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

Criteria of reliability are studied for results obtained within the sum-rul e approach in QCD and in some toy models. The criterion of validity of the approximation for current correlation functions based on operator-product e xpansion within Borel sum rules, suggested previously in the literature, is critically reexamined. A new criterion of validity of a perturbative appro ximation that makes use of the Kallen-Lehmann representation and finite-ene rgy sum rules is proposed. The stability of criteria against small variatio ns in expansion coefficients is investigated in an exactly solvable model a nd in QCD. (C) 2000 MAIK "Nauka/Interperiodica".