Weak annihilation and the effective parameters a1 and a2 in non-leptonic D decays
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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.
KeywordsRelative Phase Vector Meson Effective Parameter Complex Parameter Resonance Formation
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