PRACTICAL TECHNIQUES OF QCD VERSUS EXACT RESULTS IN SOLVABLE MODELS

We check quantitatively the validity of some popular phenomenological approaches of QCD in simple models. Dispersion sum rules are considere d within the ladder approximation of a field-theoretical model with op erator-product expansion given by ordinary loop diagrams, which are co mputable for any number of loops. A two-current correlation function f ound within the model complies with all requirements of the standard Q CD-sum-rule approach for fitting low-lying resonances, such as fast co nvergence and good stability, while the exact spectrum contains no res onances. Optimized perturbation theory as inspired by the principle of minimal sensitivity is analyzed within a quantum-mechanical model and is shown to work well as compared to a purely asymptotic expansion in the coupling constant or to the Pade approximation. The renormalon te chnique is tested within another quantum-mechanical model and is found to fail to detect its low-energy structure.