Abstract
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(q 2), corresponding to the process e + e −→ hadrons, is considered in detail. By the use of the analytical properties of Π(q 2) and a perturbation expansion of Π(q 2) for q 2<0, the function ImΠ(q 2) at q 2>0 is defined in such a way that the infrared pole is eliminated. The convergence of the perturbation series for R(q 2)=σ(e + e − →hadrons)/(e + e −→μ + μ −) is improved. After substitution of R(q 2) into the dispersion relation an improved Adler function D(q 2) is obtained, having no infrared pole and a frozen α s (q 2). Good agreement with experiment is achieved.
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Pis’ma Zh. Éksp. Teor. Fiz. 70, No. 3, 167–170 (10 August 1999)
Published in English in the original Russian journal. Edited by Steve Torstveit.