Some Remarks on the Pade Unitarization of Low-Energy Amplitudes

TL;DR

This paper critically examines Pade unitarization methods for low-energy amplitudes, highlighting potential inaccuracies and proposing that diagonal Pade sequences offer better convergence for resonance descriptions.

Contribution

It provides a systematic analysis of Pade approximants in unitarization, identifying limitations of certain methods and advocating for diagonal sequences for improved accuracy.

Findings

Inverse amplitude method yields incorrect sigma mass and width in the Linear Sigma Model

Diagonal Pade sequences ([N/N]) demonstrate superior convergence properties

Certain Pade-based methods may lead to inaccurate resonance descriptions

Abstract

We present a critical analysis of Pade-based methods for the unitarization of low energy amplitudes. We show that the use of certain Pade Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we find that in the Linear Sigma Model the unitarization of the low energy amplitude through the inverse amplitude method produces essentially incorrect results for the mass and width of the sigma. Alternative sequences of Pades are studied and we find that the diagonal sequences (i.e., [N/N]) have much better convergence properties.