Hölder Inequalities and Isospin Splitting of the Quark Scalar Mesons

Abstract

A Hölder inequality analysis of the QCD Laplace sum-rule which probes the non-strange (nn̄) 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 a0(980) and a light broad σ-resonance state as the lightest isovector and isoscalar spin-zero nn̄ mesons. This apparent decoupling of σ [≡ f0(400− 1200)] and a0(980) from the quark nn̄ scalar currents suggests either a non-qq̄ or a dominantly ss̄ interpretation of these resonances, and further suggests the possible identification of the f0(980) and a0(1450) as the lightest I = {0, 1} scalar mesons containing a substantial nn̄ component.

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Cite this paper

@inproceedings{Shi2008HolderIA, title={Hölder Inequalities and Isospin Splitting of the Quark Scalar Mesons}, author={Fang Shi and Ying Xue}, year={2008} }