Boron neutrino flux and the MSW solution of the solar neutrino problem

There are large uncertainties in the predictions of the boron neutrino flux from the Sun which cannot be considered as being of purely statistical origin. We treat the magnitude of this flux, $\Phi_B$, as a parameter to be found from experiment. The properties of the MSW solution to the solar neutrino problem for different values of $\Phi_B$ are studied. Present data give the bounds: $0.38 < \Phi_B/ \Phi_B^0 < 3.1$ (2$\sigma$), where $\Phi_B^0 \equiv 5.7 \cdot 10^6$ cm$^{-2}$s$^{-1}$ is the flux in the reference SSM. The variations of the flux in this interval enlarge the allowed region of mixing angles: $\sin^2 2\theta = 8\cdot 10^{-4} \div 2\cdot 10^{-2}$ (small mixing solutions) and $\sin^2 2\theta = 0.2 \div 0.85$ (large mixing solution). If the value of the original boron neutrino flux is about that measured by Kamiokande, a consistent description of the data is achieved for $\sin^2 2\theta \sim (0.8 \div 2)\cdot 10^{-3}$ (``very small mixing solution"). The solution is characterized by a strong suppression of the beryllium neutrino line, a weak distortion of the high energy part of the boron neutrino spectrum and a value of the double ratio $(CC/NC)^{exp}/(CC/NC)^{SSM}$ at $E > 5$ MeV close to 1. We comment on the possibility to measure the neutrino parameters and the original boron neutrino flux in future experiments.