino events motivates a fundamental restriction on neutrino energies above a few PeV. We postulate a simple scenario to terminate the neutrino spectrum that is Lorentz-invariance violating, but with a limiting neutrino velocity that is always smaller than the speed of light. If the limiting velocity of the neutrino applies also to its associated charged lepton, then a significant consequence is that the two-body decay modes of the charged pion are forbidden above two times the maximum neutrino energy, while the radiative decay modes are suppressed at higher energies. Such stabilized pions may serve as cosmic ray primaries.
The first results from the KamLAND experiment have provided confirmational evidence for the Large Mixing Angle (LMA) MSW solution to the solar neutrino problem. We do a global analysis of solar and the recently announced KamLAND data (both rate and spectrum) and investigate its effect on the allowed region in the $Delta m^2-tan^2theta$ plane. The best-fit from a combined analysis which uses the KamLAND rate plus global solar data comes at $Delta m^2 = 6.06 times 10^{-5}$ eV $^2$ and $tan^2theta=0.42$, very close to the global solar best-fit, leaving a large allowed region within the global solar LMA contour. The inclusion of the KamLAND spectral data in the global fit gives a best-fit $Delta m^2 = 7.15 times 10^{-5}$ eV $^2$ and $tan^2theta=0.42$ and constrains the allowed areas within LMA, leaving essentially two allowed zones. Maximal mixing though allowed by the KamLAND data alone is disfavored by the global solar data and remains disallowed at about $3sigma$. The LOW solution is now ruled out at about 5$sigma$ w.r.t. the LMA solution.
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.
Assuming 3 neutrino mixing and massive Majorana neutrinos, we analyze the implications of the results of the solar neutrino experiments, including the latest SNO data, which favor the LMA MSW solution of the solar neutrino problem with tan^2 theta_sol < 1, for the predictions of the effective Majorana mass |<m>| in neutrinoless double beta decay. For cos (2 theta_sol) geq 0.26, which follows from the analysis of the new solar neutrino data, we find significant lower limits on |<m>| in the cases of quasi-degenerate and inverted hierarchy neutrino mass spectrum, |<m>| geq 0.035 eV and |<m>| geq 8.5 10^-3 eV, respectively. If the spectrum is hierarchical the upper limit holds |<m>| leq 8.2 10^-3 eV. Correspondingly, not only a measured value of |<m>| eq 0, but even an experimental upper limit on |<m>| of the order of few 10^-2 eV can provide information on the type of the neutrino mass spectrum; it can provide also a significant upper limit on the mass of the lightest neutrino m1. A measured value of |<m>| geq 0.2 eV, combined with data on neutrino masses from the tritium beta-decay experiment KATRIN might allow to establish whether the CP-symmetry is violated in the lepton sector.
We find that magnetic neutrino-electron scattering is unaffected by oscillations for vacuum mixing of Dirac neutrinos with only diagonal moments and for Majorana neutrinos with two flavors. For MSW mixing, these cases again obtain, though the effective moments can depend on the neutrino energy. Thus, e.g., the magnetic moments measured with $bar{ u}_e$ from a reactor and $ u_e$ from the Sun could be different. With minimal assumptions, we find a new limit on $mu_{ u}$ using the 825-days SuperKamiokande solar neutrino data: $|mu_{ u}| le 1.5times 10^{-10} mu_B$ at 90% CL, comparable to the existing reactor limit.
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