Pade Theory and Phenomenology of Resonance Poles

Abstract

The use of Pade approximants for the description of QCD matrix elements is discussed in this talk. We will see how they prove to be an extremely useful tool, specially in the case of resonant amplitudes. It will allow the inclusion of high-energy Euclidian data to improve the determination of low-energy properties, such as the quadratic vector radius. This does not mean that the rational approximations can be arbitrarily employed for the extraction of any desired hadronic parameter. A discussion about the validity, limitations and possible issues of the Pade analysis is carried on along the paper. Finally, based on the de Montessus de Ballore's theorem, a theoretically safe new procedure for the extraction of the pole mass and width of resonances is proposed here and illustrated with the example of the rho(770).

Comments: 13 pages, 13 figs, Proceedings of the Conference on Approximation and Extrapolation of Convergent and Divergent Sequences and Series, CIRM Luminy, Marseille (France), September 28th - October 2nd 2009