The $\pi^2$ terms in the s-channel QCD observables

Abstract

We analyze the effect of $\pi^2$-terms in the QCD perturbative expansions for the s-channel effective coupling and observables, the effect known from the 80s. We remind that these terms can be collected into specific functions -- strong s-channel coupling $\tilda{\alpha}_s$ and its effective powers ${\mathfrak A}(s)$ free of ghost singularities. Further on, we study the structure of perturbation theory for observables and its reformulation in terms of nonpower perturbation expansion over the set $\{\mathfrak A}(s)\}.$\par values of $\alpha_s$ as extracted from experiments. The main result is that the common two-loop (NLO, NLLA) approximation widely used in the five-quark ($10 \GeV\lesssim \sqrt{s}\lesssim 170 \GeV$) region for a shape analysis contains a systematic negative error of a 1-2 per cent order of magnitude for the extracted $\bar{\alpha}_s^{(2)}$. Our physical conclusion is that the $\alpha_s(M_Z)$ value averaged over the f=5 data $<\alpha_s(M_Z)>_{f=5} \simeq 0.124$ appreciably differs from the currently accepted "world average" (=0.118).}