Hoelder Inequalities and Isospin Splitting of the Quark Scalar Mesons

TL;DR

This paper uses Hoelder inequalities and QCD sum-rules to analyze isospin splitting in scalar mesons, suggesting that certain light scalar resonances may not be simple quark-antiquark states and proposing alternative interpretations.

Contribution

It introduces a Hoelder inequality-based approach to QCD sum-rules, enhancing the understanding of isospin splitting and the nature of light scalar mesons.

Findings

Enhanced instanton contributions increase isospin splitting.

The lightest scalar mesons a_0(980) and sigma are unlikely to be simple nar n states.

f_0(980) and a_0(1450) may contain significant nar n components.

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.