Exclusive Hadronic D Decays to eta' and eta

Abstract

Hadronic decay modes $D^0\to(\bar K^0, \bar K^{*0})η,η'$ and $(D^+,D_s^+)\to(π^+,ρ^+)η,η'$ are studied in the generalized factorization approach. Form factors for $(D,D_s^+)\to(η,η')$ 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 $D^0\to\bar K^0η', D^+\toπ^+η$ and $D_s^+\toρ^+η'$; the calculated decay rates for the first two decay modes are too small by an order of magnitude. We show that the weak decays $D^0\to K^-π^+$ 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 $D^0\to\bar K^0η'$ and $D^+\toπ^+η$ dramatically without affecting the agreement between theory and experiment for $D^0\to\bar K^0η$ and $D^+\toπ^+η'$. We argue that it is difficult to understand the observed large decay rates of $D_s^+\to ρ^+η'$ and $ρ^+η$ 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 $D_s^+\toρ^+ η'$ and $D_s^+\toη' e^+ν$ remains as an enigma.