Sum-Rule Inequalities and a Toy Model Paradox

Abstract Fundamental inequalities for QCD sum-rules are applied to resolve a paradox recently encountered in a sum-rule calculation [A.A. Penin and A.A. Pivovarov, Phys. Lett. B 357 (1995) 427.]. This paradox was encountered in a toy model known to be free of resonances that yields an apparent resonance using a standard sum-rule stability analysis. Application of the inequalities does not support the existence of a well defined sum-rule calculation, and shows a strong distinction from typical behaviour in QCD.