Calculation of the decay constants of scalar mesons

The purpose of our work is to provide further evidence for the utility of our generalized Nambu--Jona-Lasinio model in describing the properties of light mesons. In this work we develop methods for the calculation of the decay constants of scalar mesons. Our model makes definite predictions of how scalar mesons should be organized into nonets and we use our calculation of the decay constants to support our predictions. The assignment of scalar mesons to various nonets is problematic, with various choices made in the literature for the \ensuremath{\sigma}(500--600), ${f}_{0}(980),$ ${a}_{0}(980),$ ${f}_{0}(1370),$ ${K}_{0}^{*}(1430),$ and ${f}_{0}(1500).$ Maltman has suggested that one can gain information as to how these nonets should be chosen by determining the meson decay constants of the scalar mesons. In particular, he studies the ${a}_{0}(980),$ ${a}_{0}(1450),$ and ${K}_{0}^{*}(1430)$ resonances using QCD sum rule techniques and other methods. He concludes that the ${a}_{0}(980)$ and ${K}_{0}^{*}(1430)$ have similar decay constants and therefore have similar structure. (We have come to the same conclusion by an entirely different analysis, making use of our generalized Nambu--Jona-Lasinio (NJL) model, which includes a covariant model of confinement.) In the case of the ${a}_{0}(980)$ we obtain a result for the decay constant that is about 50% larger than that of Maltman, while for the ${a}_{0}(1450)$ and ${K}_{0}^{*}(1430)$ our results are somewhat smaller than his. Our results suggest that the ${a}_{0}(980)$ may have a significant $K\overline{K}$ component, which would reduce our theoretical value. The implication of our results and those of Maltman for the organization of scalar mesons into nonets is discussed.