SUM-RULE INEQUALITIES AND A TOY MODEL PARADOX

Fundamental inequalities for QCD sum-rules are applied to resolve a pa radox recently encountered in a sum-rule calculation [A.A. Penin and A .A. Pivovarov, Phys. Lett. B 357 (1995) 427.]. This paradox was encoun tered in a toy model known to be free of resonances that yields an app arent resonance using a standard sum-rule stability analysis. Applicat ion of the inequalities does not support the existence of a well defin ed sum-rule calculation, and shows a strong distinction from typical b ehaviour in QCD.