Nonleptonic decays of charmed mesons into two pseudoscalars

We examine the role of resonant coupled channel final state interactions (FSIs), as well as weak annihilation and exchange contributions, in explaining all the two-body hadronic $D\to PP$ decay modes. In the un-unitarized amplitudes we include modified Wilson coefficients with nonfactorizable corrections as parameters. For the hadronic form factors, the z-series expansion method is used to get the $q^2$ dependence. The FSI effects are incorporated via a phenomenological approach with widths of resonances to various channels taken from observations where available, and others as additional parameters to be determined from fits of all the theoretical rates to the measured ones. Our results for the rather hard to explain $D^0\to K^{+}{K}^{-},{\pi }^{+}{\pi }^{-}$ are in agreement with measured values. We demonstrate that both weak exchange and FSI effects are required to get the correct branching ratio for the $D^0\to K^0\overline{K^0}$ mode. Using our unitarized amplitudes we evaluate the strong phase difference between the amplitudes for $D^0\to K^{-}{\pi }^{+}$ and $D^0\to K^{+}{\pi }^{-}$ and find it to be in complete agreement with the recent BES III result.

Figure 1

The dominant quark diagram amplitudes.

Figure 2

The $q^2$ dependence of the scalar form factors. The plot on the left displays $F_0(q^2)$ for the $D\to \pi$ transition, while that on the right is for the $D\to K$ transition.