50 Years of neutrino physics

Some important topics from history of neutrino physics over the last fifty years are discussed. History of neutrinos is older, at 4th December 2010 it will be eightieth anniversary of the neutrino birth. In that day W. Pauli wrote the famous letter to participants of the physics conference at Tubingen with the suggestion that “there could exist in the nuclei electrically neutral particle”. We will concentrate mostly on the 50 years of neutrino history just to show the long tradition of the Zakopane Theoretical School

Some aspects of the neutrino theory

Selected topics in the theory of neutrinos, discussed in last years, are presented. We shortly summarize properties of neutrinos in frame of the original Standard Model (SM) and give the experimental information about their masses and mixing. In the frame of the model with massive neutrinos, the so-called New SM ( SM), two controversial phenomena, the Mössbauer neutrinos problem and the GSI anomaly are explained. Beyond the SM (BSM) we focus on two issues, on the problem of small neutrino masses and large mixing in comparison to the quark sector and on how neutrino oscillation phenomena should be correctly described in the BSM

Absolute neutrino masses

Since the recent convincing evidence for massive neutrinos in oscillation experiments, the next task is to determine the absolute masses of neutrinos. A unique pattern of neutrino masses will be hopefully fixed in the future superbeam experiments and neutrino factories. However, the determination of the exact scale is more complicated and depends on the mass of the lightest neutrino (m„)min. If (rnv)min > 0.35 eV, the future tritium /3 decay experiments (e.g. KATRIN) will have a chance to establish absolute neutrino masses. For smaller masses, 0.004 eV< (m„)min < 0.35 eV, if neutrinos are Majorana particles, an additional information can be derived from the neutrinoless double /3 decay (/3/3)0i/ of nuclei and again the absolute neutrino masses can be fixed. If, however, (m„)min < 0.004 eV, none of the present and foreseeable future experiments is known to be able to fix the mass scale

Quark model predictions for the decay distributions of strange baryons produced in the reactions 1/2+1/2+to1/x+3/2+

The quark model is used to predict the joint decay distributions of pairs of strange baryons produced in the reactions -j+J + —► i +§+ with polarized target. For reactions with particles polarizedperpendicularly to the reaction plane it is possible to make absolute predictions using data obtained from reactions with unpolarized particles. Relations between the statistical tensors provide a method of evaluating the additivity angle for the 3/2+ isobar, if the polarization of the target in the reaction plane is not zero

Bound on the mass of Majorana neutrinos after SNO and KamLAND

Presently the best terrestrial limit on light neutrino masses (m<2.2 eV) are given by the tritium beta decay experiments. Not maximal mixing of solar neutrinos following from the SNO and KamLAND together with neutrinoless double beta decay (( )0 ) data open the chance for better determination of the lightest of Majorana neutrino mass. We combine all available fits for the solar neutrino parameters and collect all Nuclear Matrix Elements (NME) calculations for the 76Ge, nucleus for which presently the most stringent limit on the ( )0 decay half-life time exist. We have shown that for some NME smaller bound on (m )min can be found. Unfortunately one order of magnitude discrepancies in NME calculations do not allow to give the final answer

The gamma 5 and Dimensional Regularization

The properties c f the axial-vector current are investigated using dimensional regularization. The modified version o f anti-commuting y s in n dimensions is proposed. The VVA and AAA triangle diagrams are precisely calculated. The resulting amplitudes obey the naive vector Ward identities. In the axial vector Ward identities the Adler-Bell-Jackiw anomalies appear

Non-standard Interactions, Density Matrix and Neutrino Oscillations

We present an analysis of a neutrino production and detection processes, necessary in order to describe the oscillation phenomena in any model of neutrino interaction. We derive an oscillation probability in the presence of neutrino non-standard interactions and compare the result with the standard approach. Our results are applicable in a very wide class of New Physics models

Neutrino masses measurement in future tritium beta decay experiment

The end of the electron energy distribution in /3 decays of nuclei depends on neutrino masses and mixing angles. Various approximate parametrization of the proposed in literature, and the definition of effective neutrino masses nip are investigated. Bounds or future measured values of nip together with the oscillation parameters are a source of information about the mass of the lightest neutrino

Can we distinguish Dirac and Majorana neutrinos produced in muon decay?

Neutrinos produced in the muon decay scatter on electrons in the near (without oscillation) and in the far detector (after oscillation) and the numer of produced muons is observed. In the frame of the Standard Model the cross-section for muon production does not depend on the neutrino nature. The situation is different, if beyond the SM neutrino interactions are present. We use the Fermi contact model, where we allow only one additional coupling, the charged scalar right-handed coupling which appear in variety of models. No bounds on the new scalar coupling for Majorana neutrino are found. The cross-sections for muon production is different for Dirac and Majorana neutrinos giving in principle possibility to distinguish their nature. The differences between the Dirac and Majorana cross-sections appear in the near and in the far detector. The cross-section for both types of neutrinos is different even if neutrinos do not oscillate, but the difference is larger after oscillation, even in the vacuum

Light neutrino propagation in matter without heavy neutrino decoupling

We review the propagation of light neutrinos in matter assuming that their mixing with heavy neutrinos is close to present experimental limits. The phenomenological implications of the non-unitarity of the light neutrino mixing matrix for neutrino oscillations are discussed. In particular we show that the resonance effect in neutrino propagation in matter persists, but for slightly modified values of the parameters and with the maximum reduced by a small amount proportional to the mixing between light and heavy neutrinos squared