Semi-inclusive decayB→φXs:Rate and momentum spectrum ofφ

Abstract

We study the rate and $\ensuremath{\varphi}$ momentum distribution in semi-inclusive decays $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{X}_{s}$ induced by the quark level processes $\stackrel{\ensuremath{\rightarrow}}{b}\ensuremath{\varphi}s$ and $\stackrel{\ensuremath{\rightarrow}}{b}\ensuremath{\varphi}sg,$ in which the gluon is radiated from the internal charm quark loop or emitted from the virtual gluon of the strong penguin (inner bremsstrahlung) process. We find $\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{b}\ensuremath{\varphi}s)=6.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and $\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{b}\ensuremath{\varphi}sg)=3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}.$ The momentum spectrum of $\ensuremath{\varphi}$ produced by $\stackrel{\ensuremath{\rightarrow}}{b}\ensuremath{\varphi}\mathrm{sg}$ is very broad. With the cut $|{\mathbf{k}}_{\ensuremath{\varphi}}|>~2.0\mathrm{GeV},$ $\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{b}\ensuremath{\varphi}s)=6.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ (where the Fermi motion of the b quark in the B meson is described by a Gaussian), and $\mathcal{B}(\stackrel{\ensuremath{\rightarrow}}{b}\ensuremath{\varphi}sg)=1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}.$ Because of the special nature of $\ensuremath{\varphi},$ many difficulties that hindered a reliable theoretical prediction for $\stackrel{\ensuremath{\rightarrow}}{B}{\ensuremath{\eta}}^{\ensuremath{'}}{X}_{s}$ decay are absent in the process $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{X}_{s}.$ Therefore, theoretical predictions for $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{X}_{s}$ are relatively clean. Moreover, the clear experimental signature of the $\ensuremath{\varphi}$ is of great help. Data for $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\varphi}{X}_{s},$ both the branching ratio and the $\ensuremath{\varphi}$ momentum distribution, would teach us about the strength of strong penguin processes which might be of great importance in the search for $\mathrm{CP}$ violation and for new physics at B factories.