$B \to K^* + \gamma$ and $B_s \to \phi + \gamma$ on the Lattice

TL;DR

This paper presents a lattice QCD calculation of form factors for radiative B meson decays, providing insights into hadronization ratios and supporting theoretical models with concrete numerical results.

Contribution

It offers the first lattice calculation of form factors for $B o K^* ext{ and } B_s o ext{phi}$ radiative decays, supporting heavy quark symmetry and pole models.

Findings

Strong evidence for heavy quark symmetry scaling law.

Support for the simple pole model for $q^2$ dependence.

Numerical estimates of hadronization ratios $R_{K^*}$ and $R_{phi}$.

Abstract

A lattice calculation of the form factors that determine the ``hadronization ratios'', such as $R_{K^*}$ and $R_{\phi}$, where $R_{K^*} \equiv [\Gamma ($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 $R_{K^*} =(6.0\pm1.2\pm3.4)\%$; we also find $R_{\phi}=(6.6\pm1.3\pm3.7)\%$.