Exclusive Hadronic D Decays to eta' and eta

Abstract

Hadronic decay modes $D^0\to ({\bar{K}}^0,{\bar{K}}^{\ast 0})\eta ,{\eta }^{\prime }$ and $(D^{+},D_s^{+})\to ({\pi }^{+},{\rho }^{+})\eta ,{\eta }^{\prime }$ are studied in the generalized factorization approach. Form factors for $(D,D_s^{+})\to (\eta ,{\eta }^{\prime })$ 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 $D^0\to {\bar{K}}^0{\eta }^{\prime },D^{+}\to {\pi }^{+}\eta$ and $D_s^{+}\to {\rho }^{+}{\eta }^{\prime }$; 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 $D^0\to {\bar{K}}^0{\eta }^{\prime }$ and $D^{+}\to {\pi }^{+}\eta$ dramatically without affecting the agreement between theory and experiment for $D^0\to {\bar{K}}^0\eta$ and $D^{+}\to {\pi }^{+}{\eta }^{\prime }$. We argue that it is difficult to understand the observed large decay rates of $D_s^{+}\to {\rho }^{+}{\eta }^{\prime }$ 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 $D_s^{+}\to {\rho }^{+}{\eta }^{\prime }$ and $D_s^{+}\to {\eta }^{\prime }{e}^{+}\nu$ remains as an enigma.

Comments: 15 pages, 1 figure, to appear in Phys. Rev. D. Form factors for D to eta and eta' transitions are slightly changed