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Hoelder Inequalities and Isospin Splitting of the Quark Scalar Mesons

Fang Shi·T. G. Steele·V. Elias·K. B. Sprague·Ying Xue·A. H. Fariborz
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Abstract

A Hoelder inequality analysis of the QCD Laplace sum-rule which probes the non-strange (n\bar n) 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 a_0(980) and a light broad sigma-resonance state as the lightest isovector and isoscalar spin-zero $n\bar n$ mesons. This apparent decoupling of sigma [\equiv f_0(400-1200)] and a_0(980) from the quark n\bar n scalar currents suggests either a non-q \bar q or a dominantly s\bar s interpretation of these resonances, and further suggests the possible identification of the f_0(980) and a_0(1450) as the lightest I={0,1} scalar mesons containing a substantial n\bar n component.

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Fang Shi, T. G. Steele, V. Elias, K. B. Sprague, Ying Xue, A. H. Fariborz. 2000-01-14. Hoelder Inequalities and Isospin Splitting of the Quark Scalar Mesons. https://doi.org/10.1016/s0375-9474(99)00837-4

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