Tests of the nature and of the gluon content of the \sigma(0.6) from D and D_{s} semileptonic decays

Abstract

We summarize the different features which show that QCD spectral sum rule analyses of the scalar two- and three-point functions do not favour the $\bar uu+\bar dd$ interpretation of the broad and low mass $\sigma (0.6)$ and emphasize that a measurement of the $D_s$ semileptonic decays into $\pi\pi$ can reveal in a model-independent way its eventual gluon component $\sigma_B$. The analysis also implies that one expects an observation of the $K\bar K$ final states from the $\sigma_B$ which may compete (if phase space allowed) with the one from a low mass $\bar ss$ state assumed in the literature to be the SU(3) partner of the observed $\sigma (0.6)$ if the latter is a $\bar uu+\bar dd$ state