Energy resolution optimization through layers measurements weighting: analytical solutions and numerical strategies.

The total energy resolution measured by a multi--layers calorimeter can be optimized by applying weighting factors to the energy measured by each of the layers. The set of the optimal weights can be analytically calculated starting from the mean energies deposited in each layer and their covariance matrix. The statistical uncertainties are estimated using a numerical approach. The method is applied to a test beam data set on a production module of the ATLAS electromagnetic calorimeter barrel, showing an improvement in the energy resolution, uniformity and scale.