Restrictions on exact current correlation functions and reliability of sum-rule results

Criteria of reliability are studied for results obtained within the sum-rule approach in QCD and in some toy models. The criterion of validity of the approximation for current correlation functions based on operator-product expansion within Borel sum rules, suggested previously in the literature, is critically reexamined. A new criterion of validity of a perturbative approximation that makes use of the Källen-Lehmann representation and finite-energy sum rules is proposed. The stability of criteria against small variations in expansion coefficients is investigated in an exactly solvable model and in QCD.