Exclusive Hadronic D Decays to $\eta'$ or $\eta$: Addendum on Resonant Final-State Interactions

For hadronic two-body decays of charmed mesons involving $\eta$ or $\eta'$, resonance-induced final-state interactions (FSI) that mimic the W-exchange or the W-annihilation topology can play an essential role. In particular, the decays $D^0\to\bar K^0\eta'$ and $D^+\to\pi^+\eta$, which are largely suppressed in the absence of FSI, are enhanced dramatically by resonant FSI. It is stressed that the effect of resonant FSI is negligible for $\rho^+(\eta,\eta')$ final states because of the mismatch of the G parity of $\rho^+(\eta,\eta')$ and the J=0, I=1 meson resonance. We argue that a possible gluon-mediated process in which two gluons couple directly to the gluonic component of the $\eta'$, e.g. the gluonium, rather than to the flavor-singlet $\eta_0$, can enhance both modes $D_s^+\to\rho^+\eta'$ and $D_s^+\to\rho^+\eta$, especially the former; that is, this new mechanism can account for the unexpectedly large branching ratio of $\rho^+\eta'$ without suppressing $\rho^+\eta$.