Earth Regeneration Effect in Solar Neutrino Oscillations: An Analytic Approach

We present a simple and accurate method for computing analytically the regeneration probability of solar neutrinos in the Earth. We apply this method to the calculation of several solar model independent quantities than can be measured by the SuperKamiokande and Sudbury Neutrino Observatory experiments. PACS number(s): 26.65.+t, 13.15.+g, 14.60.Pq, 91.35.\Gammax Typeset using REVT E X I. INTRODUCTION The Mikheyev-Smirnov-Wolfenstein (MSW) mechanism of neutrino oscillations in matter [1] represents a fascinating solution to the long-standing solar neutrino problem [2]. The possible observation of the e regeneration effect in the Earth [3,4] would be a spectacular, solar model independent confirmation of this theory (for reviews, see [5,6]). The available data from the real-time solar neutrino experiment at Kamioka [7,8] are consistent with no Earth regeneration effect within the quoted uncertainties. This information can be used to exclude a region of the neutrino mass-mixing parame..