BROAD SUB-CONTINUUM RESONANCES AND THE CASE FOR FINITE-ENERGY SUM-RULES

There is a need to go beyond the narrow resonance approximation for QC D sum-rule channels which are likely to exhibit sensitivity to broad r esonance structures. We discuss how the first two Laplace sum rules ar e altered when one goes beyond the narrow resonance approximation to i nclude possible subcontinuum resonances with nonzero widths. We show t hat the corresponding first two finite energy sum rules are insensitiv e to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduc ed sensitivity of the first two finite energy sum rules to higher dime nsional condensates, and show these sum rules to be insensitive to dim ension > 6 condensates containing at least one (q) over bar q pair. We extract the direct single-instanton contribution to the F-1 sum rule for the longitudinal component of the axial-vector correlation functio n from the known single-instanton contribution to the lowest Laplace s um rule for the pseudoscalar channel. Finally, we demonstrate how incl usion of this instanton contribution to the finite-energy sum rule lea ds to both a lighter quark mass and to more phenomenologically reasona ble higher-mass-resonance contributions within the pseudoscalar channe l.