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. ReynaudPhysique 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 )
Abstract
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
, 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
