Cabibbo-angle-favored, -suppressed, and -doubly-suppressedD→PPandD→VPdecays in SU(3) symmetry with final-state interactions

We have studied Cabibbo-angle-favored, -suppressed, and -doubly-suppressed $D\to \mathrm{PP}$ and $D\to \mathrm{VP}$ decays in a nonet-symmetry and a broken-nonet-symmetry scheme, with the inclusion of final-state-interaction phases. For $D\to \mathrm{VP}$ decays, the implications of sextet dominance are also investigated. In the discussion we have argued that the symmetry approach, as also the diagrammatic approach used by other authors, does not fare as well in describing $D\to \mathrm{VP}$ decays as the factorization approach, particularly in describing $B({D_s}^{+}\to \omega {\pi }^{+})$, $B({D_s}^{+}\to \phi {\pi }^{+})$, and $B({D_s}^{+}\to {\rho }^0{\pi }^{+})$.