A lattice study of the exclusive $B \to K^* \gamma$ decay amplitude, using the Clover action at $\beta=6.0$

Abstract

We present the results of a numerical calculation of the $B\to K^* \gamma$ form factors. The results have been obtained by studying the relevant correlation functions at $\beta=6.0$, on an $18^3 \times 64$ lattice, using the ${\rm O(a)}$-improved fermion action, in the quenched approximation. From the study of the matrix element $<K^*| \bar s \sigma_{\mu\nu} b | B>$ we have obtained the form factor $T_1(0)$ which controls the exclusive decay rate. The results are compared with the recent results from CLEO. We also discuss the compatibility between the scaling laws predicted by the Heavy Quark Effective Theory (HQET) and pole dominance, by studying the mass- and $q^2$-dependence of the form factors. From our analysis, it appears that the form factors follow a mass behaviour compatible with the predictions of the HQET and that the $q^2$-dependence of $T_2$ is weaker than would be predicted by pole dominance.