Summation of threshold singularities in correlators of quark currents

Abstract

Expressions are constructed for imaginary parts of vector and axial-vector correlators of quark currents in which summation of infinite number of threshold singularities is realized. An analytical approach is applied to a description of invariant charge evolution in quantum chromodynamics. It is demonstrated that the potential term in the suggested expressions for the imaginary parts of the correlators gives the dominant contribution, whereas the chromodynamic correction remains small in a wide energy interval.