A global analysis of two-body D to VP decays within the framework of flavor symmetry

Two-body charmed meson decays $D\to VP$ are studied within the framework of the diagrammatic approach. Under flavor SU(3) symmetry, all the flavor amplitude sizes and their associated strong phases are extracted by performing a $\chi^2$ fit. Thanks to the recent measurement of $D_s^+\to\pi^+\rho^0$, the magnitudes and the strong phases of the $W$-annihilation amplitudes $A_{P,V}$ have been extracted for the first time. As a consequence, the branching fractions of all the $D\to VP$ decays are predicted, especially those modes that could not be predicted previously due to the unknown $A_{P,V}$. Our working assumption, the flavor SU(3) symmetry, is tested by comparing our predictions with experiment for the singly and doubly Cabibbo-suppressed decay modes based on the flavor amplitudes extracted from the Cabibbo-favored decays using the current data. The predictions for the doubly Cabibbo-suppressed channels are in good agreement with the data, while those for the singly Cabibbo-suppressed decay modes are seen to have flavor SU(3) symmetry breaking effects. We find that the inclusion of SU(3) symmetry breaking in color-allowed and color-suppressed tree amplitudes is needed in general in order to have a better agreement with experiment. Nevertheless, the exact flavor SU(3)-symmetric approach alone is adequate to provide an overall explanation for the current data.