Semi-inclusive Decay $B\to \varphi X_s$: Rate and Momentum Spectrum of $\varphi$

Abstract

We study the rate and $\varphi$ momentum distribution in semi-inclusive decays $B\to \varphi X_s$ induced by the quark level processes $b\to \varphi s$ and $b\to \varphi sg$, in which the gluon is radiated from the internal charm quark loop or emitted from the virtual gluon of the strong penguin (inner bremsstrahlung). We find $\mathcal{B}(b\to \varphi s)=6.7\times 10^{-5}$ and $\mathcal{B}(b\to \varphi sg)=3.8\times 10^{-5}$. The momentum spectrum of $\varphi$ produced by $b\to \varphi sg$ is very broad. With the cut $|{\mathbf{k}}_{\varphi }|\ge 2.0$ GeV, $\mathcal{B}(b\to \varphi s)=6.1\times 10^{-5}$ (where the Fermi motion of the $b$-quark in the $B$-meson is described by a Gaussian), and $\mathcal{B}(b\to \varphi sg)=1.0\times 10^{-5}$. Due to the special nature of $\varphi$, many difficulties which hindered a reliable theoretical prediction for $B\to {\eta }^{\prime }{X}_s$ decay are absent in the process $B\to \varphi X_s$. Therefore, theoretical predictions for $B\to \varphi X_s$ are relatively clean. Moreover, the clear experimental signature of the $\varphi$ is of great help. Data for $B\to \varphi X_s$, both the branching ratio and the $\varphi$ 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.

Comments: 19 pages, 4 figures