$B\to K^{\ast }{\hat{I}}^3$: Penguins on the Lattice

Abstract

We calculate the leading-order matrix element for the decay $B\to K^{\ast }{\hat{I}}^3$ in the quenched approximation of lattice QCD on a $24^3\times 48$ lattice at ${\hat{I}}^2=6.2$, using an O(a)-improved fermion action. Extrapolating the quark masses to their physical values we obtain an on-shell form factor of $T_1(q^2=0)=0.15+12-14$, where the errors quoted are purely statistical. We find $T_1$ is approximately independent of the spectator quark mass and extract $T_1(q^2=0)=0.15+5-4$ if this independence is assumed. We compare this with the same form factor derived (in the Standard Model) from the CLEO experimental branching ratio of $BR(B\to K^{\ast }{\hat{I}}^3)=(4.5\pm 1.5\pm 0.9)\times 10^{-5}$ and find the results to be consistent within statistical errors.

12 pages, LaTeX article with 4 epsf-included postscript figures, (uuencoded compressed tarfile). Minor change in form factor definitions (for posterity), to standardize on convention of Bernard et al