# A Rational Approach to Resonance Saturation in large-Nc QCD

## TL;DR

This paper demonstrates that resonance saturation in large-Nc QCD can be understood through Pade Approximants, providing insights into the relationship between various QCD expansions and the resonance spectrum.

## Contribution

It introduces a mathematical framework using Pade Approximants to explain resonance saturation in large-Nc QCD, connecting it with the Chiral and Operator Product Expansions.

## Key findings

- Pade Approximants can model Green's functions reliably in Euclidean space.
- Unphysical poles limit the accuracy of Pade Approximants in Minkowski space.
- The approach clarifies the role of finite resonances in QCD.

## Abstract

We point out that resonance saturation in QCD can be understood in the large-Nc limit from the mathematical theory of Pade Approximants to meromorphic functions. These approximants are rational functions which encompass any saturation with a finite number of resonances as a particular example, explaining several results which have appeared in the literature. We review the main properties of Pade Approximants with the help of a toy model for the <VV-AA> two-point correlator, paying particular attention to the relationship among the Chiral Expansion, the Operator Product Expansion and the resonance spectrum. In passing, we also comment on an old proposal made by Migdal in 1977 which has recently attracted much attention in the context of AdS/QCD models. Finally, we apply the simplest Pade Approximant to the <VV-AA> correlator in the real case of QCD. The general conclusion is that a rational approximant may reliably describe a Green's function in the Euclidean, but the same is not true in the Minkowski regime due to the appearance of unphysical poles and/or residues.