$B\text{rar}{K}^{\ast }\gamma$} from Hybrid Sum Rule

Abstract

Using the {\it hybrid} moments-Laplace sum rule (HSR), which is well-defined for $M_b\text{rar}\infty$, in contrast with the $popular$ double Borel (Laplace) sum rule (DLSR), which blows up in this limit when applied to the heavy-to-light processes, we show that the form factor of the $B\text{rar}{K}^{\ast }\gamma$ radiative transition is dominated by the light-quark condensate for $M_b\text{rar}\infty$ and behaves like ${\sqrt{M}}_b$. The form factor is found to be $F_1^{B\text{rar}{K}^{\ast }}(0)\simeq (30.8\pm 1.3\pm 3.6\pm 0.6)\times 10^{-2},$ where the errors come respectively from the procedure in the sum rule analysis, the errors in the input and in the $SU(3{)}_f$-breaking parameters. This result leads to $Br(B\text{rar}{K}^{\ast }\gamma )\simeq (4.45\pm 1.12)\times 10^{-5}$ in agreement with the recent CLEO data. Parametrization of the $M_b$-dependence of the form factor including the $SU(3{)}_f$-breaking effects is given in (26), which leads to $F_1^{B\text{rar}{K}^{\ast }}(0)/F_1^{B\text{rar}\rho }(0)\simeq (1.14\pm 0.02)$.

Comments: 10 pages, 1 figure available on request, Latex file, CERN-TH.7166/94 (to appear as Phys. Lett. B)