QCD Sum-Rule Consistency of Lowest-Lying Quark Scalar Resonances

Abstract

We investigate lowest-lying scalar meson properties predicted from QCD Laplace sum rules based upon isovector and isoscalar non-strange $\bar{q}q$ currents. The hadronic content of these sum rules incorporates deviations from the narrow resonance approximation anticipated from physical resonance widths. The field theoretical content of these sum rules incorporates purely-perturbative QCD contributions to three-loop order, the direct single-instanton contribution in the instanton liquid model, and leading contributions from QCD-vacuum condensates. In the isovector channel, the results we obtain are compatible with a$_0$(1450) being the lowest-lying $q\bar{q}$ resonance, and are indicative of a non-$q\bar{q}$ interpretation for a$_0$(980). In the isoscalar channel, the results we obtain are compatible with the lowest lying $q\bar{q}$ resonance being f$_0$(980) or a state somewhat lighter than f$_0$(980) whose width is less than half of its mass. The dilaton scenario for such a narrower $\sigma$-resonance is discussed in detail, and is found compatible with sum rule predictions for the resonance coupling only if the anomalous gluon-field portion of $\Theta_\mu^\mu$ dominates the matrix element $<\sigma|\Theta_\mu^\mu|0>$. A linear sigma-model interpretation of the lowest-lying resonance's coupling, when compared to the coupling predicted by sum rules, is indicative of a renormalization-group invariant light-quark mass between 4 and 6 MeV.