Weak Annihilation and the Effective Parameters a_1 and a_2 in Nonleptonic D Decays

Abstract

Based on SU(3) flavor symmetry, many of the quark-graph amplitudes in two-body nonleptonic decays of charmed mesons can be extracted from experiment, which enable us to see the relevance and importance of weak annihilation topologies and to determine the complex parameters $a_1$ and $a_2$ to test the factorization approach. It is found that $a_2$ in $D\to {\bar{K}}^{\ast }\pi$ and $D\to \bar{K}\rho$ can be different by a factor of 2, indicating that nonfactorizable corrections to the latter are far more important than the former. The relative phase between $a_1$ and $a_2$ is about $150^{\circ }$. Weak annihilation topologies induced by nearby resonances via final-state rescattering can be described in a model-independent manner. Although the W-exchange contribution in $D\to PP$ decays is dominated by resonant final-state interactions (FSIs), its amplitude in VP decays (V: vector meson, P: pseudoscalar meson) receives little contributions from FSIs in the quark-antiquark resonance formation. As a consequence, the sign flip of the W-exchange amplitude in $D\to {\bar{K}}^{\ast }\pi$ and $\bar{K}\rho$ decays, which is needed to explain the relatively real decay amplitudes of $D\to \bar{K}\rho$, remains unexplained. SU(3) symmetry is badly broken in some Cabibbo-suppressed modes and it can be accounted for by the accumulation of some modest SU(3) violation in individual quark-graph amplitudes.

29 pages, 3 figures. The Close-Lipkin description of D-> Kρdecays is added and discussed

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