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

TL;DR

This paper investigates power corrections in the Adler function within the operator product expansion for $e^+e^-$ annihilation, finding no significant contribution from dimension 2 operators and revealing correlations between string tension and gluon condensate.

Contribution

It provides a high-precision analysis of experimental data using Borel transform methods, specifically examining the role of dimension 2 operators in the Adler function.

Findings

Dimension 2 operator contribution is negative and compatible with zero.

Strong anti-correlation between short string tension and gluon condensate.

High-precision fits confirm the negligible role of dimension 2 operators.

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.