$B \rar K^* \ γ$} from Hybrid Sum Rule

Details $B \rar K^* \ γ$} from Hybrid Sum Rule $B \rar K^* \ γ$} from Hybrid Sum Rule

1994-03-27

arxiv.org/abs/hep-ph/9403370v1

Phys.Lett. B327 (1994) 354-360

Physics

High Energy Physics

High Energy Physics - Phenomenology

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

Scientific paper

10.1016/0370-2693(94)90741-2

Using the {\it hybrid} moments-Laplace sum rule (HSR), which is well-defined for $M_b \rar \infty$, 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 $B \rar K^* \ \gamma$ radiative transition is dominated by the light-quark condensate for $M_b \rar \infty$ and behaves like $\sqrt M_b$. The form factor is found to be $ F^{B\rar K^*}_1(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 $Br(B\rar K^* \ \gamma) \simeq (4.45 \pm 1.12) \times 10^{-5}$ 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 $F^{B\rar K^*}_1(0)/ F^{B\rar \rho}_1(0) \simeq (1.14 \pm 0.02)$.

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