# Superasymptotic and hyperasymptotic approximation to the operator product expansion

## TL;DR

This paper develops superasymptotic and hyperasymptotic methods to accurately separate perturbative and non-perturbative contributions in the operator product expansion, demonstrated on the static potential.

## Contribution

It introduces a novel organization of OPE terms along super/hyper-asymptotic expansions with precise non-perturbative power accuracy.

## Key findings

- Successful application to the static potential in large β₀ approximation
- Clear demonstration of superasymptotic and hyperasymptotic structures
- Enhanced analytic control over perturbative and non-perturbative separation

## Abstract

Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\alpha$ from the non-perturbative (NP) corrections. This splitting is done with NP power accuracy. Analytic control of the splitting is achieved and the organization of the different terms is done along an super/hyper-asymptotic expansion. As a test we apply the methods to the static potential in the large $\beta_0$ approximation. We see the superasymptotic and hyperasymptotic structure of the observable in full glory.