Exclusive Hadronic D Decays to ${\eta }^{\prime }$ or $\eta$: Addendum on Resonant Final-State Interactions

Abstract

For hadronic two-body decays of charmed mesons involving $\eta$ or ${\eta }^{\prime }$, 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 $D^0\to {\bar{K}}^0{\eta }^{\prime }$ 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 ${\rho }^{+}(\eta ,{\eta }^{\prime })$ final states because of the mismatch of the G parity of ${\rho }^{+}(\eta ,{\eta }^{\prime })$ 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 ${\eta }^{\prime }$, e.g. the gluonium, rather than to the flavor-singlet ${\eta }_0$, can enhance both modes $D_s^{+}\to {\rho }^{+}{\eta }^{\prime }$ and $D_s^{+}\to {\rho }^{+}\eta$, especially the former; that is, this new mechanism can account for the unexpectedly large branching ratio of ${\rho }^{+}{\eta }^{\prime }$ without suppressing ${\rho }^{+}\eta$.

Comments: 13 pages