Improvement of perturbation theory in QCD for e(+)e(-)-> hadrons and the problem of alpha(s) 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 Pi(q(2)), corresponding to the process e(+)e(-)--> hadrons, is considered in detail. By the use of the analytical properties of Pi(q(2)) and a pertur bation expansion of Pi(q(2)) for q(2)< 0, the function Im Pi(q(2)) at q(2)> 0 is defined in such a way that the infrared pole is eliminated. The conve rgence of the perturbation series for R(q(2))=sigma(e(+)e(-)--> hadrons)/(e (+)e(-)-->mu(+)mu(-)) is improved. After substitution of R(q(2)) into the d ispersion relation an improved Adler function D(q(2)) is obtained, having n o infrared pole and a frozen alpha(s)(q(2)). Good agreement with experiment is achieved. (C) 1999 American Institute of Physics. [S0021- 3640(99)00215 -7].