Analytic Perturbation Theory: A New Approach to the Analytic Continuation of the Strong Coupling Constant $\alpha_S$ into the Timelike Region

摘要

The renormalization group applied to perturbation theory is ordinarily usedto define the running coupling constant in the spacelike region. However, todescribe processes with timelike momenta transfers, it is important to have aself-consistent determination of the running coupling constant in the timelikeregion. The technique called analytic perturbation theory (APT) allows aconsistent determination of this running coupling constant. The results arefound to disagree significantly with those obtained in the standardperturbative approach. Comparison between the standard approach and APT iscarried out to two loops, and threshold matching in APT is applied in thetimelike region.