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Particles and Fields

Eur. Phys. J. C 24, 323-329 (2002)
DOI: 10.1007/s100520200951

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

J.-L. Kneur and D. Reynaud

Physique Mathématique et Théorique, UMR-5825-CNRS, Université Montpellier II, 34095 Montpellier Cedex 5, France

(Received: 25 February 2002 / Published online: 8 May 2002 - © Springer-Verlag / Società Italiana di Fisica 2002 )

A modification of perturbation theory, known as the 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 the variationally improved perturbation technique 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 $m_{\mathrm {v}} \lesssim 0$, with mv 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.

© Società Italiana di Fisica, Springer-Verlag 2002