Search for short strings in~$e^+e^-$-annihilation

Abstract

In this work the behavior of power corrections to Adler finction in operator product expansion (OPE) is studied, in particular the possible contribution of operator of dimension 2. The OPE terms of dimension 4 and 6 are taken into account. Various experimental data on reactions of $e^+e^-$-annihilation to pion channels ($\pi^+\pi^-$, $2\pi^+2\pi^-$, $\pi^+\pi^-2\pi^0$, $3\pi^+3\pi^-$, $2\pi^+2\pi^-2\pi^0$) are used. The high-precision fits of the experimental data are obtained and used. The method based on Borel transform of Adler function is applied. It is shown that the contribution of operator of dimension 2 is negative being compatible to zero at three standard deviations level. The strong (anti)corellation between short string and local gluon condensate is found.