Hadronic D Decays Involving Scalar Mesons

The nonleptonic weak decays of charmed mesons into a scalar meson and a pseudoscalar meson are studied. The scalar mesons under consideration are $\sigma$ [or $f_0(600)$], $\kappa$, $f_0(980)$, $a_0(980)$ and $K^*_0(1430)$. A consistent picture provided by the data implies that the light scalars below or near 1 GeV form an SU(3) flavor nonet and are predominately the $q^2\bar q^2$ states, while the scalar mesons above 1 GeV can be described as a $q\bar q$ nonet. Hence, we designate $q^2\bar q^2$ to $\sigma, \kappa, a_0(980), f_0(980)$ and $q\bar q$ to $K^*_0$. Sizable weak annihilation contributions induced from final-state interactions are essential for understanding the data. Except for the Cabibbo doubly suppressed channel $D^+\to f_0K^+$, the data of $D\to\sigma\pi, f_0\pi, f_0K, K^*_0\pi$ can be accommodated in the generalized factorization approach. However, the predicted rates for $D\to a_0\pi, a_0K$ are too small by one to two orders of magnitude when compared with the preliminary measurements. Whether or not one can differentiate between the two-quark and four-quark pictures for the $f_0(980)$ produced in the hadronic charm decays depends on the isoscalar $f_0-\sigma$ mixing angle in the $q\bar q$ model.