Nonlinear Phenomena in Complex Systems, 2019, Vol.22, No.2, pp.151

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2019, Vol.22, No.2, pp.151 - 163

Precise Study of Non-Perturbative Contributions in e⁺e⁻ - Annihilation
M. E. Kozhevnikova, A. G. Oganesian, and O. V. Teryaev

We develop a new mathematical tool to study non-perturbative QCD effects in low-energy processes using ordinary and analytic perturbation theory. We apply this tool to extract the lowest dimensional condensates from the high-precision fits of the data on e⁺e⁻-annihilation to pion channels: π⁺ π⁻, 2π⁺ 2π⁻, π⁺ π⁻ 2π⁰, 3π⁺ 3π⁻, and 2π⁺ 2π⁻ 2π⁰. We verify whether the operator with dimension 2 exists. Our consideration is based on the Borel transform of the Adler function corresponding to e⁺e⁻-annihilation into pions. It is shown that within the framework of the proposed method the C₂ coefficient of the dimension 2 operator is negative and is closer to zero for analytic perturbation theory, which may therefore be partially responsible for the effect of short strings.

Key words: quantum chromodynamics, perturbation theory, dispersion relations, Borel transform, hadron production in e⁺e⁻-annihilation, non-perturbative corrections

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