Statistical Pattern Recognition: Application to $\nu_{\mu}\to\nu_{\tau}$ Oscillation Searches Based on Kinematic Criteria

Classic statistical techniques (like the multi-dimensional likelihood and the Fisher discriminant method) together with Multi-layer Perceptron and Learning Vector Quantization Neural Networks have been systematically used in order to find the best sensitivity when searching for $\nu_\mu \to \nu_{\tau}$ oscillations. We discovered that for a general direct $\nu_\tau$ appearance search based on kinematic criteria: a) An optimal discrimination power is obtained using only three variables ($E_{visible}$, $P_{T}^{miss}$ and $\rho_{l}$) and their correlations. Increasing the number of variables (or combinations of variables) only increases the complexity of the problem, but does not result in a sensible change of the expected sensitivity. b) The multi-layer perceptron approach offers the best performance. As an example to assert numerically those points, we have considered the problem of $\nu_\tau$ appearance at the CNGS beam using a Liquid Argon TPC detector.