From the standard seesaw mechanism of neutrino mass generation, which is based on the assumption that the lepton number is violated at a large (~10exp(+15) GeV) scale, follows that the neutrinoless double-beta decay is ruled by the Majorana neutrino
mass mechanism. Within this notion, for the inverted neutrino-mass hierarchy we derive allowed ranges of half-lives of the neutrinoless double-beta decay for nuclei of experimental interest with different sets of nuclear matrix elements. The present-day results of the calculation of the neutrinoless double-beta decay nuclear matrix elements are briefly discussed. We argue that if neutrinoless double-beta decay will be observed in future experiments sensitive to the effective Majorana mass in the inverted mass hierarchy region, a comparison of the derived ranges with measured half-lives will allow us to probe the standard seesaw mechanism assuming that future cosmological data will establish the sum of neutrino masses to be about 0.2 eV.
Electromagnetic form factors of proton and neutron, obtained from a new fit of data, are presented. The proton form factors are obtained from a simultaneous fit to the ratio $mu_p G_{Ep}/G_{Mp}$ determined from polarization transfer measurements and
to $ep$ elastic cross section data. Phenomenological two-photon exchange corrections are taken into account. The present fit for proton was performed in the kinematical region $Q^2in (0,6)$ GeV$^2$. Both for protons and neutrons we use the latest available data. For all form factors the uncertainties and correlations of form factor parameters are investigated with the $chi^2$ method.
We present predictions for the value of the cross section ratio $sigma(e^+p to e^+p)/sigma(e^-p to e^-p)$, determined from our fit of the elastic $ep$ cross section and polarization data. In this fit we took into account the phenomenological two-phot
on exchange dispersive correction. The cross section ratios which are expected to be measured by the VEPP-3 experiment are computed. The kinematical region which will be covered by the E04-116 JLab experiment is also considered. It is shown that for both experiments the predicted cross section ratios deviate from unity within more than $3sigma$.
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) product
ion 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 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 (s
ee 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.
We discuss neutrino oscillations in an experiment with Mossbauer recoilless resonance absorbtion of tritium antineutrinos, proposed recently by Raghavan. We demonstrate that small energy uncertainty of antineutrinos which ensures a large resonance ab
sorption cross section is in a conflict with the energy uncertainty which, according to the time-energy uncertainty relation, is necessary for neutrino oscillations to happen. The search for neutrino oscillations in the Mossbauer neutrino experiment would be an important test of the applicability of the time-energy uncertainty relation to a newly discovered interference phenomenon.
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.
