Precise Study of Non-Perturbative Contributions in e+e−-Annihilation

Abstract

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.