KamLAND, solar antineutrinos, and the solar magnetic field

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 ${\ensuremath{\varphi}}_{\overline{\ensuremath{\nu}}}l3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\ensuremath{\varphi}{(}^{8}\mathrm{B})$ at 95% C.L. For 90% C.L. this becomes ${\ensuremath{\varphi}}_{\overline{\ensuremath{\nu}}}l3.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}\ensuremath{\varphi}{(}^{8}\mathrm{B}),$ an improvement by a factor of 3\char21{}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 $\ensuremath{\mu}Bl2.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\mathrm{MeV}$ or ${B}_{0}l~4.9\ifmmode\times\else\texttimes\fi{}{10}^{7}\mathrm{G}$ for ${\ensuremath{\mu}}_{\ensuremath{\nu}}{=10}^{\ensuremath{-}12}{\ensuremath{\mu}}_{B}.$