Ka. Milton et Op. Solovtsova, ANALYTIC PERTURBATION-THEORY - A NEW APPROACH TO THE ANALYTIC CONTINUATION OF THE STRONG-COUPLING CONSTANT ALPHA(S) INTO THE TIME-LIKE REGION, Physical review. D. Particles and fields, 57(9), 1998, pp. 5402-5409
The renormalization group applied to perturbation theory is ordinarily
used to define the running coupling constant in the spacelike region.
However, to describe processes with timelike momenta transfers, it is
important to have a self-consistent determination of the running coup
ling constant in the timelike region. The technique called analytic pe
rturbation theory (APT) allows a consistent determination of this runn
ing coupling constant. The results are found to disagree significantly
with those obtained in the standard perturbative approach. Comparison
between the standard approach and APT is carried out to two loops, an
d threshold matching in APT is applied in the timelike region.