Unfolding the Second Riemann sheet with Padé Approximants: hunting resonance poles

Based on the mathematically well defined Padé Theory, a theoretically safe new procedure for the extraction of the pole mass and width of resonances is proposed. In particular, thanks to the Montessus de Ballore theorem we are able to unfold the Second Riemann sheet of a amplitude to search the position of the resonant pole in the complex plane. The main advantage of that method is it systematical and model-independent treatment of the prediction and the corresponding errors of the approximation.