Weak annihilation and the effective parameters a ₁ and a ₂ in non-leptonic D decays

Abstract.

Based on SU(3) flavor symmetry, many of the quark-graph amplitudes in two-body non-leptonic 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 a₁ and a₂ to test the factorization approach. It is found that a ₂ /a ₁ in $D\to \overline K^*\pi$ and $D\to \overline K\rho$ can be different by a factor of 2, indicating that non-factorizable corrections to the latter are far more important than the former. The relative phase between a₁ and a₂ is about 150°. 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 $D\to \overline K^*\pi$ and $\overline K\rho$ decays, which is needed to explain the relatively real decay amplitudes of $D\to \overline K\rho$, remains unexplained. SU(3) symmetry is badly broken in some Cabibbo-suppressed modes and this can be accounted for by the accumulation of some modest SU(3) violation in individual quark-graph amplitudes.