Probing with Penguins: A lattice calculation of the branching ratio for some of the exclusive modes of $b\to s\gamma$

Abstract

We calculate the leading-order matrix element for exclusive decays of $b\to s\gamma$ in the quenched approximation of lattice QCD on a $24^3\times 48$ lattice at $\beta =6.2$, using an O(a)-improved fermion action. The matrix element is used to extract the on-shell form factor $T_1(q^2=0)$ for $B\to K^{\ast }\gamma$ and $B_s\to \varphi \gamma$, using two different assumptions about the $q^2$ dependence of the form factors for these decays. For $B\to K^{\ast }\gamma$, $T_1(q^2=0)$ is determined to be $0.159_{-33}^{+34}\pm 0.067$ or $0.124_{-18}^{+20}\pm 0.022$ in the two cases. We find the results to be consistent (in the Standard Model) with the CLEO experimental branching ratio of $BR(B\to K^{\ast }\gamma )=(4.5\pm 1.5\pm 0.9)\times 10^{-5}$.

Comments: 41 pages + 12 figures. 1 LaTeX file (requires revtex.sty, aps.sty, aps12.sty and epsf.sty) and 1 uuencoded file of postscript figures. The paper can also be downloaded from the web site http://wwwhep.phys.soton.ac.uk/hepwww/papers/ukqcd-bsgamma-2.0/ This is a revised version of the paper, accepted for publication in Phys. Rev. D, including an analysis of the data suggested by Guido Martinelli