B to eta' + X and The QCD Anomaly

Abstract

Mechanisms for the observed large $Br(B\to {\eta }^{\prime }+X_s)$ are examined. We propose that the dominant fraction of the $B\to {\eta }^{\prime }+X_s$ rate is due mainly to $b\to s{g}^{\ast }$, where $g^{\ast }$ is an off-shell gluon, followed by $g^{\ast }\to g{\eta }^{\prime }$ via the anomalous coupling of the ${\eta }^{\prime }$ to two gluons. The calculated rate for $B\to {\eta }^{\prime }+X_s$ is in rough accord with experiment using a fairly constant glue-glue-${\eta }^{\prime }$ form factor. This behavior of the form factor may be indicative of glueball dominance of the channel. Searches via the modes ${\eta }^{\prime }{h}^{+}{h}^{-}$ ($h=\pi$ or $K$) may be worthwhile. Charmonia contributions [i.e $B\to {\eta }_c,\psi (\to {\eta }^{\prime }+X)+X_s$] can only account for at most 20% of the central value of the signal. Implications for $B\to {\eta }^{\prime }+X_d$ and for the corresponding $\eta$ modes are also given.

Comments: 19 pages, 5 figures