Improvement of perturbation theory in QCD for e+e- -> hadrons and the problem of αs freezing
Abstract
We develope the method of improvement of perturbative theory in QCD, applied to any polarization operator. The case of polarization operator (q2), corresponding to the process e+e- -> hadrons is considered in details. Using the analytical properties of (q2) and perturbative expansion of (q2) at q2<0, Im(q2) at q2>0 is determined in such a way, that the infared pole is eliminated. The convergence of perturbative series for R(q2)=σ(e+e- -> hadrons)/(e+e- -> μ+μ-) is improved. After substitution of R(q2) into dispersion relation the improved Adler function D(q2) with no infrared pole and frozen αs(q2) has been obtained. A good agreement with experiment has been achieved.
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