Semi-inclusive Decay $B\to ϕX_s$: Rate and Momentum Spectrum of $ϕ$

Abstract

We study the rate and $ϕ$ momentum distribution in semi-inclusive decays $B \toϕX_s $ induced by the quark level processes $b\toϕs$ and $b\toϕs g$, in which the gluon is radiated from the internal charm quark loop or emitted from the virtual gluon of the strong penguin (inner bremsstrahlung). We find ${\cal B}(b\toϕs)=6.7\times 10^{-5}$ and ${\cal B}(b\toϕs g)=3.8\times 10^{-5}$. The momentum spectrum of $ϕ$ produced by $b\toϕs g $ is very broad. With the cut $|{\bf k}_ϕ|\geq 2.0$ GeV, ${\cal B}(b\toϕs)=6.1\times 10^{-5}$ (where the Fermi motion of the $b$-quark in the $B$-meson is described by a Gaussian), and ${\cal B}(b\toϕs g)=1.0\times 10^{-5}$. Due to the special nature of $ϕ$, many difficulties which hindered a reliable theoretical prediction for $B\to η' X_s$ decay are absent in the process $B\to ϕX_s$. Therefore, theoretical predictions for $B\to ϕX_s$ are relatively clean. Moreover, the clear experimental signature of the $ϕ$ is of great help. Data for $B\toϕX_s$, both the branching ratio and the $ϕ$ momentum distribution, would teach us about the strength of strong penguins which might be of great importance in the search for CP violation and for new physics at $B$ factories.