${\bar{B}}^0\to {\pi }^{+}X$ in the Standard Model

Abstract

In this paper we investigate the possibility of studying $B\to \pi$ form factor using the semi-inclusive decays ${\bar{B}}^0\to {\pi }^{+}+X_q$. In general $B\to PX$ semi-inclusive decays involve several hadronic parameters. But for ${\bar{B}}^0\to {\pi }^{+}{X}_q$ decays we find that in the factorization approximation, the only unknown hadronic parameters are the form factors $F_{0,1}^{B\to \pi }$. Therefore these form factors can be studied in ${\bar{B}}^0\to {\pi }^{+}{X}_q$ decays. Using theoretical model calculations for the form factors the branching ratios for ${\bar{B}}^0\to {\pi }^{+}{X}_d(\Delta S=0)$ and ${\bar{B}}^0\to {\pi }^{+}{X}_s(\Delta S=-1)$, with the cut $E_{\pi }>2.1$ GeV, are estimated to be in the ranges of $(3.1\sim 4.9)\times 10^{-5}(F_1^{B\to \pi }(0)/0.33{)}^2$ and $(2.5\sim 4.2)\times 10^{-5}(F_1^{B\to \pi }(0)/0.33{)}^2$, respectively, depending on the value of $\gamma$. The combined branching ratio for ${\bar{B}}^0\to {\pi }^{+}(X_d+X_s)$ is about $7.4\times 10^{-5}(F_1^{B\to \pi }(0)/0.33{)}^2$ and is insensitive to $\gamma$. We also discuss CP asymmetries in these decay modes.

Comments: RevTex 8 pages and two figures