Pade Theory and Phenomenology of Resonance Poles

TL;DR

This paper explores the application of Pade approximants in QCD to analyze resonance poles, demonstrating their usefulness in extracting resonance parameters while discussing their limitations and proposing a new, theoretically sound method for determining resonance masses and widths.

Contribution

It introduces a new, theoretically validated procedure based on de Montessus de Ballore's theorem for extracting resonance pole parameters in QCD.

Findings

Pade approximants effectively describe resonant amplitudes in QCD.

A new method for resonance pole extraction is proposed and illustrated with the rho(770).

Discussion of limitations and validity of Pade analysis in hadronic physics.

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).