Optimization of Neutrino Oscillation Parameters using Differential Evolution

Abstract

We combine Differential Evolution, a new technique, with the traditional grid based method for optimization of solar neutrino oscillation parameters $Δm^2$ and $\tan^{2}θ$ for the case of two neutrinos. The Differential Evolution is a population based stochastic algorithm for optimization of real valued non-linear non-differentiable objective functions that has become very popular during the last decade. We calculate well known chi-square ($χ^2$) function for neutrino oscillations for a grid of the parameters using total event rates of chlorine (Homestake), Gallax+GNO, SAGE, Superkamiokande and SNO detectors and theoretically calculated event rates. We find minimum $χ^2$ values in different regions of the parameter space. We explore regions around these minima using Differential Evolution for the fine tuning of the parameters allowing even those values of the parameters which do not lie on any grid. We note as much as 4 times decrease in $χ^2$ value in the SMA region and even better goodness-of-fit as compared to our grid-based results. All this indicates a way out of the impasse faced due to CPU limitations of the larger grid method.