Neutrino mass and lepton number violation are a key to understand the universe. At present there is no compelling reason for neutrinos to be massless.On the contrary, the See-Saw mechanism naturally explains the extremely small neutrino mass by introducing > GeV physics. Even further, in some of the GUTs models, finite Majorana neutrino mass is required for baryon genesis in the universe.

Once the existence of neutrino oscillation is established, this means that the neutrino mass is finite and lepton number is not conserved. There will be a rich field of physics in the lepton sector. Contrary to the case of muon or kaon rare decay experiments, where of neutrino mass to W mass, , neutrino oscillations do not suffer from this factor. This makes neutrino oscillations the only practical tool for studying mixing in the lepton sector, i.e. the leptonic Kobayashi-Maskawa angles.

Despite no definite theoretical or experimental evidence of the neutrino mass and mixing angle exists, there are a few indications from cosmology which imply finite neutrino mass and mixing. One is the existence of dark matter in the universe. If the dark matter is all due to massive neutrinos, the heaviest neutrino should have a mass greater than several eV. This is the main motivation of so called "short baseline" experiments, now being carried out by the CHORUS and NOMAD collaborations at CERN.

The other indication of the finite neutrino mass and mixing is, on the other hand, experimental. The results from Kamiokande on neutrinos produced in the atmosphere, which have been confirmed by the IMB and the Soudan II groups, provide a strong hint that neutrinos do have mass and do mix each other. The results on solar neutrinos also suggest neutrino oscillation.

Table-1 summarizes the atmospheric-neutrino results. The quantity is the ratio of muons to electrons produced by atmospheric neutrinos with energies of the order of a GeV, thus measuring the flux ratio of muon-type neutrinos () to electron-type neutrinos (). This is compared with the Monte Carlo prediction, i.e. . The results clearly show that either the muon-neutrino flux is decreased and/or the electron-neutrino flux is increased. If the --> oscillation causes this discrepancy,the flux will be decreased and the e-neu flux will be increased. On the other hand, the --> oscillation will reduce the flux while keeping the flux constant. In order to discriminate those alternatives, one needs knowledge of the absolute neutrino flux of each type of neutrinos.

Table-1 Atmospheric Neutrino Results
Experiment / Exposure (kton*year)
Super Kamiokande (Sub-GeV)0.61+_0.03+_0.0525.5
Super Kamiokande (Multi-GeV)0.66+_0.06+_0.0825.5
Kamiokande (Sub-GeV) 0.60+_0.06+_0.057.5
Kamiokande (Multi-GeV) 0.57+_0.08+_0.078.2(FC) 6.0(PC)
IMB 3 0.54+_0.05+_0.07 7.7
Frejus 1.00+_0.15+_0.08 2.0
NUSEX 0.96+_0.32 0.74
Soudan 2 0.580+_0.108+_0.050 3.5?

Kamiokande data also indicates the zenith angle dependence of the ratio / for the higher energy neutrinos. This is consistent with the picture where the different path length of the upward- and downward-going neutrinos produce different oscillation effects. The neutrino oscillation interpretations of the Kamiokande atmospheric neutrino data restrict the -neutrino mixing () regions as shown in Fig1.

Fig.1 The 90%CL allowed neutrino oscillation parameters - region from the Kamiokande atmospheric neutrino data.

The relevant oscillation length in the atmosphere is from 10km to 10000km with the neutrino energy of the order of a GeV. These parameter regions can be explored with a high intensity neutrino beam from a proton accelerator and with massive detectors.

The other possible neutrino oscillation phenomenon is the solar neutrino deficit.

Table-2 summerize the results if the solar neutrino experiments.

Table-2 Solar Neutrino Results
Experiment Data/Expected Neutrino Energy Threshold
Homestake 0.285+-0.029 814keV
Kamiokande 0.47+-0.05+-0.06 7.5MeV
SAGE 0.44+0.13-0.18+-0.10 233.2keV
GALLEX 0.66+-0.11+-0.05 233.2keV

The "Data/Expected" is the ratio of the observed flux to the expected one from the Standard Solar model. The results indicates that a significant fraction of the 's is lost or transformed into other type of neutrinos, which interact with less cross section or do not interact at all in the detector. Combining the four experimental results, gives the allowed - regions shown in Fig.2.

Fig.2 The 90%CL allowed - regions by GALLEX and SAGE (solid line), Kamiokande (dashed line) and Cl37 (dotted line) for solar neutrinos () to oscillate into other types of neutrinos. The hatched area is the region allowed simultaneously by the three results.

If the Standard Solar model and the atmospheric and solar experiments are all correct, two distinct neutrino oscillations must be exist in nature, i.e. --> and -->, where and are or . We believe that it is now of utmost importance to confirm the Kamiokande atmospheric neutrino results and to further study the neutrino oscillation phenomena with well defined accelerator neutrino beams.


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