Various versions of analytic QCD and skeleton-motivated evaluation of observables

Abstract

We present skeleton-motivated evaluation of QCD observables. The approach can be applied in analytic versions of QCD in certain classes of renormalization schemes. We present two versions of analytic QCD which can be regarded as low-energy modifications of the ``minimal'' analytic QCD and which reproduce the measured value of the semihadronic $\ensuremath{\tau}$ decay ratio ${r}_{\ensuremath{\tau}}$. Further, we describe an approach of calculating the higher-order analytic couplings ${\mathcal{A}}_{k}$ $(k=2,3,\dots{})$ on the basis of logarithmic derivatives of the analytic coupling ${\mathcal{A}}_{1}({Q}^{2})$. This approach can be applied in any version of analytic QCD. We adjust the free parameters of the aforementioned two analytic models in such a way that the skeleton-motivated evaluation reproduces the correct known values of ${r}_{\ensuremath{\tau}}$ and of the Bjorken polarized sum rule (BjPSR) ${d}_{b}({Q}^{2})$ at a given point (e.g., at ${Q}^{2}=2\text{ }\text{ }{\mathrm{GeV}}^{2}$). We then evaluate the low-energy behavior of the Adler function ${d}_{v}({Q}^{2})$ and the BjPSR ${d}_{b}({Q}^{2})$ in the aforementioned evaluation approach, in the three analytic versions of QCD. We compare with the results obtained in the minimal analytic QCD and with the evaluation approach of Milton et al. and Shirkov.