Practical techniques of QCD vs exact results of solvable models
  We check quantitatively the validity of some popular phenomenological approaches of QCD in simple models. Dispersion sum rules are considered within the ladder approximation of a field-theoretic model with OPE given by ordinary loop diagrams which are computable for any number of loops. A correlator of two currents within the model complies with all requirements of standard QCD sum rules approach for fitting low-lying resonances such as fast convergence and good stability while the exact spectrum contains no resonance. Optimized PT as it is inspired by the principle of minimal sensitivity is analyzed within a quantum mechanical model and is shown to work well as compared to pure asymptotic expansion in the coupling constant or Pad\'e approximation. Renormalon technique is tested within another quantum mechanical model and is found to fail to detect its low-energy structure. 
A.A.Penin and A.A.Pivovarov