Pad\'e approximants and the prediction of non-perturbative parameters in particle physics

TL;DR

This paper reviews the connection between Padé approximants and non-perturbative methods in particle physics, highlighting potential new applications for predicting parameters beyond traditional techniques.

Contribution

It emphasizes the recent recognition of Padé approximants' role in non-perturbative strong interaction studies and explores open problems where they could be particularly useful.

Findings

Padé approximants are deeply connected to non-perturbative techniques.

Potential for Padé approximants to address open problems in strong interactions.

Encourages further exploration of rational approximants in particle physics.

Abstract

Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Pad\'e approximants to meromorphic functions. However, only recently this connection has been acknowledged and efforts at fully exploiting it are only starting. In this article I will briefly review the most prominent techniques used in non-perturbative strong interactions with special emphasis on its relation with Pad\'e approximants. I will then concentrate on a set of open problems outside the scope of these conventional techniques where Pad\'e approximants might be extremely useful.