Large-order perturbation theory for the electromagnetic current-current correlation function

Details Large-order perturbation theory for the electromagnetic current-current correlation function Large-order perturbation theory for the electromagnetic current-current correlation function

1992-05-09

arxiv.org/abs/hep-ph/9205213v1

Phys.Rev. D46 (1992) 4712-4735

Physics

High Energy Physics

High Energy Physics - Phenomenology

62 pages

Scientific paper

10.1103/PhysRevD.46.4712

The constraints imposed by asymptotic freedom and analyticity on the large-order behavior of perturbation theory for the electromagnetic current-current correlation function are examined. By suitably applying the renormalization group, the coefficients of the asymptotic expansion in the deep Euclidean region may be expressed explicitly in terms of the perturbative coefficients of the Minkowski space discontinuity (the $R$-ratio in $e^+ e^-$ scattering). This relation yields a ``generic'' prediction for the large-order behavior of the Euclidean perturbation series and suggests the presence of non-perturbative $1/q^2$ correction in the Euclidian correlation function. No such ``generic'' prediction can be made for the physically measurable $R$-ratio. A novel functional method is developed to obtain these results.

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