An analytic method of describing $R$-related quantities in QCD
  A model based on the analytic approach to QCD, involving a summation of threshold singularities and taking into account the nonperturbative character of the light quark masses, is applied to find hadronic contributions to different physical quantities. It is shown that the suggested model allows us to describe well such objects as the hadronic contribution to the anomalous magnetic moment of the muon, the ratio of hadronic to leptonic $\tau$-decay widths in the vector channel, the Adler $D$-function, the smeared $R_\Delta$-function, and the hadronic contribution to the evolution of the fine structure constant. 
K. A. Milton, I. L. Solovtsov, and O. P. Solovtsova