On Reconciling Atmospheric, LSND, and Solar Neutrino-Oscillation Data

The L/E-flatness of the e-like events observed in the recent atmospheric-neutrino data from super-Kamiokande (SuperK) is interpreted to reflect a new symmetry of the neutrino-oscillation mixing matrix. From that we obtain an analytical set of constraints yielding a class of mixing matrices of the property to simultaneously fit both the SuperK and the LSND data. The resulting mass squared difference relevant for the LSND experiment is found as 0.3 eV2. The discussed symmetry, e.g., carries the nature that expectation values of masses for numu and nutau are identical. These considerations are purely data dictated. A different framework is then applied to the solar neutrino problem. It is argued that a single sterile neutrino is an unlikely candidate to accommodate the data from the four solar neutrino experiments. A scenario is discussed which violates CPT symmetry, and favors the nu e - {bar nu }e system to belong to the "self"-"anti-self" charge conjugate construct in the (1/2, 0)⊕(0,1/2) representation space, where the needed helicity flipping amplitudes are preferred, rather than the usual Dirac, or Majorana, constructs. In the presented framework the emerging SuperK data on solar neutrino flux is reconciled with the Homestake, GALLEX, and SAGE experiments. This happens because the former detects not only the solar nue but also, at a lower cross-section, the oscillated solar {bar nu }e; while the latter are sensitive only to the oscillation-diminished solar nue flux. A direct observation of solar {bar nu }e by SNO will confirm our scenario. Finally, we consider the possibility for flavor-dependent gravitational couplings of neutrinos as emerging out of the noncommutativity of the quantum operators associated with the measurements of energy and flavor.