Intrinsic and dynamically generated scalar meson states - art. no. 014019

Recent work by Maltman has given us confidence that our assignment of scala r meson states to various nonets based upon our generalized Nambu-Jona-Lasi nio (NJL) model is correct. [For example, in our model the a(0)(980) and th e 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" resonance s and "dynamically generated" resonances when considering various scalar me sons. [This distinction has been noted by Meissner in his characterization of the f(0)(400-1200) as nonpreexisting.] We define preexisting (or intrins ic) resonances as those that appear as singularities of the q(q) over bar T matrix and are in correspondence with q(q) over bar states bound in the co nfining field. [Additional singularities may be found when studying the T m atrices describing pi-pi or pi -K scattering, for example. Such features ma y be seen to arise, in part, from t-channel and u-channel rho exchange in t he case of pi-pi scattering, leading to the introduction of the sigma (500- 600). In addition, threshold effects in the q(q) over bar T matrix can give rise to significant broad cross section enhancements. The latter is, in pa rt, responsible for the introduction of the kappa (900) in a study of pi -K scattering, for example.] We suggest that it is only the intrinsic resonan ces which correspond to q(q) over bar quark-model states, and it is only th e intrinsic states that are to be used to form quark-model q(q) over bar no nets of states. [While the kappa (900) and 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 s igma (500-600) and the kappa (900) are generated in studies of pi-pi and pi -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 obtaine d 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 K(K) over bar component. We find rather goad agreement with Maltman's values for the decay constant s 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 ana lysis.