B--> eta' X_s in the Standard Model

Abstract

We study $B\to {\eta }^{\prime }{X}_s$ within the framework of the Standard Model. Several mechanisms such as $b\to {\eta }^{\prime }sg$ through the QCD anomaly, and $b\to {\eta }^{\prime }s$ and $B\to {\eta }^{\prime }s\bar{q}$ arising from four-quark operators are treated simultaneously. Using QCD equations of motion, we relate the effective Hamiltonian for the first mechanism to that for the latter two. By incorporating next-to-leading-logarithmic(NLL) contributions, the first mechanism is shown to give a significant branching ratio for $B\to {\eta }^{\prime }{X}_s$, while the other two mechanisms account for about 15% of the experimental value. The Standard Model prediction for $B\to {\eta }^{\prime }{X}_s$ is consistent with the CLEO data.

Comments: 9 pages, 1 figure, revtex; final version to appear in Phys. Lett. B