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 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 $D\to \bar K^*\pi$ 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 $D\to\bar K^*\pi$ 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.