Holder inequalities and isospin splitting of the quark scalar mesons

A Holder inequality analysis of the QCD Laplace sum rule which probes the non-strange (nn) components of the I = {0,1} (light-quark) scalar mesons supports the methodological consistency of an effective continuum contribution from instanton effects. This revised formulation enhances the magnitude of the instanton contributions which split the degeneracy between the I = 0 and I = I channels. Despite this enhanced isospin splitting effect, analysis of the Laplace and finite-energy sum rules seems to preclude identification of either a0(980) or a light broad (sigma)-resonance as states with predominant nn components, in which case their dominant components could then be meson-meson ((pi)(pi) or KK), multiquark, or glueball states. This apparent decoupling of (sigma)[= f0(400-1200)] and a0(980) from the quark nn scalar currents suggests the possible identification of the f0(980) and a0(1450) as the lightest I = {0,1} scalar mesons in which the nn component is dominant.