Confronting theoretical predictions with experimental data; fitting strategy for multi-dimensional distributions

Abstract

After developing a Resonance Chiral Lagrangian (RχL) model to describe hadronic τ lepton decays [18], the model was confronted with experimental data. This was accomplished using a fitting framework which was developed to take into account the complexity of the model and to ensure the numerical stability for the algorithms used in the fitting. Since the model used in the fit contained 15 parameters and there were only three 1-dimensional distributions available, we could expect multiple local minima or even whole regions of equal potential to appear. Our methods had to thoroughly explore the whole parameter space and ensure, as well as possible, that the result is a global minimum. This paper is focused on the technical aspects of the fitting strategy used. The first approach was based on re-weighting algorithm published in [17] and produced results in around two weeks. Later approach, with improved theoretical model and simple parallelization algorithm based on Inter-Process Communication (IPC) methods of UNIX system, reduced computation time down to 2-3 days. Additional approximations were introduced to the model decreasing time to obtain the preliminary results down to 8 hours. This allowed to better validate the results leading to a more robust analysis published in [12].