Broad sub-continuum resonances and the case
1 Department of Applied
Mathematics, The University of Western Ontario, London, Ontario
N6A 5B7, Canada
2 Department of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan S7N 5C6, Canada
Received: 15 September 1997 / Revised version: 15 November 1997 / Published online: 26 February 1998
There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension > 6 condensates containing at least one pair. We extract the direct single-instanton contribution to the F1 sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel.