Weak annihilation and the effective parameters $a_1$ and $a_2$ in non-leptonic $D$ decays

H.-Y. Cheng

doi:doi:10.1140/epjc/s2002-01065-6

2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 26, 551-565 (2003)
DOI: 10.1140/epjc/s2002-01065-6

Weak annihilation and the effective parameters a₁ and a₂ in non-leptonic D decays

H.-Y. Cheng^{1, 2}

¹ Institute of Physics, Academia Sinica, Taipei, 115 Taiwan, R.O.C.
² C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794, USA

(Received: 19 July 2002 / Published online: 20 November 2002 )

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 a₂/a₁ 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 $150^\circ$ . 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 $D\to \overline K^*\pi$ 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.