Open questions remain after the confirmation of LMA as the dominant solution to the solar neutrino deficit. These are the apparent time modulation of the solar neutrino event rates in the Homestake, Gallium and SuperKamiokande experiments, possibly related to solar magnetic activity, the discrepancy between the event rate in the Homestake experiment and its theoretical prediction and the absence of the electron spectrum upturn in SuperKamiokande at energies below 6-8 MeV. We search for a possible understanding of these questions in the context of resonant spin flavour precession to sterile neutrinos, assuming a class of magnetic field profiles anchored in the upper radiation/lower convection zone. We consider the simplest such model beyond the standard 2ν flavour LMA one, with one single magnetic moment transition between active and sterile state and vanishing vacuum mixing. The preferred mass square difference is ∆m 2 10 = O(10 −8 eV 2 ). The Ga rate appears to be the most sensitive of all to solar activity. It is also found that a field profile extending within a longer region in the radial direction is favoured over another with a shorter span, and leads to a stronger suppression than in the LMA case of the intermediate energy neutrinos and some of the 8 B ones.

The possibility that the Gallium data effectively indicates a time modulation of the solar active neutrino flux in possible connection to solar activity is examined on the light of spin flavour precession to sterile neutrinos as a subdominant process in addition to oscillations. We distinguish two sets of Gallium data, relating them to high and low solar activity. Such modulation affects principally the low energy neutrinos (pp and 7 Be) so that the effect, if it exists, will become most clear in the forthcoming Borexino and LENS experiments and will provide evidence for a neutrino magnetic moment. Using a model previously developed, we perform two separate fits in relation to low and high activity periods to all solar neutrino data. These fits include the very recent charged current spectrum from the SNO experiment. We also derive the model predictions for Borexino and LENS experiments.

The complementarity between the quark and lepton mixing matrices is shown to provide a robust prediction for the neutrino mixing angle θ P M N S 13. We obtain this prediction by first showing that the matrix V M , product of the CKM and PMNS mixing matrices, may have a zero (1,3) entry which is favored by experimental data. Hence models with bimaximal or tribimaximal forms of the correlation matrix V M are quite possible. Any theoretical model with a vanishing (1,3) entry of V M that is in agreement with quark data, solar, and atmospheric mixing angle leads to θ P M N S 13 = (9 +1−2 ) • . This value is consistent with the present 90% CL experimental upper limit.

In this work the possibility of detecting solar electron antineutrinos produced by a solar core magnetic field from the KamLAND recent observations is investigated. We find a scaling of the antineutrino probability with respect to the magnetic field profile in the sense that the same probability function can be reproduced by any profile with a suitable peak field value. In this way the solar electron antineutrino spectrum can be unambiguously predicted. We use this scaling and the negative results indicated by the KamLAND experiment to obtain upper bounds on the solar electron antineutrino flux. We get Ͻ3.8ϫ10 Ϫ3 ( 8 B) at 95% C.L. For 90% C.L. this becomes Ͻ3.4ϫ10 Ϫ3 ( 8 B), an improvement by a factor of 3-5 with respect to existing bounds. These limits are independent of the detailed structure of the magnetic field in the solar interior. We also derive upper bounds on the peak field value which are uniquely determined for a fixed solar field profile. In the most efficient antineutrino producing case, we get ͑95% C.L.͒ an upper limit on the product of the neutrino magnetic moment by the solar field BϽ2.8ϫ10 Ϫ19 MeV or B 0 р4.9ϫ10 7 G for ϭ10 Ϫ12 B .

We reexamine the possibility of a time modulation of the low energy solar neutrino flux which is hinted by the average decrease of the Ga data in line with our previous arguments. We perform two separate fits to solar neutrino data, one corresponding to 'high' and the other to 'low' Ga data, associated with low and high solar activity respectively. We therefore consider an alternative to the conventional solar+KamLAND fitting, which allows one to explore the much wider range of the θ 12 angle permitted by the KamLAND fitting alone. We propose a solution with parameters ∆m 2 21 = 8.4 × 10 −5 eV 2 , tan 2 θ = 0.27 in which the 'high' and the 'low' Ga rates lie far apart and are close to their central values, in contrast to the global best fit solution where these rates lie close to each other. This is an indication that the best fit in which all solar and KamLAND data are used is not a good measure of the separation of the two Ga data, as the information from the low energy neutrino modulation is dissimulated in the wealth of data. Furthermore for the parameter set proposed one obtains an equally good fit to the KamLAND energy spectrum and an even better fit than the 'conventional' LMA one for the reactor antineutrino survival probability as measured by KamLAND.