Exclusive Hadronic D Decays to eta' and eta

Abstract

Hadronic decay modes $D^0\to(\bar K^0, \bar K^{*0})\eta,\eta'$ and $(D^+,D_s^+)\to(\pi^+,\rho^+)\eta,\eta'$ are studied in the generalized factorization approach. Form factors for $(D,D_s^+)\to(\eta,\eta')$ transitions are carefully evaluated by taking into account the wave function normalization of the eta and eta'. The predicted branching ratios are generally in agreement with experiment except for $D^0\to\bar K^0\eta', D^+\to\pi^+\eta$ and $D_s^+\to\rho^+\eta'$; the calculated decay rates for the first two decay modes are too small by an order of magnitude. We show that the weak decays $D^0\to K^-\pi^+$ and $D^+\to K^+\bar K^0$ followed by resonance-induced final-state interactions (FSI), which are amenable technically, are able to enhance the branching ratios of $D^0\to\bar K^0\eta'$ and $D^+\to\pi^+\eta$ dramatically without affecting the agreement between theory and experiment for $D^0\to\bar K^0\eta$ and $D^+\to\pi^+\eta'$. We argue that it is difficult to understand the observed large decay rates of $D_s^+\to \rho^+\eta'$ and $\rho^+\eta$ simultaneously; FSI, W-annihilation and the production of excess eta' from gluons are not helpful in this regard. The large discrepancy between the factorization hypothesis and experiment for the ratio of $D_s^+\to\rho^+ \eta'$ and $D_s^+\to\eta' e^+\nu$ remains as an enigma.