Improvement of perturbation theory in QCD for e+e− →hadrons and the problem of αs freezing

A method of improving perturbation theory in QCD is developed which can be applied to any polarization operator. The case of the polarization operator Π(q2), corresponding to the process e+e−→ hadrons, is considered in detail. By the use of the analytical properties of Π(q2) and a perturbation expansion of Π(q2) for q2<0, the function ImΠ(q2) at q2>0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R(q2)=σ(e+e− →hadrons)/(e+e−→μ+μ−) is improved. After substitution of R(q2) into the dispersion relation an improved Adler function D(q2) is obtained, having no infrared pole and a frozen αs(q2). Good agreement with experiment is achieved.