At Which Order Should we Truncate Perturbative Series?

TL;DR

This paper examines the optimal truncation of divergent perturbative series in quantum field theory, proposing a systematic approach based on controlling large field configurations to improve accuracy.

Contribution

It introduces a systematic method for truncating perturbative series by managing large field configurations, advancing beyond the common minimal term prescription.

Findings

Analysis of factorial growth of coefficients

Connection between lattice QCD and continuum convergence issues

Proposal of a systematic truncation approach

Abstract

Perturbative coefficients grow factorially with the order and one needs a prescription to truncate the series in order to obtain a finite result. A common prescription consists in dropping the smallest contribution at a given coupling and all the higher orders terms. We discuss the error associated with this procedure. We advocate a more systematic approach which consists in controlling the large field configurations in the functional integral. We summarize our best understanding of these issues for lattice QCD in the quenched approximation and their connection with convergence problems found in the continuum.