Scalar Meson Decay Constants and the Nature of the a0(980)

The a0(980), a0(1450) and K ∗ 0(1430) decay constants are determined using a form of QCD sum rules known to produce a very accurate determination of the ρ decay constant. The ratio of a0(980) toK ∗ 0 (1430) decay constants is shown to be ∼ 0.6, ruling out both the “loosely-bound-KK̄-molecule” and Gribov minion scenarios for the a0(980). Solutions for the isovector scalar spectral function obtained in the literature from sum rule analyses employing a more restrictive single-resonance-plus-continuum form of the input spectral ansatz, are also investigated. These solutions, which suggest, in contrast to the present results, negligible coupling of the a0(980) to the isovector scalar density are shown to produce a very poor match between the OPE and hadronic sides of the sum rules employed here, and hence to be ruled out.