Statistically improved Analysis of Neutrino Oscillation Data with the latest KamLAND result

We present an updated analysis of all available solar and reactor neutrino data, emphasizing in particular the totality of the KamLAND (314d live time) results and including for the first time the solar $SNO$ (391d live time, phase II NaCl-enhanced) spectrum data. As a novelty of the statistical analysis, we study the variability of the KamLand results with respect the use of diverse statistics. A new statistic, not used before is proposed. Moreover, in the analysis of the SNO spectrum a novel technique is used in order to include full correlated errors among bins. Combining all data, we obtain the following best-fit parameters: we determine individual neutrino mixing parameters and their errors $\Delta m^2= 8.2\pm 0.08\times 10^{-5} \eV^2,\quad \tan^2\theta= 0.50^{+0.12}_{-0.07}.$ The impact of these results is discussed. We also estimate the individual elements of the neutrino mass matrix. In the framework of three neutrino oscillations we obtain the mass matrix: \begin{eqnarray}M&=& eV \pmatrix{1.0+ 4.0\pm 3.2 10^{-5}& 4.2\pm 3.2 10^{-5} &-13.5\pm 14.0 10^{-5} \cr 4.2\pm 3.2 10^{-5}& 1.0+4.3\pm 3.5 10^{-5} &-13.5\pm 14.5 10^{-5} \cr 13.5\pm 14.0 10^{-5}& -13.5\pm 14.5 10^{-5} &1.0+100.0\pm 30.0\ 10^{-5}}.\end{eqnarray}