Borel convergence of the variationally improved mass expansion and dynamical symmetry breaking

TL;DR

This paper demonstrates that a modified perturbation theory technique, delta-expansion, achieves Borel convergence in certain quantum field theories, enabling more reliable estimates of quantities related to dynamical symmetry breaking.

Contribution

It extends variationally improved perturbation to asymptotically free theories and proves Borel convergence for specific physical quantities, aiding non-perturbative analysis.

Findings

Proves Borel convergence of the series for certain mass parameters.

Shows the method's potential for non-ambiguous estimates in QCD.

Extends delta-expansion to more complex theories.

Abstract

A modification of perturbation theory, known as delta-expansion (variationally improved perturbation), gave rigorously convergent series in some D=1 models (oscillator energy levels) with factorially divergent ordinary perturbative expansions. In a generalization of variationally improved perturbation appropriate to renormalizable asymptotically free theories, we show that the large expansion orders of certain physical quantities are similarly improved, and prove the Borel convergence of the corresponding series for $m_v \lsim 0$, with $m_v$ the new (arbitrary) mass perturbation parameter. We argue that non-ambiguous estimates of quantities relevant to dynamical (chiral) symmetry breaking in QCD, are possible in this resummation framework.