$B\to K^{\ast }+\gamma$ and $B_s\to \varphi +\gamma$ on the Lattice

Abstract

A lattice calculation of the form factors that determine the ``hadronization ratios'', such as $R_{K^{\ast }}$ and $R_{\varphi }$, where $R_{K^{\ast }}\equiv [\Gamma ($B \to K^* \gamma$)/\Gamma (b\to s\gamma )]$, is presented in the quenched approximation. Lattice data shows strong evidence for the scaling law suggested by heavy quark symmetry for one of the form factors ({\it i.e.}\ $T_2$). The data also gives strong support for the simple pole ansatz for the $q^2$ dependence of $T_2$ in the range of available $q^2$. We thus find $T_2(0)=.10\pm .01\pm .03$ yielding $R_{K^{\ast }}=(6.0\pm 1.2\pm 3.4)\%$; we also find $R_{\varphi }=(6.6\pm 1.3\pm 3.7)\%$.

Comments: 13 pages (Latex), Wash. U. HEP/93-35. (Revised: we have corrected and extended the table of phenomenological results for $R_{K^{\ast }}$, eliminated a discussion of $V_{ts}/V_{cb}$ which contained too many unstated assumptions, and made a few other minor corrections.)