A new approach to resummation: Parametric Perturbation Theory

TL;DR

Parametric Perturbation Theory (PPT) offers a non-perturbative resummation technique that constrains solutions to be linear in an unphysical parameter, effectively handling divergent series and predicting series coefficients with high accuracy.

Contribution

This paper introduces PPT, a novel non-perturbative method that resums divergent series and predicts perturbative coefficients by constraining solutions to a linear unphysical parameter.

Findings

Successfully resums divergent perturbative series.

Accurately extracts strong coupling behavior.

Predicts perturbative series coefficients with high precision.

Abstract

We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are constrained to be linear in a certain (unphysical) parameter. The perturbative expansion is carried out in this parameter and not in the physical coupling (as in ordinary perturbation theory). We show that the method is capable to resum the divergent perturbative series, to {\sl extract} the leading asymptotic (strong coupling) behavior and {\sl predict} with high accuracy the coefficients of the perturbative series.