We discuss the limits on the neutrino magnetic moment and hypothetical interactions with a hidden unparticle sector, coming from the first neutrino data release of the Borexino experiment. The observed spectrum in Borexino depends weakly on the solar model used in the analysis, since most of the signal comes from the monoenergetic ${}^7\mathrm{Be}$ neutrinos. This fact allows us to calibrate the $\nu -e$ scattering cross section through the spectral shape. In this way, we have derived a limit on the magnetic moment for the neutrinos coming from the Sun (in which a ${\nu }_{\mu }$ and ${\nu }_{\tau }$ component is present): ${\mu }_{\nu }\le 8.4\times {10}^{-11}{\mu }_B$ (90% CL) which is comparable with those obtained from low-energy reactor experiments. Moreover, we improve the previous upper limit on magnetic moment of the ${\nu }_{\tau }$ by 3 orders of magnitude and the limit on the coupling constant of the neutrino with a hidden unparticle sector.

The complementarity between the quark and lepton mixing matrices is shown to provide a robust prediction for the neutrino mixing angle θ₁₃ ^PMNS. 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 the 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, which is in agreement with the quark data, and the solar and the atmospheric mixing angle leads to θ₁₃ ^PMNS=(9⁺¹ _-2)^°. This value is consistent with the present 90% CL experimental upper limit.

Assuming that the observed deficit of solar neutrinos is due to the interaction of their transition magnetic moment with the solar magnetic field we derive the predictions for the forthcoming Borexino experiment. Three different model magnetic field profiles which give very good global fits of the currently available solar neutrino data are used. The expected signal at Borexino is significantly lower than those predicted by the LMA, LOW and VO neutrino oscillation solutions of the solar neutrino problem. It is similar to that of the SMA oscillation solution which, however, is strongly disfavoured by the Super-Kamiokande data on day and night spectra and zenith angle distribution of the events. Thus, the neutrino magnetic moment solution of the solar neutrino problem can be unambiguously distinguished from the currently favoured oscillation solutions at Borexino.