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

Abstract

For hadronic two-body decays of charmed mesons involving $η$ or $η'$, 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 $D^0\to\bar K^0η'$ and $D^+\toπ^+η$, 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 $ρ^+(η,η')$ final states because of the mismatch of the G parity of $ρ^+(η,η')$ 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 $η'$, e.g. the gluonium, rather than to the flavor-singlet $η_0$, can enhance both modes $D_s^+\toρ^+η'$ and $D_s^+\toρ^+η$, especially the former; that is, this new mechanism can account for the unexpectedly large branching ratio of $ρ^+η'$ without suppressing $ρ^+η$.