The effect of random matter density perturbations on the MSW solution to the solar neutrino problem

We consider the implications of solar matter density random noise upon resonant neutrino conversion. The evolution equation describing MSW-like conversion is derived in the framework of the Schr\'odinger approach. We study quantitatively their effect upon both large and small mixing angle MSW solutions to the solar neutrino problem. This is carried out both for the active-active $\nu_e \ra \nu_{\mu,\tau}$ as well as active-sterile $\nu_e \ra \nu_s$ conversion channels. We find that the small mixing MSW solution is much more stable (especially in Δm2) than the large mixing solution. The possible existence of solar matter density noise at the few percent level could be tested at future solar neutrino experiments, especially Borexino.