Measuring the energy dependence of the $\nu_e$ survival probability at the Sudbury Neutrino Observatory

The Sudbury Neutrino Observatory has excellent sensitivity to the solar neutrino energy spectrum through the charged-current interaction with deuterium. Assuming a known $^8$B neutrino spectrum at the production point in the Sun, we can obtain the $\nu_e$ survival probability on Earth as a function of neutrino energy. This talk describes a new method for obtaining these survival probability functions directly from the SNO data set using a maximum likelihood fit. The kernel estimation technique is used to build unbinned, non-parametric, multidimensional probability density functions from Monte Carlo event samples which can be reweighted on-the-fly as the fit parameters describing the survival probability function are varied. This method also allows the survival probability function to be obtained simultaneously for upward and downward-going (night and day) neutrinos for tests of $\nu_e$ regeneration in the Earth.