Improvement of perturbation theory in QCD for e^+e^- -> hadrons and the problem of α_s freezing

B. V. Geshkenbein; B. L. Ioffe

doi:10.1134/1.568146

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arXiv · hep-ph/9906406

Improvement of perturbation theory in QCD for e^+e^- -> hadrons and the problem of α_s freezing

B. V. Geshkenbein·B. L. Ioffe

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Abstract

We develope the method of improvement of perturbative theory in QCD, applied to any polarization operator. The case of polarization operator Π(q^2), corresponding to the process e^+e^- -> hadrons is considered in details. Using the analytical properties of Π(q^2) and perturbative expansion of Π(q^2) at q^2<0, ImΠ(q^2) at q^2>0 is determined in such a way, that the infared pole is eliminated. The convergence of perturbative series for R(q^2)=σ(e^+e^- -> hadrons)/(e^+e^- -> μ^+μ^-) is improved. After substitution of R(q^2) into dispersion relation the improved Adler function D(q^2) with no infrared pole and frozen α_s(q^2) has been obtained. A good agreement with experiment has been achieved.

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B. V. Geshkenbein, B. L. Ioffe. 1999-06-29. Improvement of perturbation theory in QCD for e^+e^- -> hadrons and the problem of α_s freezing. https://doi.org/10.1134/1.568146

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