Hölder inequalities and isospin splitting of the quark scalar mesons Original Research Article

A Hölder inequality analysis of the QCD Laplace sum rule which probes the non-strange (View the MathML source) 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=1 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 σ-resonance as states with predominant View the MathML source components, in which case their dominant components could then be meson–meson (ππ or View the MathML source), multiquark, or glueball states. This apparent decoupling of View the MathML source and a0(980) from the quark View the MathML source scalar currents suggests the possible identification of the f0(980) and a0(1450) as the lightest I={0,1} scalar mesons in which the View the MathML source component is dominant.