Neutrino Oscillation Parameters and Optimization Techniques

Abstract

We present a global analysis, through traditional and a new technique, of the solar neutrino data using total event rates of chlorine (Homestake), Gallax+GNO, SAGE, Superkamiokande and SNO detectors for the two neutrino case. The traditional is the grid search technique, where we calculate well known chi-square (χ 2 ) function for neutrino oscillations for a grid of the parameters ∆m2 and tan2 θ. We find our global minima in the LMA region with ∆m2 = 2.512 · 10−5 eV2 and tan2 θ = 0.3981. We also find local minimum χ 2 values in different regions of the parameter space. The new technique we chose is Differential Evolution. 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 combined this with the traditional grid based method for optimization of solar neutrino oscillation parameters ∆m2 and tan2 θ. We explore regions around the minima found in the global analysis 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.