Solar $\bar{\nu}_e$ flux: Revisiting bounds on neutrino magnetic moments and solar magnetic field

The interaction of neutrino transition magnetic dipole moments with magnetic fields can give rise to the phenomenon of neutrino spin-flavour precession (SFP). For Majorana neutrinos, the combined action of SFP of solar neutrinos and flavour oscillations would manifest itself as a small, yet potentially detectable, flux of electron antineutrinos coming from the Sun. Non-observation of such a flux constrains the product of the neutrino magnetic moment $\mu$ and the strength of the solar magnetic field $B$. We derive a simple analytical expression for the expected $\bar{\nu}_e$ appearance probability in the three-flavour framework and we use it to revisit the existing experimental bounds on $\mu B$. A full numerical calculation has also been performed to check the validity of the analytical result. We also present our numerical results in energy-binned form, convenient for analyses of the data of the current and future experiments searching for the solar $\bar{\nu}_e$ flux. In addition, we give a comprehensive compilation of other existing limits on neutrino magnetic moments and of the expressions for the probed effective magnetic moments in terms of the fundamental neutrino magnetic moments and leptonic mixing parameters.