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- W2007151056 abstract "Recent work by Maltman has given us confidence that our assignment of scalar meson states to various nonets based upon our generalized Nambu--Jona-Lasinio (NJL) model is correct. [For example, in our model the ${a}_{0}(980)$ and the ${f}_{0}(980)$ are in the same nonet as the ${K}_{0}^{*}(1430).]$ In this work we make use of our model to provide a precise definition of ``preexisting'' resonances and ``dynamically generated'' resonances when considering various scalar mesons. [This distinction has been noted by Meissner in his characterization of the ${f}_{0}(400--1200)$ as nonpreexisting.] We define preexisting (or intrinsic) resonances as those that appear as singularities of the $qoverline{q} T$ matrix and are in correspondence with $qoverline{q}$ states bound in the confining field. [Additional singularities may be found when studying the T matrices describing ensuremath{pi}-ensuremath{pi} or $ensuremath{pi}ensuremath{-}K$ scattering, for example. Such features may be seen to arise, in part, from t-channel and u-channel ensuremath{rho} exchange in the case of ensuremath{pi}-ensuremath{pi} scattering, leading to the introduction of the ensuremath{sigma}(500--600). In addition, threshold effects in the $qoverline{q} T$ matrix can give rise to significant broad cross section enhancements. The latter is, in part, responsible for the introduction of the ensuremath{kappa}(900) in a study of $ensuremath{pi}ensuremath{-}K$ scattering, for example.] We suggest that it is only the intrinsic resonances which correspond to $qoverline{q}$ quark-model states, and it is only the intrinsic states that are to be used to form quark-model $qoverline{q}$ nonets of states. [While the ensuremath{kappa}(900) and ensuremath{sigma}(500--600) could be placed in a nonet of dynamically generated states, it is unclear whether there is evidence that requires the introduction of other members of such a nonet.] In this work we show how the phenomena related to the introduction of the ensuremath{sigma}(500--600) and the ensuremath{kappa}(900) are generated in studies of ensuremath{pi}-ensuremath{pi} and $ensuremath{pi}ensuremath{-}K$ scattering, making use of our generalized Nambu--Jona-Lasinio model. We also calculate the decay constants for the ${a}_{0}$ and ${K}_{0}^{*}$ mesons and compare our results with those obtained by Maltman. We find that the value obtained using QCD sum-rule techniques for the ${a}_{0}(980)$ decay constant is smaller than the decay constant calculated using our generalized NJL model, which suggests that the ${a}_{0}(980)$ may have a significant $Koverline{K}$ component. We find rather good agreement with Maltman's values for the decay constants of the ${a}_{0}(1450)$ and ${K}_{0}^{*}(1430).$ Maltman suggests that the ${a}_{0}(980)$ and ${K}_{0}^{*}(1430)$ should be in the same nonet, a result in agreement with our analysis." @default.
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- W2007151056 date "2000-12-11" @default.
- W2007151056 modified "2023-09-27" @default.
- W2007151056 title "Intrinsic and dynamically generated scalar meson states" @default.
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- W2007151056 doi "https://doi.org/10.1103/physrevd.63.014019" @default.
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